Publications
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Control :: Metrology :: Simulation
 M. Hirose and P. Cappellaro "Coherent feedback control of a single qubit in diamond"
 M. Hirose and P. Cappellaro "Timeoptimal control with finite bandwidth"
 M. Chen, M. Hirose and P. Cappellaro "Measurement of transverse hyperfine interaction by forbidden transitions"
 C. Aiello, M. Allegra, B. Hemmerling, X. Wan and P. Cappellaro "Algebraic synthesis of timeoptimal unitaries in SU(2) with alternating controls"
 P. Cappellaro "Polarizing Nuclear Spins in Silicon Carbide"
 M. Chen, M. Hirose and P. Cappellaro "Measurement of transverse hyperfine interaction by forbidden transitions"
 C. D. Aiello and P. Cappellaro "Timeoptimal control by a quantum actuator"
 C. Belthangady, N. BarGill, L. M. Pham, K. Arai, D. Le Sage, P. Cappellaro and R. L. Walsworth "DressedState Resonant Coupling between Bright and Dark Spins in Diamond"
 E. Magesan and P. Cappellaro "Experimentally efficient methods for estimating the performance of quantum measurements"
 F. Ticozzi, R. Lucchese, P. Cappellaro and L. Viola "Hamiltonian Control of Quantum Dynamical Semigroups: Stabilization and Convergence Speed"
 C. Altafini, P. Cappellaro and D. Cory "Feedback schemes for radiation damping suppression in NMR: A controltheoretical perspective"
 P. L. Stanwix, L. M. Pham, J. R. Maze, D. Le Sage, T. K. Yeung, P. Cappellaro, P. R. Hemmer, A. Yacoby, M. D. Lukin and R. L. Walsworth "Coherence of nitrogenvacancy electronic spin ensembles in diamond"
 C. Altafini, P. Cappellaro and D. Cory "Feedback schemes for radiation damping suppression in NMR: a controltheoretical perspective"
 P. Cappellaro, L. Jiang, J. S. Hodges and M. D. Lukin "Coherence and Control of Quantum Registers Based on Electronic Spin in a Nuclear Spin Bath"
 P. Rabl, P. Cappellaro, M. V. G. Dutt, L. Jiang, J. R. Maze and M. D. Lukin "Strong magnetic coupling between an electronic spin qubit and a mechanical resonator"
 L. Jiang, M. V. G. Dutt, E. Togan, L. Childress, P. Cappellaro, J. M. Taylor and M. D. Lukin "Coherence of an Optically Illuminated Single Nuclear Spin Qubit"
 P. Cappellaro, J. S. Hodges, T. F. Havel and D. G. Cory "Subsystem pseudopure states"
 P. Cappellaro, J. S. Hodges, T. F. Havel and D. G. Cory "Control of qubits encoded in decoherencefree subspaces"
 J. S. Hodges, P. Cappellaro, T. F. Havel, R. Martinez and D. G. Cory "Experimental implementation of a logical Bell state encoding"
 P. Cappellaro "Quantum Information Processing in MultiSpin Systems"
 P. Cappellaro, J. S. Hodges, T. F. Havel and D. G. Cory "Principles of Control for DecoherenceFree Subsystems"
 H. J. Cho, P. Cappellaro, D. G. Cory and C. Ramanathan "Decay of highly correlated spin states in a dipolarcoupled solid: NMR study of CaF2"
 J. Hodges, P. Cappellaro, T. Havel and D. Cory "Quantum Control of Nuclear Spins"
 T. Havel, P. Cappellaro, C. Ramanathan and D. Cory "Quantum Information Processing with Nuclear SpinBased Devices"
 G. S. Boutis, P. Cappellaro, H. Cho, C. Ramanathan and D. G. Cory "Pulse error compensating symmetric magicecho trains"
 P. G. B. C. Ramanathan H. Cho and D. Cory "Exploring large nuclear spin systems in the solid state using NMR"
 C. Ramanathan, H. Cho, P. Cappellaro, G. S. Boutis and D. G. Cory "Encoding multiple quantum coherences in noncommuting bases"
 A. Ajoy, Y. X. Liu, K. Saha, L. Marseglia, J.C. Jaskula, U. Bissbort and P. Cappellaro "Quantum Interpolation for High Resolution Sensing"
 L. M. Pham, S. J. DeVience, F. Casola, I. Lovchinsky, A. O. Sushkov, E. Bersin, J. Lee, E. Urbach, P. Cappellaro, H. Park, A. Yacoby, M. Lukin and R. L. Walsworth "NMR technique for determining the depth of shallow nitrogenvacancy centers in diamond"
 K. Arai, C. Belthangady, H. Zhang, N. BarGill, S. DeVience, P. Cappellaro, A. Yacoby and R. Walsworth "Fourier magnetic imaging with nanoscale resolution and compressed sensing speedup using electronic spins in diamond"
 A. Ajoy, U. Bissbort, M. D. Lukin, R. L. Walsworth and P. Cappellaro "AtomicScale Nuclear Spin Imaging Using QuantumAssisted Sensors in Diamond"
 A. Cooper, E. Magesan, H. Yum and P. Cappellaro "Timeresolved magnetic sensing with electronic spins in diamond"
 E. Magesan, A. Cooper and P. Cappellaro "Compressing measurements in quantum dynamic parameter estimation,"
 C. D. Aiello, M. Hirose and P. Cappellaro "Compositepulse magnetometry with a solidstate quantum sensor"
 E. Magesan, A. Cooper, H. Yum and P. Cappellaro "Reconstructing the profile of timevarying magnetic fields with quantum sensors"
 A. Ajoy and P. Cappellaro "Stable threeaxis nuclearspin gyroscope in diamond"
 N. BarGill, L. Pham, C. Belthangady, D. Le Sage, P. Cappellaro, J. Maze, M. Lukin, A. Yacoby and R. Walsworth "Suppression of spinbath dynamics for improved coherence of multispinqubit systems"
 P. Cappellaro "Spinbath narrowing with adaptive parameter estimation"
 P. Cappellaro, G. Goldstein, J. S. Hodges, L. Jiang, J. R. Maze, A. S. Sørensen and M. D. Lukin "Environmentassisted metrology with spin qubits"
 M. Hirose, C. D. Aiello and P. Cappellaro "Continuous dynamical decoupling magnetometry"
 L. M. Pham, N. BarGill, C. Belthangady, D. Le Sage, P. Cappellaro, M. D. Lukin, A. Yacoby and R. L. Walsworth "Enhanced solidstate multispin metrology using dynamical decoupling"
 G. Goldstein, P. Cappellaro, J. R. Maze, J. S. Hodges, L. Jiang, A. S. Sørensen and M. D. Lukin "Environment Assisted Precision Measurement"
 L. M. Pham, D. Le Sage, P. L. Stanwix, T. K. Yeung, D. Glenn, A. Trifonov, P. Cappellaro, P. R. Hemmer, M. D. Lukin, H. Park, A. Yacoby and R. L. Walsworth "Magnetic field imaging with nitrogenvacancy ensembles"
 G. Goldstein, M. D. Lukin and P. Cappellaro "Quantum Limits on Parameter Estimation"
 C. A. Meriles, L. Jiang, G. Goldstein, J. S. Hodges, J. Maze, M. D. Lukin and P. Cappellaro "Imaging mesoscopic nuclear spin noise with a diamond magnetometer"
 P. Cappellaro and M. D. Lukin "Quantum correlation in disordered spin systems: Applications to magnetic sensing"
 P. Cappellaro, J. Maze, L. Childress, M. Dutt, J. Hodges, S. Hong, L. Jiang, P. Stanwix, J. Taylor, E. Togan and others "Quantum Control of Spins and Photons at Nanoscales"
 J. R. Maze, P. Cappellaro, L. Childress, M. V. G. Dutt, J. S. Hodges, S. Hong, L. Jiang, P. L. Stanwix, J. M. Taylor, E. Togan, A. S. Zibrov, P. Hemmer, A. Yacoby, R. L. Walsworth and M. D. Lukin "Nanoscale magnetic sensing using spin qubits in diamond"
 J. R. Maze, P. L. Stanwix, J. S. Hodges, S. Hong, J. M. Taylor, P. Cappellaro, L. Jiang, A. Zibrov, A. Yacoby, R. Walsworth and M. D. Lukin "Nanoscale magnetic sensing with an individual electronic spin qubit in diamond"
 J. M. Taylor, P. Cappellaro, L. Childress, L. Jiang, D. Budker, P. R. Hemmer, A. Yacoby, R. Walsworth and M. D. Lukin "Highsensitivity diamond magnetometer with nanoscale resolution"
 P. Cappellaro, J. Emerson, N. Boulant, C. Ramanathan, S. Lloyd and D. G. Cory "Spin amplifier for single spin measurement"
 C. A. PerezDelgado, M. Mosca, P. Cappellaro and D. G. Cory "Single Spin Measurement Using Cellular Automata Techniques"
 P. Cappellaro, J. Emerson, N. Boulant, C. Ramanathan, S. Lloyd and D. G. Cory "Entanglement Assisted Metrology"
 C. Birattari, P. Cappellaro, A. Mitaroff and M. Silari "Development of an Extended Range Bonner Sphere Spectrometer"
 P. Cappellaro "Implementation of State Transfer Hamiltonians in Spin Chains with Magnetic Resonance Techniques"
 A. Ajoy and P. Cappellaro "Perfect quantum transport in arbitrary spin networks"
 A. Ajoy and P. Cappellaro "Quantum simulation via filtered Hamiltonian engineering: application to perfect quantum transport in spin networks"
 G. Kaur, A. Ajoy and P. Cappellaro "Decay of spin coherences in onedimensional spin systems"
 A. Ajoy and P. Cappellaro "Mixedstate quantum transport in correlated spin networks"
 G. Kaur and P. Cappellaro "Initialization and readout of spin chains for quantum information transport"
 P. Cappellaro, L. Viola and C. Ramanathan "Coherentstate transfer via highly mixed quantum spin chains"
 C. Ramanathan, P. Cappellaro, L. Viola and D. G. Cory "Experimental characterization of coherent magnetization transport in a onedimensional spin system"
 W. Zhang, P. Cappellaro, N. Antler, B. Pepper, D. G. Cory, V. V. Dobrovitski, C. Ramanathan and L. Viola "NMR multiple quantum coherences in quasionedimensional spin systems: Comparison with ideal spinchain dynamics"
 P. Cappellaro, C. Ramanathan and D. G. Cory "Dynamics and control of a quasionedimensional spin system"
 P. Cappellaro, C. Ramanathan and D. G. Cory "Simulations of Information Transport in Spin Chains"
Quantum Control  UP ↑ 
Nature 532, 7780 (2016) 

Abstract: Engineering desired operations on qubits subjected to the deleterious effects of their environment is a critical task in quantum information processing, quantum simulation and sensing. The most common approach relies on openloop quantum control techniques, including optimalcontrol algorithms based on analytical or numerical solutions, Lyapunov design3 and Hamiltonian engineering. An alternative strategy, inspired by the success of classical control, is feedback contro. Because of the complications introduced by quantum measurement, closedloop control is less pervasive in the quantum setting and, with exceptions, its experimental implementations have been mainly limited to quantum optics experiments. Here we implement a feedbackcontrol algorithm using a solidstate spin qubit system associated with the nitrogen vacancy centre in diamond, using coherent feedback to overcome the limitations of measurementbased feedback, and show that it can protect the qubit against intrinsic dephasing noise for milliseconds. In coherent feedback, the quantum system is connected to an auxiliary quantum controller (ancilla) that acquires information about the output state of the system (by an entangling operation) and performs an appropriate feedback action (by a conditional gate). In contrast to openloop dynamical decoupling techniques, feedback control can protect the qubit even against Markovian noise and for an arbitrary period of time (limited only by the coherence time of the ancilla), while allowing gate operations. It is thus more closely related to quantum errorcorrection schemes, although these require larger and increasing qubit overheads. Increasing the number of fresh ancillas enables protection beyond their coherence time. We further evaluate the robustness of the feedback protocol, which could be applied to quantum computation and sensing, by exploring a tradeoff between information gain and decoherence protection, as measurement of the ancillaqubit correlation after the feedback algorithm voids the protection, even if the rest of the dynamics is unchanged.  
BibTeX:
@article{Hirose16, author = {Hirose, Masashi and Cappellaro, Paola}, title = {Coherent feedback control of a single qubit in diamond}, journal = {Nature}, year = {2016}, volume = {532}, number = {7597}, pages = {7780}, doi = {10.1038/nature17404} } 

Arxiv:1510.06801(2015) 

Abstract: Optimal control theory provides recipes to achieve quantum operations with high fidelity and speed, as required in quantum technologies such as quantum sensing and computation. While technical advances have achieved the ultrastrong driving regime in many physical systems, these capabilities have yet to be fully exploited for the precise control of quantum systems, as other limitations, such as the generation of higher harmonics or the finite bandwidth of the control fields, prevent the implementation of theoretical timeoptimal control. Here we present a method to achieve timeoptimal control of qubit systems that can take advantage of fast driving beyond the rotating wave approximation. We exploit results from optimal control theory to design driving protocols that can be implemented with realistic, finitebandwidth control and we find a relationship between bandwidth limitations and achievable control fidelity.  
BibTeX:
@article{Hirose15x, author = {Hirose, M. and Cappellaro, P.}, title = {Timeoptimal control with finite bandwidth}, journal = {Arxiv:1510.06801}, year = {2015} } 

Phys. Rev. B 92, 020101 (2015) 

Abstract: Precise characterization of a system's Hamiltonian is crucial to its highfidelity control that would enable many quantum technologies, ranging from quantum computation to communication and sensing. In particular, nonsecular parts of the Hamiltonian are usually more difficult to characterize, even if they can give rise to subtle but nonnegligible effects. Here we present a strategy for the precise estimation of the transverse hyperfine coupling between an electronic and a nuclear spin, exploiting effects due to forbidden transitions during the Rabi driving of the nuclear spin. We applied the method to precisely determine the transverse coupling between a NitrogenVacancy center electronic spin and its Nitrogen nuclear spin. In addition, we show how this transverse hyperfine, that has been often neglected in experiments, is crucial to achieving large enhancements of the nuclear Rabi driving.  
BibTeX:
@article{Chen15, author = {Chen, Mo and Hirose, Masashi and Cappellaro, Paola}, title = {Measurement of transverse hyperfine interaction by forbidden transitions}, journal = {Phys. Rev. B}, publisher = {American Physical Society}, year = {2015}, volume = {92}, pages = {020101}, doi = {10.1103/PhysRevB.92.020101} } 

Quantum Information Processing , 124 (2015) 

Abstract: We present an algebraic framework to study the timeoptimal synthesis of arbitrary unitaries in SU(2), when the control set is restricted to rotations around two nonparallel axes in the Bloch sphere. Our method bypasses commonly used controltheoretical techniques and easily imposes necessary conditions on timeoptimal sequences. In a straightforward fashion, we prove that timeoptimal sequences are solely parametrized by three rotation angles and derive general bounds on those angles as a function of the relative rotation speed of each control and the angle between the axes. Results are substantially different whether both clockwise and counterclockwise rotations about the given axes are allowed, or only clockwise rotations. In the first case, we prove that any finite timeoptimal sequence is composed at most of five control concatenations, while for the more restrictive case, we present scaling laws on the maximum length of any finite timeoptimal sequence. The bounds we find for both cases are stricter than previously published ones and severely constrain the structure of timeoptimal sequences, allowing for an efficient numerical search of the timeoptimal solution. Our results can be used to find the timeoptimal evolution of qubit systems under the action of the considered control set and thus potentially increase the number of realizable unitaries before decoherence.  
BibTeX:
@article{Aiello15q, author = {Aiello, ClariceD. and Allegra, Michele and Hemmerling, Boerge and Wan, Xiaoting and Cappellaro, Paola}, title = {Algebraic synthesis of timeoptimal unitaries in SU(2) with alternating controls}, journal = {Quantum Information Processing}, publisher = {Springer US}, year = {2015}, pages = {124}, doi = {10.1007/s1112801510456} } 

Physics , 56 (2015) 

Abstract: An optical technique polarizes the spin of nuclei in silicon carbide, offering a potential new route to nuclear spinbased quantum memory. A Viewpoint on: Optical Polarization of Nuclear Spins in Silicon Carbide Abram L. Falk, Paul V. Klimov, Viktor Ivady, Krisztian Szasz, David J. Christle, William F. Koehl, Adam Gali, and, and David D. Awschalom Physical Review Letters 114, 247603 2015 

BibTeX:
@article{Cappellaro15, author = {Cappellaro, P.}, title = {Polarizing Nuclear Spins in Silicon Carbide}, journal = {Physics}, year = {2015}, number = {8}, pages = {56}, doi = {10.1103/Physics.8.56} } 

arXiv:1503.08858 (2015) 

Phys. Rev. A 91, 042340 (2015) 

Abstract: Indirect control of qubits by a quantum actuator has been proposed as an appealing strategy to manipulate qubits that couple only weakly to external fields. While universal quantum control can be easily achieved when the actuatorqubit coupling is anisotropic, the efficiency of this approach is less clear. Here we analyze the time efficiency of quantum actuator control. We describe a strategy to find timeoptimal control sequences by the quantum actuator and compare their gate times with direct driving, identifying regimes where the actuator control performs faster. As a paradigmatic example, we focus on a specific implementation based on the nitrogenvacancy center electronic spin in diamond (the actuator) and nearby C13 nuclear spins (the qubits).  
BibTeX:
@article{Aiello15, author = {Aiello, Clarice D. and Cappellaro, Paola}, title = {Timeoptimal control by a quantum actuator}, journal = {Phys. Rev. A}, publisher = {American Physical Society}, year = {2015}, volume = {91}, pages = {042340}, doi = {10.1103/PhysRevA.91.042340} } 

Phys. Rev. Lett. 110, 157601 (2013) 

Abstract: Under ambient conditions, spin impurities in solidstate systems are found in thermally mixed states and are optically "dark"; i.e., the spin states cannot be optically controlled. Nitrogenvacancy (NV) centers in diamond are an exception in that the electronic spin states are "bright"; i.e., they can be polarized by optical pumping, coherently manipulated with spinresonance techniques, and read out optically, all at room temperature. Here we demonstrate a scheme to resonantly couple bright NV electronic spins to dark substitutionalnitrogen (P1) electronic spins by dressing their spin states with oscillating magnetic fields. This resonant coupling mechanism can be used to transfer spin polarization from NV spins to nearby dark spins and could be used to cool a mesoscopic bath of dark spins to nearzero temperature, thus providing a resource for quantum information and sensing, and aiding studies of quantum effects in manybody spin systems.  
BibTeX:
@article{Belthangady13, author = {Belthangady, C. and BarGill, N. and Pham, L. M. and Arai, K. and Le Sage, D. and Cappellaro, P. and Walsworth, R. L.}, title = {DressedState Resonant Coupling between Bright and Dark Spins in Diamond}, journal = {Phys. Rev. Lett.}, year = {2013}, volume = {110}, pages = {157601}, doi = {10.1103/PhysRevLett.110.157601} } 

Phys. Rev. A 88, 022127 (2013) 

Abstract: Efficient methods for characterizing the performance of quantum measurements are important in the experimental quantum sciences. Ideally, one requires both a physically relevant distinguishability measure between measurement operations and a welldefined experimental procedure for estimating the distinguishability measure. Here, we propose the average measurement fidelity and error between quantum measurements as distinguishability measures. We present protocols for obtaining bounds on these quantities that are both estimable using experimentally accessible quantities and scalable in the size of the quantum system. We also explain why the bounds should be valid in large generality and illustrate the method via numerical examples.  
BibTeX:
@article{Magesan13a, author = {Magesan, Easwar and Cappellaro, Paola}, title = {Experimentally efficient methods for estimating the performance of quantum measurements}, journal = {Phys. Rev. A}, year = {2013}, volume = {88}, pages = {022127}, doi = {10.1103/PhysRevA.88.022127} } 

IEEE TAC 57, 1931 1944 (2012) 

Abstract: We consider finitedimensional Markovian open quantum systems, and characterize the extent to which timeindependent Hamiltonian control may allow to stabilize a target quantum state or subspace and optimize the resulting convergence speed. For a generic Lindblad master equation, we introduce a dissipationinduced decomposition of the associated Hilbert space, and show how it serves both as a tool to analyze global stability properties for given control resources and as the starting point to synthesize controls that ensure rapid convergence. The resulting design principles are illustrated in realistic Markovian control settings motivated by quantum information processing, including quantumoptical systems and nitrogenvacancy centers in diamond.  
BibTeX:
@article{Ticozzi12, author = {Ticozzi, F. and Lucchese, R. and Cappellaro, P. and Viola, L.}, title = {Hamiltonian Control of Quantum Dynamical Semigroups: Stabilization and Convergence Speed}, journal = {IEEE TAC}, year = {2012}, volume = {57}, number = {8}, pages = {1931 1944}, doi = {10.1109/TAC.2012.2195858} } 

Systems & Control Letters 59, 782  786 (2010) 

Abstract: In Nuclear Magnetic Resonance (NMR) spectroscopy, the measurement of the collective spin magnetization is weakly invasive and its backaction is called radiation damping. The aim of this paper is to provide a controltheoretical analysis of the problem of suppressing radiation damping effects. We show that the various realtime feedback schemes commonly used in NMR can be cast in terms of high gain feedback, of exact cancellation based on knowledge of the radiation damping field, and of 2degree of freedom control designs, with the exact cancellation as prefeedback. We further show that the formulation in controltheoretical terms naturally leads to devising other possible closedloop schemes, such as a general high gain feedback stabilization design not requiring the knowledge of the radiation damping field.  
BibTeX:
@article{Altafini10, author = {C. Altafini and P. Cappellaro and D. Cory}, title = {Feedback schemes for radiation damping suppression in NMR: A controltheoretical perspective}, journal = {Systems & Control Letters}, year = {2010}, volume = {59}, number = {12}, pages = {782  786}, doi = {10.1016/j.sysconle.2010.09.004} } 

Phys. Rev. B 82, 201201 (2010) 

Abstract: We present an experimental and theoretical study of electronic spin decoherence in ensembles of nitrogenvacancy (NV) color centers in bulk highpurity diamond at room temperature. Under appropriate conditions, we find ensemble NV spin coherence times (T2) comparable to that of single NV with T2>600??s for a sample with natural abundance of 13C and paramagnetic impurity density ?1015?cm?3. We also observe a sharp decrease in the coherence time with misalignment of the static magnetic field relative to the NV electronic spin axis, consistent with theoretical modeling of NV coupling to a 13C nuclearspin bath. The long coherence times and increased signaltonoise provided by roomtemperature NV ensembles will aid many applications of NV centers in precision magnetometry and quantum information.  
BibTeX:
@article{Stanwix10, author = {Stanwix, P. L. and Pham, L. M. and Maze, J. R. and Le Sage, D. and Yeung, T. K. and Cappellaro, P. and Hemmer, P. R. and Yacoby, A. and Lukin, M. D. and Walsworth, R. L.}, title = {Coherence of nitrogenvacancy electronic spin ensembles in diamond}, journal = {Phys. Rev. B}, year = {2010}, volume = {82}, pages = {201201}, doi = {10.1103/PhysRevB.82.201201} } 

In Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009. Proceedings of the 48th IEEE Conference on , 1445 1450 (2009) 

Abstract: In NMR spectroscopy, the collective measurement is weakly invasive and its backaction is called radiation damping. The aim of this paper is to provide a controltheoretical analysis of the problem of suppressing this radiation damping. It is shown that the two feedback schemes commonly used in the NMR practice correspond one to a high gain output feedback for the simple case of maintaining the spin 1/2 in its inverted state, and the second to a 2degree of freedom control design with a prefeedback that exactly cancels the radiation damping field. A general high gain feedback stabilization design not requiring the knowledge of the radiation damping time constant is also investigated.  
BibTeX:
@inproceedings{Altafini09, author = {Altafini, C. and Cappellaro, P. and Cory, D.}, title = {Feedback schemes for radiation damping suppression in NMR: a controltheoretical perspective}, booktitle = {Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009. Proceedings of the 48th IEEE Conference on}, year = {2009}, pages = {1445 1450}, doi = {10.1109/CDC.2009.5400761} } 

Phys. Rev. Lett. 102, 210502 (2009) 

Abstract: We consider a protocol for the control of fewqubit registers comprising one electronic spin embedded in a nuclear spin bath. We show how to isolate a few proximal nuclear spins from the rest of the bath and use them as building blocks for a potentially scalable quantum information processor. We describe how coherent control techniques based on magnetic resonance methods can be adapted to these solidstate spin systems, to provide not only efficient, high fidelity manipulation but also decoupling from the spin bath. As an example, we analyze feasible performances and practical limitations in the realistic setting of nitrogenvacancy centers in diamond.  
BibTeX:
@article{Cappellaro09, author = {P. Cappellaro and L. Jiang and J. S. Hodges and M. D. Lukin}, title = {Coherence and Control of Quantum Registers Based on Electronic Spin in a Nuclear Spin Bath}, journal = {Phys. Rev. Lett.}, year = {2009}, volume = {102}, number = {21}, pages = {210502}, doi = {10.1103/PhysRevLett.102.210502} } 

Phys. Rev. B 79, 041302 (2009) 

Abstract: We describe a technique that enables a strong coherent coupling between a single electronic spin qubit associated with a nitrogenvacancy impurity in diamond and the quantized motion of a magnetized nanomechanical resonator tip. This coupling is achieved via careful preparation of dressed spin states which are highly sensitive to the motion of the resonator but insensitive to perturbations from the nuclearspin bath. In combination with optical pumping techniques, the coherent exchange between spin and motional excitations enables groundstate cooling and controlled generation of arbitrary quantum superpositions of resonator states. Optical spin readout techniques provide a general measurement toolbox for the resonator with quantum limited precision.  
BibTeX:
@article{Rabl09, author = {P. Rabl and P. Cappellaro and M. V. Gurudev Dutt and L. Jiang and J. R. Maze and M. D. Lukin}, title = {Strong magnetic coupling between an electronic spin qubit and a mechanical resonator}, journal = {Phys. Rev. B}, year = {2009}, volume = {79}, number = {4}, pages = {041302}, doi = {10.1103/PhysRevB.79.041302} } 

Phys. Rev. Lett. 100, 073001 (2008) 

Abstract: We investigate the coherence properties of individual nuclear spin quantum bits in diamond [Dutt et al., Science 316, 1312 (2007)] when a proximal electronic spin associated with a nitrogenvacancy (NV) center is being interrogated by optical radiation. The resulting nuclear spin dynamics are governed by timedependent hyperfine interaction associated with rapid electronic transitions, which can be described by a spinfluctuator model. We show that due to a process analogous to motional averaging in nuclear magnetic resonance, the nuclear spin coherence can be preserved after a large number of optical excitation cycles. Our theoretical analysis is in good agreement with experimental results. It indicates a novel approach that could potentially isolate the nuclear spin system completely from the electronic environment.  
BibTeX:
@article{Jiang08, author = {L. Jiang and M. V. Gurudev Dutt and E. Togan and L. Childress and P. Cappellaro and J. M. Taylor and M. D. Lukin}, title = {Coherence of an Optically Illuminated Single Nuclear Spin Qubit}, journal = {Phys. Rev. Lett.}, year = {2008}, volume = {100}, number = {7}, pages = {073001}, doi = {10.1103/PhysRevLett.100.073001} } 

Phys. Rev. A 75, 042321 (2007) 

Abstract: A critical step in experimental quantum information processing (QIP) is to implement control of quantum systems protected against decoherence via informational encodings, such as quantum errorcorrecting codes, noiseless subsystems, and decoherencefree subspaces. These encodings lead to the promise of faulttolerant QIP, but they come at the expense of resource overheads. Part of the challenge in studying control over multiple logical qubits is that QIP testbeds have not had sufficient resources to analyze encodings beyond the simplest ones. The most relevant resources are the number of available qubits and the cost to initialize and control them. Here we demonstrate an encoding of logical information that permits control over multiple logical qubits without full initialization, an issue that is particularly challenging in liquidstate NMR. The method of subsystem pseudopure states will allow the study of decoherence control schemes on up to six logical qubits using liquidstate NMR implementations.  
BibTeX:
@article{Cappellaro07, author = {Cappellaro, P. and Hodges, J. S. and Havel, T. F. and Cory, D. G.}, title = {Subsystem pseudopure states}, journal = {Phys. Rev. A}, year = {2007}, volume = {75}, pages = {042321}, doi = {10.1103/PhysRevA.75.042321} } 

Las. Phys. 17, 545551 (2007) 

Abstract: Decoherencefree subspaces protect quantum information from the effects of noise that is correlated across the physical qubits used to implement them. Given the ability to impose suitable Hamiltonians upon such a multiqubit system, one can also implement a set of logical gates which enables universal computation on this information without compromising this protection. Real physical systems, however, seldom come with the correct Hamiltonians builtin, let alone the ability to turn them off and on at will. In the course of our development of quantum information processing devices based on liquidstate NMR, we have found the task of operating on quantum information encoded in decoherencefree subspaces rather more challenging than is commonly assumed. This contribution presents an overview of these challenges and the methods we have developed for overcoming them in practice. These methods promise to be broadly applicable to many of the physical systems proposed for the implementation of quantum information processing devices.  
BibTeX:
@article{Cappellaro07p, author = {Cappellaro, P. and Hodges, J.~S. and Havel, T.~F. and Cory, D.~G.}, title = {Control of qubits encoded in decoherencefree subspaces}, journal = {Las. Phys.}, year = {2007}, volume = {17}, pages = {545551}, doi = {10.1134/S1054660X0704038X} } 

Phys. Rev. A 75, 042320 (2007) 

Abstract: Liquidphase NMR is a generalpurpose testbed for developing methods of coherent control relevant to quantum information processing. Here we extend these studies to the coherent control of logical qubits and in particular to the unitary gates necessary to create entanglement between logical qubits. We report an experimental implementation of a conditional logical gate between two logical qubits that are each in decoherencefree subspaces that protect the quantum information from fully correlated dephasing.  
BibTeX:
@article{Hodges07, author = {Hodges, J. S. and Cappellaro, P. and Havel, T. F. and Martinez, R. and Cory, D. G.}, title = {Experimental implementation of a logical Bell state encoding}, journal = {Phys. Rev. A}, year = {2007}, volume = {75}, number = {4}, pages = {042320}, doi = {10.1103/PhysRevA.75.042320} } 

Thesis at: Massachusetts Institute of Technology, Department of Nuclear Science and Engineering (2006) 

Abstract: Coherence and entanglement in multispin systems are valuable resources for quantum information processing. In this thesis, I explore the manipulation of quantum information in complex multispin systems, with particular reference to Nuclear Magnetic Resonance implementations. In systems with a few spins, such as molecules in the liquid phase, the use of multispin coherent states provides a hedge against the noise, via the encoding of information in logical degrees of freedom distributed over several spins. Manipulating multispin coherent states also increases the complexity of quantum operations required in a quantum processor. Here I present schemes to mitigate this problem, both in the state initialization, with particular attention to bulk ensemble quantum information processing, and in the coherent control and gate implementations. In the manybody limit provided by nuclear spins in single crystals, the limitations in the available control increase the complexity of manipulating the system; also, the equations of motion are no longer exactly solvable even in the closedsystem limit. Entanglement and multispin coherences are essential for extending the control and the accessible information on the system. I employ entanglement in a large ensemble of spins in order to obtain an amplification of the small perturbation created by a single spin on the spin ensemble, in a scheme for the measurement of a single nuclear spin state. I furthermore use multiple quantum coherences in mixed multispin states as a tool to explore manybody behavior of linear chain of spins, showing their ability to perform quantum information processing tasks such as simulations and transport of information. The theoretical and experimental results of this thesis suggest that although coherent multispin states are particularly fragile and complex to control they could make possible the execution of quantum information processing tasks that have no classical counterparts.  
BibTeX:
@phdthesis{Cappellaro06t, author = {Paola Cappellaro}, title = {Quantum Information Processing in MultiSpin Systems}, school = {Massachusetts Institute of Technology}, year = {2006} } 

J. Chem. Phys. 125, 044514 (2006) 

Abstract: Decoherencefree subsystems (DFSs) are a powerful means of protecting quantum information against noise with known symmetry properties. Although Hamiltonians that can implement a universal set of logic gates on DFS encoded qubits without ever leaving the protected subsystem theoretically exist, the natural Hamiltonians that are available in specific implementations do not necessarily have this property. Here we describe some of the principles that can be used in such cases to operate on encoded qubits without losing the protection offered by the DFSs. In particular, we show how dynamical decoupling can be used to control decoherence during the unavoidable excursions outside of the DFS. By means of cumulant expansions, we show how the fidelity of quantum gates implemented by this method on a simple two physical qubit DFS depends on the correlation time of the noise responsible for decoherence. We further show by means of numerical simulations how our previously introduced ?strongly modulating pulses? for NMR quantum information processing can permit highfidelity operations on multiple DFS encoded qubits in practice, provided that the rate at which the system can be modulated is fast compared to the correlation time of the noise. The principles thereby illustrated are expected to be broadly applicable to many implementations of quantum information processors based on DFS encoded qubits.  
BibTeX:
@article{Cappellaro06, author = {Cappellaro, P. and Hodges, J. S. and Havel, T. F. and Cory, D. G}, title = {Principles of Control for DecoherenceFree Subsystems}, journal = {J. Chem. Phys.}, year = {2006}, volume = {125}, pages = {044514}, doi = {10.1063/1.2216702} } 

Phys. Rev. B 74, 224434 (2006) 

Abstract: We have measured the decay of NMR multiple quantum coherence intensities both under the internal dipolar Hamiltonian as well as when this interaction is effectively averaged to zero, in the cubic calcium fluoride (CaF2) spin system and the pseudoonedimensional system of fluoroapatite. In calcium fluoride the decay rates depend both on the number of correlated spins in the cluster, as well as on the coherence number. For smaller clusters, the decays depend strongly on coherence number, but this dependence weakens as the size of the cluster increases. The same scaling was observed when the coherence distribution was measured in both the usual Zeeman or z basis and the x basis. The coherence decay in the onedimensional fluoroapatite system did not change significantly as a function of the multiple quantum growth time, in contrast to the calcium fluoride case. While the growth of coherence orders is severely restricted in this case, the number of correlated spins should continue to grow, albeit more slowly. All coherence intensities were observed to decay as Gaussian functions in time. In all cases the standard deviation of the observed decay appeared to scale linearly with coherence number.  
BibTeX:
@article{Cho06, author = {Hyung Joon Cho and Paola Cappellaro and David G. Cory and Chandrasekhar Ramanathan}, title = {Decay of highly correlated spin states in a dipolarcoupled solid: NMR study of CaF2}, journal = {Phys. Rev. B}, year = {2006}, volume = {74}, number = {22}, pages = {224434}, doi = {10.1103/PhysRevB.74.224434} } 

In Decision and Control, 2006 45th IEEE Conference on , 2488 2494 (2006) 

Abstract: Nuclear magnetic resonance (NMR) spectroscopy has proven to be a facile means of achieving smallscale demonstrations of quantum information processing. This was in large part made possible by the sophisticated methods of quantum control that have been developed by the NMR community over a span of more than 50 years. The traditional control methods, already perhaps the most complex examples of openloop control available, were nevertheless designed primarily to assist in identifying the physical parameters of the underlying spin system, rather than to control the system with high precision. We have therefore extended the traditional methods in a variety of ways so as to achieve precise control, by taking advantage of prior knowledge of the physical parameters as determined by traditional methods. Due to the experimental challenges of realtime control, these developments relied upon our ability to simulate the evolution of the system under the action of radiofrequency control fields with essentially arbitrary precision, subject only to the available computing power. This talk presents an overview of our work in quantum control together with some of the ongoing challenges still facing us  
BibTeX:
@inproceedings{Hodges06, author = {Hodges, J. and Cappellaro, P. and Havel, T.F. and Cory, D.G.}, title = {Quantum Control of Nuclear Spins}, booktitle = {Decision and Control, 2006 45th IEEE Conference on}, year = {2006}, pages = {2488 2494}, doi = {10.1109/CDC.2006.377562} } 

In Technical Proceedings of the 2005 NSTI Nanotechnology Conference and Trade Show 3, 161  164 (2005) 

Abstract: This talk will illustrate the benefits offered by QIP with two devices which use quantum entanglement among nuclear spins to defeat the Heisenberg limits: (1) a spin gyroscope that operates by detecting the frequency shift in the spins? precession rate in the rotating frame, which is potentially more accurate than mechanical or optical devices; (2) a quantum amplifier which correlates the states of a macroscopic number of nuclear spins with the state of a single target spin, so that a collective measurement of the state of the amplifier?s spins reveals that of the target spin.  
BibTeX:
@inproceedings{Havel05, author = {T.F. Havel and P. Cappellaro and C. Ramanathan and D.G. Cory}, title = {Quantum Information Processing with Nuclear SpinBased Devices}, booktitle = {Technical Proceedings of the 2005 NSTI Nanotechnology Conference and Trade Show}, year = {2005}, volume = {3}, pages = {161  164} } 

J. Mag. Res. 161, 132137 (2003) 

Abstract: We present improved linenarrowing sequences for dipolar coupled spin systems, based on a train of magicechoes which are compensated for the effects of finite pulse widths and utilize symmetry properties of supercycles. Sequences are introduced for spectroscopy and imaging by proper choice of a phase alternating scheme. Using a 16 pulse timesuspension magicecho cycle, the highest level of linenarrowing achieved was 2.7 Hz for the [100] direction of a single crystal of calcium fluoride, a reduction in linewidth by 4 orders of magnitude.  
BibTeX:
@article{Boutis03, author = {Boutis, G. S. and Cappellaro, P. and Cho, H. and Ramanathan, C. and Cory, D. G.}, title = {Pulse error compensating symmetric magicecho trains}, journal = {J. Mag. Res.}, year = {2003}, volume = {161}, pages = {132137}, doi = {10.1016/S10907807(03)000107} } 

In Proceedings of the 6th International Conference on Quantum Communication, Measurement and Computing. , 267270 (2003) 

BibTeX:
@inproceedings{Ramanathan03p, author = {C. Ramanathan, H. Cho, P.Cappellaro,G.S. Boutis and D.G. Cory}, editor = {Jeffrey H. Shapiro and Osamu Hirota}, title = {Exploring large nuclear spin systems in the solid state using NMR}, booktitle = {Proceedings of the 6th International Conference on Quantum Communication, Measurement and Computing.}, publisher = {Rinton Press}, year = {2003}, pages = {267270} } 

Chem. Phys. Lett. 369, 311 (2003) 

Abstract: Multiple quantum (MQ) coherences are characterized by their coherence number and the number of spins that make up the state, though only the coherence number is normally measured. We present a simple set of measurements that extend our knowledge of the MQ state by recording the coherences in two noncommuting bases, the x and the z bases (related by a similarity transformation). The measurement of coherences in a basis other than the usual z basis also permits the study of spin dynamics under Hamiltonians that conserve z basis coherence number.  
BibTeX:
@article{Ramanathan03, author = {Chandrasekhar Ramanathan and Hyungjoon Cho and Paola Cappellaro and Gregory S Boutis and David G Cory}, title = {Encoding multiple quantum coherences in noncommuting bases}, journal = {Chem. Phys. Lett.}, year = {2003}, volume = {369}, pages = {311}, doi = {10.1016/S00092614(02)020201} } 

Quantum Metrology  UP ↑ 
Arxiv:1604.01677 (2016) 

Abstract: Recent advances in engineering and control of nanoscale quantum sensors have opened new paradigms in precision metrology. Unfortunately, hardware restrictions often limit the sensor performance. In nanoscale magnetic resonance probes, for instance, finite sampling times greatly limit the achievable sensitivity and spectral resolution. We develop a technique for coherent quantum interpolation that can overcome these problems. Using a quantum sensor associated with the Nitrogen Vacancy center in diamond, we experimentally demonstrate that quantum interpolation can achieve spectroscopy of classical magnetic fields and individual quantum spins with orders of magnitude finer frequency resolution than conventionally possible. Not only is quantum interpolation an enabling technique to extract structural and chemical information from single biomolecules, but it can be directly applied to other quantum systems for superresolution quantum spectroscopy.  
BibTeX:
@article{Ajoy16x, author = {Ajoy, A. and Liu, Y. X. and Saha, K. and Marseglia, L. and Jaskula, J.C. and Bissbort, U. and Cappellaro, P.}, title = {Quantum Interpolation for High Resolution Sensing}, journal = {Arxiv:1604.01677}, year = {2016} } 

Phys. Rev. B 93, 045425 (2016) 

Abstract: We demonstrate a robust experimental method for determining the depth of individual shallow nitrogenvacancy (NV) centers in diamond with ~1nm uncertainty. We use a confocal microscope to observe single NV centers and detect the proton nuclear magnetic resonance (NMR) signal produced by objective immersion oil, which has well understood nuclear spin properties, on the diamond surface. We determine the NV center depth by analyzing the NV NMR data using a model that describes the interaction of a single NV center with the statistically polarized proton spin bath. We repeat this procedure for a large number of individual, shallow NV centers and compare the resulting NV depths to the mean value expected from simulations of the ion implantation process used to create the NV centers, with reasonable agreement.  
BibTeX:
@article{Pham16, author = {Pham, Linh M. and DeVience, Stephen J. and Casola, Francesco and Lovchinsky, Igor and Sushkov, Alexander O. and Bersin, Eric and Lee, Junghyun and Urbach, Elana and Cappellaro, Paola and Park, Hongkun and Yacoby, Amir and Lukin, Mikhail and Walsworth, Ronald L.}, title = {NMR technique for determining the depth of shallow nitrogenvacancy centers in diamond}, journal = {Phys. Rev. B}, publisher = {American Physical Society}, year = {2016}, volume = {93}, pages = {045425}, doi = {10.1103/PhysRevB.93.045425} } 

Nat Nano 10, 859864 (2015) 

Abstract: Optically detected magnetic resonance using nitrogen?vacancy (NV) colour centres in diamond is a leading modality for nanoscale magnetic field imaging, as it provides single electron spin sensitivity, threedimensional resolution better than 1?nm and applicability to a wide range of physical and biological, samples under ambient conditions. To date, however, NVdiamond magnetic imaging has been performed using 'realspace' techniques, which are either limited by optical diffraction to ~250?nm resolution or require slow, pointbypoint scanning for nanoscale resolution, for example, using an atomic force microscope, magnetic tip, or superresolution optical imaging. Here, we introduce an alternative technique of Fourier magnetic imaging using NVdiamond. In analogy with conventional magnetic resonance imaging (MRI), we employ pulsed magnetic field gradients to phaseencode spatial information on NV electronic spins in wavenumber or 'kspace' followed by a fast Fourier transform to yield realspace images with nanoscale resolution, wide field of view and compressed sensing speedup.  
BibTeX:
@article{Arai15, author = {Arai, K. and Belthangady, C. and Zhang, H. and BarGill, N. and DeVience, S.J. and Cappellaro, P. and Yacoby, A. and Walsworth, R.L.}, title = {Fourier magnetic imaging with nanoscale resolution and compressed sensing speedup using electronic spins in diamond}, journal = {Nat Nano}, publisher = {Nature Publishing Group}, Number = {10}, Pages = {859864}, Volume = {10}, year = {2015} } 

Phys. Rev. X 5, 011001 (2015) 

Abstract: Nuclear spin imaging at the atomic level is essential for the understanding of fundamental biological phenomena and for applications such as drug discovery. The advent of novel nanoscale sensors promises to achieve the longstanding goal of singleprotein, high spatialresolution structure determination under ambient conditions. In particular, quantum sensors based on the spindependent photoluminescence of nitrogenvacancy (NV) centers in diamond have recently been used to detect nanoscale ensembles of external nuclear spins. While NV sensitivity is approaching singlespin levels, extracting relevant information from a very complex structure is a further challenge since it requires not only the ability to sense the magnetic field of an isolated nuclear spin but also to achieve atomicscale spatial resolution. Here, we propose a method that, by exploiting the coupling of the NV center to an intrinsic quantum memory associated with the nitrogen nuclear spin, can reach a tenfold improvement in spatial resolution, down to atomic scales. The spatial resolution enhancement is achieved through coherent control of the sensor spin, which creates a dynamic frequency filter selecting only a few nuclear spins at a time. We propose and analyze a protocol that would allow not only sensing individual spins in a complex biomolecule, but also unraveling couplings among them, thus elucidating local characteristics of the molecule structure.  
BibTeX:
@article{Ajoy15, author = {Ajoy, A. and Bissbort, U. and Lukin, M.D. and Walsworth, R.L. and Cappellaro, P.}, title = {AtomicScale Nuclear Spin Imaging Using QuantumAssisted Sensors in Diamond}, journal = {Phys. Rev. X}, publisher = {American Physical Society}, year = {2015}, volume = {5}, pages = {011001}, doi = {10.1103/PhysRevX.5.011001} } 

Nature Comms. 5, 3141 (2014) 

Abstract: Quantum probes enable the sensitive detection of timevarying fields with high spatial resolution, opening the possibility to explore biological functions as well as materials and physical phenomena at the nanometer scale. In particular, nitrogenvacancy (NV) centers in diamond have recently emerged as promising sensors of magnetic and electric fields. Although coherent control techniques have measured the amplitude of constant or oscillating fields, these techniques are unable to measure timevarying fields with unknown dynamics. Here we introduce a coherent acquisition method to accurately reconstruct the arbitrary profile of timevarying fields using coherent control sequences associated with the Walsh functions. These sequences act as digital filters that efficiently extract information about the dynamics of the field while suppressing decoherence. We experimentally demonstrate the Walsh reconstruction method by performing proofofprinciple reconstruction of the magnetic field radiated by a physical model of a neuron using a single electronic spin in diamond. These results will be useful for performing timeresolved magnetic sensing with quantum probes in a broad array of physical and biological systems at the nanometer scale.  
BibTeX:
@article{Cooper14, author = {Cooper, A. and Magesan, E. and Yum, H.N. and Cappellaro, P.}, title = {Timeresolved magnetic sensing with electronic spins in diamond}, journal = {Nature Comms.}, year = {2014}, volume = {5}, pages = {3141}, doi = {10.1038/ncomms4141} } 

Phys. Rev A 88, 062109 (2013) 

Abstract: We present methods that can provide an exponential savings in the resources required to perform dynamic parameter estimation using quantum systems. The key idea is to merge classical compressive sensing techniques with quantum control methods to efficiently estimate timedependent parameters in the system Hamiltonian. We show that incoherent measurement bases and, more generally, suitable random measurement matrices can be created by performing simple control sequences on the quantum system. Since random measurement matrices satisfying the restricted isometry property can be used to reconstruct any sparse signal in an efficient manner, and many physical processes are approximately sparse in some basis, these methods can potentially be useful in a variety of applications such as quantum sensing and magnetometry. We illustrate the theoretical results throughout the presentation with various practically relevant numerical examples.  
BibTeX: @article{Magesan13c, author = {Magesan, E. and Cooper, A and Yum, H.N. and Cappellaro, P.}, title = {Compressing measurements in quantum dynamic parameter estimation}, journal = {Phys. Rev. A}, abstract = {We present methods that can provide an exponential savings in the resources required to perform dynamic parameter estimation using quantum systems. The key idea is to merge classical compressive sensing techniques with quantum control methods to efficiently estimate timedependent parameters in the system Hamiltonian. We show that incoherent measurement bases and, more generally, suitable random measurement matrices can be created by performing simple control sequences on the quantum system. Since random measurement matrices satisfying the restricted isometry property can be used to reconstruct any sparse signal in an efficient manner, and many physical processes are approximately sparse in some basis, these methods can potentially be useful in a variety of applications such as quantum sensing and magnetometry. We illustrate the theoretical results throughout the presentation with various practically relevant numerical examples.}, year = {2013}, volume = {88}, pages = {062109}, doi = {10.1103/PhysRevA.88.062109}, url={http://link.aps.org/doi/10.1103/PhysRevA.88.062109} }  
Nature Comms. 4, 1419 (2013) 

Abstract: The sensitivity of quantum magnetometer is challenged by control errors and, especially in the solid state, by their short coherence times. Refocusing techniques can overcome these limitations and improve the sensitivity to periodic fields, but they come at the cost of reduced bandwidth and cannot be applied to sense static or aperiodic fields. Here we experimentally demonstrate that continuous driving of the sensor spin by a composite pulse known as rotaryecho yields a flexible magnetometry scheme, mitigating both driving power imperfections and decoherence. A suitable choice of rotaryecho parameters compensates for different scenarios of noise strength and origin. The method can be applied to nanoscale sensing in variable environments or to realize noise spectroscopy. In a roomtemperature implementation, based on a single electronic spin in diamond, compositepulse magnetometry provides a tunable tradeoff between sensitivities in the mTHz^1/2 range, comparable with those obtained with Ramsey spectroscopy, and coherence times approaching T1.  
BibTeX:
@article{Aiello13, author = {Aiello, Clarice D. and Hirose, Masashi and Cappellaro, Paola}, title = {Compositepulse magnetometry with a solidstate quantum sensor}, journal = {Nat. Commun.}, publisher = {Nat Publishing Group, a division of Macmillan Publishers Limited. All Rights Reserved.}, year = {2013}, volume = {4}, pages = {1419}, doi = {10.1038/ncomms2375} } 

Phys. Rev. A 88, 032107 (2013) 

Abstract: Quantum systems have shown great promise for precision metrology thanks to advances in their control. This has allowed not only the sensitive estimation of external parameters but also the reconstruction of their temporal profile. In particular, quantum control techniques and orthogonal function theory have been applied to the reconstruction of the complete profiles of timevarying magnetic fields. Here, we provide a detailed theoretical analysis of the reconstruction method based on the Walsh functions, highlighting the relationship between the orthonormal Walsh basis, sensitivity of field reconstructions, data compression techniques, and dynamical decoupling theory. Specifically, we show how properties of the Walsh basis and a detailed sensitivity analysis of the reconstruction protocol provide a method to characterize the error between the reconstructed and true fields. In addition, we prove various results about the negligibility function on binary sequences which lead to data compression techniques in the Walsh basis and a more resourceefficient reconstruction protocol. The negligibility proves a fruitful concept to unify the information content of Walsh functions and their dynamical decoupling power, which makes the reconstruction method robust against noise.  
BibTeX:
@article{Magesan13, author = {Magesan, Easwar and Cooper, Alexandre and Yum, Honam and Cappellaro, Paola}, title = {Reconstructing the profile of timevarying magnetic fields with quantum sensors}, journal = {Phys. Rev. A}, year = {2013}, volume = {88}, pages = {032107}, doi = {10.1103/PhysRevA.88.032107} } 

Phys. Rev. A 86, 062104 (2012) 

Abstract: Gyroscopes find wide applications in everyday life from navigation and inertial sensing to rotation sensors in handheld devices and automobiles. Current devices, based on either atomic or solidstate systems, impose a choice between longtime stability and high sensitivity in a miniaturized system. Here, we introduce a quantum sensor that overcomes these limitations by providing a sensitive and stable threeaxis gyroscope in the solid state. We achieve high sensitivity by exploiting the long coherence time of the 14N nuclear spin associated with the nitrogenvacancy center in diamond, combined with the efficient polarization and measurement of its electronic spin. Although the gyroscope is based on a simple Ramsey interferometry scheme, we use coherent control of the quantum sensor to improve its coherence time and robustness against longtime drifts. Such a sensor can achieve a sensitivity of eta~0.5 (mdeg s1)/Root Hz mm3 while offering enhanced stability in a small footprint. In addition, we exploit the four axes of delocalization of the nitrogenvacancy center to measure not only the rate of rotation, but also its direction, thus obtaining a compact threeaxis gyroscope.  
BibTeX:
@article{Ajoy12g, author = {Ajoy, Ashok and Cappellaro, Paola}, title = {Stable threeaxis nuclearspin gyroscope in diamond}, journal = {Phys. Rev. A}, year = {2012}, volume = {86}, pages = {062104}, doi = {10.1103/PhysRevA.86.062104} } 

Nat. Commun. 3, 858 (2012) 

Abstract: Multiqubit systems are crucial for the advancement and application of quantum science. Such systems require maintaining long coherence times while increasing the number of qubits available for coherent manipulation. For solidstate spin systems, qubit coherence is closely related to fundamental questions of manybody spin dynamics. Here we apply a coherent spectroscopic technique to characterize the dynamics of the composite solidstate spin environment of nitrogenvacancy colour centres in room temperature diamond. We identify a possible new mechanism in diamond for suppression of electronic spinbath dynamics in the presence of a nuclear spin bath of sufficient concentration. This suppression enhances the efficacy of dynamical decoupling techniques, resulting in increased coherence times for multispinqubit systems, thus paving the way for applications in quantum information, sensing and metrology.  
BibTeX:
@article{BarGill12, author = {BarGill, N. and Pham, L.M. and Belthangady, C. and Le Sage, D. and Cappellaro, P. and Maze, J.R. and Lukin, M.D. and Yacoby, A. and Walsworth, R.}, title = {Suppression of spinbath dynamics for improved coherence of multispinqubit systems}, journal = {Nat. Commun.}, year = {2012}, volume = {3}, pages = {858}, doi = {10.1038/ncomms1856} } 

Phys. Rev. A 85, 030301(R) (2012) 

Abstract: We present a measurement scheme capable of achieving the quantum limit of parameter estimation using an adaptive strategy that minimizes the parameter's variance at each step. The adaptive rule we propose makes the scheme robust against errors, in particular imperfect readouts, a critical requirement to extend adaptive schemes from quantum optics to solidstate sensors. Thanks to recent advances in singleshot readout capabilities for electronic spins in the solid state (such as nitrogen vacancy centers in diamond), this scheme can also be applied to estimate the polarization of a spin bath coupled to the sensor spin. In turns, the measurement process decreases the entropy of the spin bath resulting in longer coherence times of the sensor spin.  
BibTeX:
@article{Cappellaro12, author = {Cappellaro, Paola}, title = {Spinbath narrowing with adaptive parameter estimation}, journal = {Phys. Rev. A}, year = {2012}, volume = {85}, pages = {030301(R)}, doi = {10.1103/PhysRevA.85.030301} } 

Phys. Rev. A 85, 032336 (2012) 

Abstract: We investigate the sensitivity of a recently proposed method for precision measurement [ Phys. Rev. Lett. 106 140502 (2011)], focusing on an implementation based on solidstate spin systems. The scheme amplifies a quantum sensor response to weak external fields by exploiting its coupling to spin impurities in the environment. We analyze the limits to the sensitivity due to decoherence and propose dynamical decoupling schemes to increase the spin coherence time. The sensitivity is also limited by the environment spin polarization; therefore, we discuss strategies to polarize the environment spins and present a method to extend the scheme to the case of zero polarization. The coherence time and polarization determine a figure of merit for the environment's ability to enhance the sensitivity compared to echobased sensing schemes. This figure of merit can be used to engineer optimized samples for highsensitivity nanoscale magnetic sensing, such as diamond nanocrystals with controlled impurity density.  
BibTeX:
@article{Cappellaro12a, author = {Cappellaro, P. and Goldstein, G. and Hodges, J. S. and Jiang, L. and Maze, J. R. and Sørensen, A. S. and Lukin, M. D.}, title = {Environmentassisted metrology with spin qubits}, journal = {Phys. Rev. A}, year = {2012}, volume = {85}, pages = {032336}, doi = {10.1103/PhysRevA.85.032336} } 

Phys. Rev. A 86, 062320 (2012) 

Abstract: Solidstate qubits hold the promise to achieve an unmatched combination of sensitivity and spatial resolution. To achieve their potential, the qubits need, however, to be shielded from the deleterious effects of the environment. While dynamical decoupling techniques can improve the coherence time, they impose a compromise between sensitivity and the frequency range of the field to be measured. Moreover, the performance of pulse sequences is ultimately limited by control bounds and errors. Here we analyze a versatile alternative based on continuous driving. We find that continuous dynamical decoupling schemes can be used for ac magnetometry, providing similar frequency constraints on the ac field and improved sensitivity for some noise regimes. In addition, the flexibility of phase and amplitude modulation could yield superior robustness to driving errors and a better adaptability to external experimental scenarios.  
BibTeX:
@article{Hirose12, author = {Hirose, Masashi and Aiello, Clarice D. and Cappellaro, Paola}, title = {Continuous dynamical decoupling magnetometry}, journal = {Phys. Rev. A}, year = {2012}, volume = {86}, pages = {062320}, doi = {10.1103/PhysRevA.86.062320} } 

Phys. Rev. B 86, 045214 (2012) 

Abstract: We use multipulse dynamical decoupling to increase the coherence lifetime (T2) of large numbers of nitrogenvacancy (NV) electronic spins in room temperature diamond, thus enabling scalable applications of multispin quantum information processing and metrology. We realize an orderofmagnitude extension of the NV multispin T2 in three diamond samples with widely differing spin impurity environments. In particular, for samples with nitrogen impurity concentration ?1 ppm, we extend T2 to >2 ms, comparable to the longest coherence time reported for single NV centers, and demonstrate a tenfold enhancement in NV multispin sensing of ac magnetic fields.  
BibTeX:
@article{Pham12, author = {Pham, L. M. and BarGill, N. and Belthangady, C. and Le Sage, D. and Cappellaro, P. and Lukin, M. D. and Yacoby, A. and Walsworth, R. L.}, title = {Enhanced solidstate multispin metrology using dynamical decoupling}, journal = {Phys. Rev. B}, year = {2012}, volume = {86}, pages = {045214}, doi = {10.1103/PhysRevB.86.045214} } 

Phys. Rev. Lett. 106, 140502 (2011) 

Abstract: We describe a method to enhance the sensitivity of precision measurements that takes advantage of the environment of a quantum sensor to amplify the response of the sensor to weak external perturbations. An individual qubit is used to sense the dynamics of surrounding ancillary qubits, which are in turn affected by the external field to be measured. The resulting sensitivity enhancement is determined by the number of ancillas that are coupled strongly to the sensor qubit; it does not depend on the exact values of the coupling strengths and is resilient to many forms of decoherence. The method achieves nearly Heisenberglimited precision measurement, using a novel class of entangled states. We discuss specific applications to improve clock sensitivity using trapped ions and magnetic sensing based on electronic spins in diamond.  
BibTeX:
@article{Goldstein11, author = {Goldstein, G. and Cappellaro, P. and Maze, J.~R. and Hodges, J.~S. and Jiang, L. and Sørensen, A.~S. and Lukin, M.~D.}, title = {Environment Assisted Precision Measurement}, journal = {Phys. Rev. Lett.}, year = {2011}, volume = {106}, number = {14}, pages = {140502}, doi = {10.1103/PhysRevLett.106.140502} } 

New J. Phys. 13, 045021 (2011) 

Abstract: We demonstrate a method of imaging spatially varying magnetic fields using a thin layer of nitrogenvacancy (NV) centers at the surface of a diamond chip. Fluorescence emitted by the twodimensional NV ensemble is detected by a CCD array, from which a vector magnetic field pattern is reconstructed. As a demonstration, ac current is passed through wires placed on the diamond chip surface, and the resulting ac magnetic field patterns are imaged using an echobased technique with submicron resolution over a 140� um 140 um field of view, giving singlepixel sensitivity . We discuss ongoing efforts to further improve the sensitivity, as well as potential bioimaging applications such as realtime imaging of activity in functional, cultured networks of neurons.  
BibTeX:
@article{Pham11, author = {Pham, L M and Le Sage, D and Stanwix, P L and Yeung, T K and Glenn, D and Trifonov, A and Cappellaro, P and Hemmer, P R and Lukin, M D and Park, H and Yacoby, A and Walsworth, R L}, title = {Magnetic field imaging with nitrogenvacancy ensembles}, journal = {New J. Phys.}, publisher = {IOP Publishing}, year = {2011}, volume = {13}, number = {4}, pages = {045021}, doi = {10.1088/13672630/13/4/045021} } 

ArXiv:1001.4804 (2010) 

Abstract: We present a new proof of the quantum CramerRao bound for precision parameter estimation [13] and extend it to a more general class of measurement procedures. We analyze a generalized framework for parameter estimation that covers most experimentally accessible situations, where multiple rounds of measurements, auxiliary systems or external control of the evolution are available. The proof presented demonstrates the equivalence of these more general metrology procedures to the simplest optimal strategy for which the bound is proven: a single measurement of a twolevel system interacting with a timeindependent Hamiltonian.  
BibTeX:
@article{Goldstein10x, author = {Goldstein, G. and Lukin, M.~D. and Cappellaro, P.}, title = {Quantum Limits on Parameter Estimation}, journal = {ArXiv:1001.4804}, year = {2010} } 

J. Chem. Phys. 133, 124105 (2010) 

Abstract: Magnetic resonance imaging can characterize and discriminate among tissues using their diverse physical and biochemical properties. Unfortunately, submicrometer screening of biological specimens is presently not possible, mainly due to lack of detection sensitivity. Here we analyze the use of a nitrogenvacancy center in diamond as a magnetic sensor for nanoscale nuclear spin imaging and spectroscopy. We examine the ability of such a sensor to probe the fluctuations of the "classical" dipolar field due to a large number of neighboring nuclear spins in a densely protonated sample. We identify detection protocols that appropriately take into account the quantum character of the sensor and find a signaltonoise ratio compatible with realistic experimental parameters. Through various example calculations we illustrate different kinds of image contrast. In particular, we show how to exploit the comparatively long nuclear spin correlation times to reconstruct a local, highresolution sample spectrum.  
BibTeX:
@article{Meriles10, author = {Carlos A. Meriles and Liang Jiang and Garry Goldstein and Jonathan S. Hodges and Jeronimo Maze and Mikhail D. Lukin and Paola Cappellaro}, title = {Imaging mesoscopic nuclear spin noise with a diamond magnetometer}, journal = {J. Chem. Phys.}, publisher = {AIP}, year = {2010}, volume = {133}, number = {12}, pages = {124105}, doi = {10.1063/1.3483676} } 

Phys. Rev. A 80, 032311 (2009) 

Abstract: We propose a strategy to generate a manybody entangled state in a collection of randomly placed, dipolarly coupled electronic spins in the solid state. By using coherent control to restrict the evolution into a suitable collective subspace, this method enables the preparation of GHZlike and spinsqueezed states even for randomly positioned spins, while in addition protecting the entangled states against decoherence. We consider the application of this squeezing method to improve the sensitivity of nanoscale magnetometer based on nitrogenvacancy spin qubits in diamond.  
BibTeX:
@article{Cappellaro09b, author = {P. Cappellaro and M. D. Lukin}, title = {Quantum correlation in disordered spin systems: Applications to magnetic sensing}, journal = {Phys. Rev. A}, year = {2009}, volume = {80}, number = {3}, pages = {032311}, doi = {10.1103/PhysRevA.80.032311} } 

21st International Conference on Atomic Physics 21, 78 (2009) 

Abstract: The detection of weak magnetic fields with high spatial resolution is an outstanding problem in diverse areas ranging from fundamental physics and material science to data storage and bioimaging. Here we describe an innovative approach to magnetometry that takes advantage of recently developed techniques for coherent control of solidstate spin qubits. We experimentally demonstrate this novel magnetometer employing an individual electronic spin associated with a NitrogenVacancy (NV) center in diamond. Using an ultrapure diamond sample, we achieve shotnoiselimited detection of nanotesla magnetic fields at kHz frequencies after 100 seconds of averaging. In addition, we demonstrate 0.5 microtesla/$Hz$ sensitivity for a diamond nanocrystal with volume of (30 nm)$^3$. This magnetic sensor provides an unprecedented combination of high sensitivity and spatial resolution potentially allowing for the detection of a single nuclear spin's precession within one second.  
BibTeX:
@inproceedings{Cappellaro09p, author = {Cappellaro, P. and Maze, JM and Childress, L. and Dutt, MVG and Hodges, JS and Hong, S. and Jiang, L. and Stanwix, PL and Taylor, JM and Togan, E. and others}, title = {Quantum Control of Spins and Photons at Nanoscales}, journal = {21st International Conference on Atomic Physics}, publisher = {World Scientific}, year = {2009}, volume = {21}, pages = {78}, doi = {10.1142/9789814273008_0009} } 

Advanced Optical Concepts in Quantum Computing, Memory, and Communication II In Advanced Optical Concepts in Quantum Computing, Memory, and Communication II 7225, 722509 (2009) 

Abstract: The ability to sense nanotelsa magnetic fields with nanoscale spatial resolution is an outstanding technical challenge relevant to the physical and biological sciences. For example, detection of such weak localized fields will enable sensing of magnetic resonance signals from individual electron or nuclear spins in complex biological molecules and the readout of classical or quantum bits of information encoded in an electron or nuclear spin memory. Here we present a novel approach to nanoscale magnetic sensing based on coherent control of an individual electronic spin contained in the NitrogenVacancy (NV) center in diamond. At room temperature, using an ultrapure diamond sample, we achieve shotnoiselimited detection of 3 nanotesla magnetic fields oscillating at kHz frequencies after 100 seconds of signal averaging. Furthermore, we experimentally demonstrate nanoscale resolution using a diamond nanocrystal of 30 nm diameter for which we achieve a sensitivity of 0.5 microtesla / Hz1/2.  
BibTeX:
@inproceedings{Maze09p, author = {J. R. Maze and P. Cappellaro and L. Childress and M. V. G. Dutt and J. S. Hodges and S. Hong and L. Jiang and P. L. Stanwix and J. M. Taylor and E. Togan and A. S. Zibrov and P. Hemmer and A. Yacoby and R. L. Walsworth and M. D. Lukin}, editor = {Zameer U. Hasan and Alan E. Craig and Philip R. Hemmer}, title = {Nanoscale magnetic sensing using spin qubits in diamond}, booktitle = {Advanced Optical Concepts in Quantum Computing, Memory, and Communication II}, journal = {Advanced Optical Concepts in Quantum Computing, Memory, and Communication II}, publisher = {SPIE}, year = {2009}, volume = {7225}, number = {1}, pages = {722509}, doi = {10.1117/12.813802} } 

Nature 455, 644647 (2008) 

Abstract: Detection of weak magnetic fields with nanoscale spatial resolution is an outstanding problem in the biological and physical sciences. For example, at a distance of 10 nm, the spin of a single electron produces a magnetic field of about 1 muT, and the corresponding field from a single proton is a few nanoteslas. A sensor able to detect such magnetic fields with nanometre spatial resolution would enable powerful applications, ranging from the detection of magnetic resonance signals from individual electron or nuclear spins in complex biological molecules to readout of classical or quantum bits of information encoded in an electron or nuclear spin memory. Here we experimentally demonstrate an approach to such nanoscale magnetic sensing, using coherent manipulation of an individual electronic spin qubit associated with a nitrogenvacancy impurity in diamond at room temperature8. Using an ultrapure diamond sample, we achieve detection of 3 nT magnetic fields at kilohertz frequencies after 100 s of averaging. In addition, we demonstrate a sensitivity of 0.5 muT Hz1/2 for a diamond nanocrystal with a diameter of 30 nm.  
BibTeX:
@article{Maze08, author = {J. R. Maze and P. L. Stanwix and J. S. Hodges and S. Hong and J. M. Taylor and P. Cappellaro and L. Jiang and A.S. Zibrov and A. Yacoby and R. Walsworth and M. D. Lukin}, title = {Nanoscale magnetic sensing with an individual electronic spin qubit in diamond}, journal = {Nature}, year = {2008}, volume = {455}, pages = {644647}, doi = {10.1038/nature07279} } 

Nat Phys. 4, 810816 (2008) 

Abstract: The detection of weak magnetic fields with high spatial resolution is an important problem in diverse areas ranging from fundamental physics and material science to data storage and biomedical science. Here, we explore a novel approach to the detection of weak magnetic fields that takes advantage of recently developed techniques for the coherent control of solidstate electron spin quantum bits. Specifically, we investigate a magnetic sensor based on nitrogenvacancy centres in roomtemperature diamond. We discuss two important applications of this technique: a nanoscale magnetometer that could potentially detect precession of single nuclear spins and an optical magneticfield imager combining spatial resolution ranging from micrometres to millimetres with a sensitivity approaching a few fT Hz1/2.  
BibTeX:
@article{Taylor08, author = {Taylor, J. M. and Cappellaro, P. and Childress, L. and Jiang, L. and Budker, D. and Hemmer, P. R. and Yacoby, A. and Walsworth, R. and Lukin, M. D.}, title = {Highsensitivity diamond magnetometer with nanoscale resolution}, journal = {Nat Phys.}, publisher = {Nature Publishing Group}, year = {2008}, volume = {4}, number = {10}, pages = {810816}, doi = {10.1038/nphys1075} } 

In Quantum Computing in Solid State Systems , 306312 (2006) 

Abstract: A new approach to the measurement of the state of a collapsed single spin is described by using many entangled spins as an amplifier. A single target spin is coupled via the natural dipolar Hamiltonian to a large collection of spins. Applying external radio frequency (r.f.) pulses, we can control the evolution of the system so that the ensemble spins reach one of two orthogonal states whose collective properties differ depending on the state of the target spin and are easily measured. The result of an experiment simulating this method on an ensemble liquid state NMR quantum processor is reported. That entanglement assisted metrology is compatible with the real control we have over physical spins is suggested, since the measurement process can actually be described in terms of the physical Hamiltonian of the spin system. By building on this work, and with the needed technical advances, it should be possible to detect a single nuclear spin.  
BibTeX:
@incollection{Cappellaro06p, author = {Cappellaro, Paola and Emerson, Joseph and Boulant, Nicolas and Ramanathan, Chandrasekhar and Lloyd, Seth and Cory, David G.}, editor = {Ruggiero, B. and Delsing, P. and Granata, C. and Pashkin, Y. and Silvestrini, P.}, title = {Spin amplifier for single spin measurement}, booktitle = {Quantum Computing in Solid State Systems}, publisher = {Springer New York}, year = {2006}, pages = {306312}, doi = {10.1007/0387311432_37} } 

Phys. Rev. Lett. 97, 100501 (2006) 

Abstract: We analyze a conceptual approach to singlespin measurement. The method uses techniques from the theory of quantum cellular automata to correlate a large number of ancillary spins to the one to be measured. It has the distinct advantage of being efficient: under ideal conditions, it requires the application of only O(3 N) steps (each requiring a constant number of rf pulses) to create a system of N correlated spins. Numerical simulations suggest that it is also, to a certain extent, robust against pulse errors, and imperfect initial polarization of the ancilla spin system.  
BibTeX:
@article{PerezDelgado06, author = {Carlos A. PerezDelgado and Michele Mosca and Paola Cappellaro and David G. Cory}, title = {Single Spin Measurement Using Cellular Automata Techniques}, journal = {Phys. Rev. Lett.}, year = {2006}, volume = {97}, number = {10}, pages = {100501}, doi = {10.1103/PhysRevLett.97.100501} } 

Phys. Rev. Lett. 94, 020502 (2005) 

Abstract: We propose a new approach to the measurement of a single spin state, based on nuclear magnetic resonance (NMR) techniques and inspired by the coherent control over manybody systems envisaged by quantum information processing. A single target spin is coupled via the magnetic dipolar interaction to a large ensemble of spins. Applying radio frequency pulses, we can control the evolution so that the spin ensemble reaches one of two orthogonal states whose collective properties differ depending on the state of the target spin and are easily measured. We first describe this measurement process using quantum gates; then we show how equivalent schemes can be defined in terms of the Hamiltonian and thus implemented under conditions of real control, using well established NMR techniques. We demonstrate this method with a proof of principle experiment in ensemble liquid state NMR and simulations for small spin systems.  
BibTeX:
@article{Cappellaro05, author = {Paola Cappellaro and Joseph Emerson and Nicolas Boulant and Chandrasekhar Ramanathan and Seth Lloyd and David G Cory}, title = {Entanglement Assisted Metrology}, journal = {Phys. Rev. Lett.}, year = {2005}, volume = {94}, pages = {020502}, doi = {10.1103/PhysRevLett.94.020502} } 

In Advanced Monte Carlo for Radiation Physics, Particle Transport Simulation and Applications , 1157 (2001) 

BibTeX:
@inproceedings{Birattari01, author = {Birattari, C. and Cappellaro, P. and Mitaroff, A. and Silari, M.}, editor = {Kling, A. and Barão, F. and Nakagawa, M. and Távora, L. and Vaz, P.}, title = {Development of an Extended Range Bonner Sphere Spectrometer}, booktitle = {Advanced Monte Carlo for Radiation Physics, Particle Transport Simulation and Applications}, year = {2001}, pages = {1157} } 

Quantum Simulation & Information Transport  UP ↑ 
In Quantum State Transfer and Network Engineering , 183222 (2014) 

Abstract: Nuclear spin systems and magnetic resonance techniques have provided a fertile platform for experimental investigation of quantum state transfer in spin chains. From the first observation of polarization transfer, predating the formal definition of quantum state transfer, to the realization of state transfer simulations in small molecules and in larger solidstate spin systems, the experiments have drawn on the strengths of nuclear magnetic resonance (NMR), in particular on its long history of welldeveloped control techniques. NMR implementations have been invaluable both as proofofprinciple demonstrations of quantum state transfer protocols and to explore dynamics occurring in real systems that go beyond what can be analytically solved or numerically simulated. In addition, control techniques developed in these systems to engineer the Hamiltonians required for transport can be adopted in potentially scalable quantum information processing architectures. In this contribution we describe recent results and outline future directions of research in magneticresonance based implementation of quantum state transfer in spin chains.  
BibTeX:
@incollection{Cappellaro14, author = {Cappellaro, Paola}, editor = {Nikolopoulos, Georgios M. and Jex, Igor}, title = {Implementation of State Transfer Hamiltonians in Spin Chains with Magnetic Resonance Techniques}, booktitle = {Quantum State Transfer and Network Engineering}, publisher = {Springer Berlin Heidelberg}, year = {2014}, pages = {183222}, doi = {10.1007/9783642399374_6} } 

Phys. Rev. B 87, 064303 (2013) 

Abstract: Spin chains have been proposed as wires to transport information between distributed registers in a quantum information processor. Unfortunately, the challenges in manufacturing linear chains with engineered couplings has hindered experimental implementations. Here we present strategies to achieve perfect quantum information transport in arbitrary spin networks. Our proposal is based on the weak coupling limit for pure state transport, where information is transferred between two end spins that are only weakly coupled to the rest of the network. This regime allows ignoring the complex, internal dynamics of the bulk network and relying on virtual transitions or on the coupling to a single bulk eigenmode. We further introduce control methods capable of tuning the transport process and achieve perfect fidelity with limited resources, involving only manipulation of the end qubits. These strategies could be thus applied not only to engineered systems with relaxed fabrication precision, but also to naturally occurring networks; specifically, we discuss the practical implementation of quantum state transfer between two separated nitrogen vacancy (NV) centers through a network of nitrogen substitutional impurities.  
BibTeX:
@article{Ajoy13, author = {Ajoy, Ashok and Cappellaro, Paola}, title = {Perfect quantum transport in arbitrary spin networks}, journal = {Phys. Rev. B}, year = {2013}, volume = {87}, pages = {064303}, doi = {10.1103/PhysRevB.87.064303} } 

Phys. Rev. Lett. 110, 220503 (2013) 

Abstract: We propose a method for Hamiltonian engineering that requires no local control but only relies on collective qubit rotations and field gradients. The technique achieves a spatial modulation of the coupling strengths via a dynamical construction of a weighting function combined with a Bragg grating. As an example, we demonstrate how to generate the ideal Hamiltonian for perfect quantum information transport between two separated nodes of a large spin network. We engineer a spin chain with optimal couplings starting from a large spin network, such as one naturally occurring in crystals, while decoupling all unwanted interactions. For realistic experimental parameters, our method can be used to drive almost perfect quantum information transport at room temperature. The Hamiltonian engineering method can be made more robust under decoherence and coupling disorder by a novel apodization scheme. Thus, the method is quite general and can be used to engineer the Hamiltonian of many complex spin lattices with different topologies and interactions.  
BibTeX:
@article{Ajoy13l, author = {Ajoy, A. and Cappellaro, P.}, title = {Quantum simulation via filtered Hamiltonian engineering: application to perfect quantum transport in spin networks}, journal = {Phys. Rev. Lett.}, year = {2013}, volume = {110}, pages = {220503}, doi = {10.1103/PhysRevLett.110.220503} } 

New J. Phys. 15, 093035 (2013) 

Abstract: Strategies to protect multiqubit states against decoherence are difficult to formulate because of their complex manybody dynamics. A better knowledge of the decay dynamics would help in the construction of dynamical decoupling control schemes. Here we use solidstate nuclear magnetic resonance techniques to experimentally investigate decay of coherent multispin states in linear spin chains. Leveraging on the quasionedimension geometry of fluorapatite crystal spin systems, we can gain a deeper insight on the multispin states created by the coherent evolution, and their subsequent decay, than it is possible in threedimensional (3D) systems. We are then able to formulate an analytical model that captures the key features of the decay. We can thus compare the decoherence behavior for different initial states of the spin chain and link their decay rate to the state characteristics, in particular their coherence and longrange correlation among spins. Our experimental and theoretical study shows that the spin chains undergo a rich dynamics, with a slower decay rate than for the 3D case, and thus might be more amenable to decoupling techniques.  
BibTeX:
@article{Kaur13, author = {G Kaur and A Ajoy and P Cappellaro}, title = {Decay of spin coherences in onedimensional spin systems}, journal = {New J. Phys.}, year = {2013}, volume = {15}, number = {9}, pages = {093035}, doi = {10.1088/13672630/15/9/093035} } 

Phys. Rev. A 85, 042305 (2012) 

Abstract: Quantum spin networks can be used to transport information between separated registers in a quantuminformation processor. To find a practical implementation, the strict requirements of ideal models for perfect state transfer need to be relaxed, allowing for complex coupling topologies and general initial states. Here we analyze transport in complex quantum spin networks in the maximally mixed state and derive explicit conditions that should be satisfied by propagators for perfect state transport. Using a description of the transport process as a quantum walk over the network, we show that it is necessary to phasecorrelate the transport processes occurring along all the possible paths in the network. We provide a Hamiltonian that achieves this correlation and use it in a constructive method to derive engineered couplings for perfect transport in complicated network topologies.  
BibTeX:
@article{Ajoy12, author = {Ajoy, Ashok and Cappellaro, Paola}, title = {Mixedstate quantum transport in correlated spin networks}, journal = {Phys. Rev. A}, year = {2012}, volume = {85}, pages = {042305}, doi = {10.1103/PhysRevA.85.042305} } 

New J. Phys. 14, 083005 (2012) 

Abstract: Linear chains of spins acting as quantum wires are a promising approach for achieving scalable quantum information processors. Nuclear spins in apatite crystals provide an ideal test bed for the experimental study of quantum information transport, as they closely emulate a onedimensional spin chain, while magnetic resonance techniques can be used to drive the spin chain dynamics and probe the accompanying transport mechanisms. Here we demonstrate initialization and readout capabilities in these spin chains, even in the absence of singlespin addressability. These control schemes enable preparing desired states for quantum information transport and probing their evolution under the transport Hamiltonian. We further optimize the control schemes by a detailed analysis of 19 F NMR lineshape.  
BibTeX:
@article{Kaur12, author = {Gurneet Kaur and Paola Cappellaro}, title = {Initialization and readout of spin chains for quantum information transport}, journal = {New J. Phys.}, year = {2012}, volume = {14}, number = {8}, pages = {083005}, doi = {10.1088/13672630/14/8/083005} } 

Phys. Rev. A 83, 032304 (2011) 

Abstract: Spin chains have been proposed as quantum wires in many quantuminformation processing architectures. Coherent transmission of quantum information in spin chains over short distances is enabled by their internal dynamics, which drives the transport of singlespin excitations in perfectly polarized chains. Given the practical challenge of preparing the chain in a pure state, we propose to use a chain that is initially in the maximally mixed state. We compare the transport properties of pure and mixedstate chains and find similarities that enable the experimental study of purestate transfer via mixedstate chains. We also demonstrate protocols for the perfect transfer of quantum information in these chains. Remarkably, mixedstate chains allow the use of Hamiltonians that do not preserve the total number of singlespin excitations and are more readily obtainable from the naturally occurring magnetic dipolar interaction. We discuss experimental implementations using solidstate nuclear magnetic resonance and defect centers in diamond.  
BibTeX:
@article{Cappellaro11, author = {Cappellaro, Paola and Viola, Lorenza and Ramanathan, Chandrasekhar }, title = {Coherentstate transfer via highly mixed quantum spin chains}, journal = {Phys. Rev. A}, year = {2011}, volume = {83}, number = {3}, pages = {032304}, doi = {10.1103/PhysRevA.83.032304} } 

New J. Phys. 13, 103015 (2011) 

Abstract: We experimentally characterize the nonequilibrium, roomtemperature magnetization dynamics of a spin chain evolving under an effective doublequantum (DQ) Hamiltonian. We show that the Liouville space operators corresponding to the magnetization and the twospin correlations evolve 90 degrees out of phase with each other, and drive the transport dynamics. For a nearestneighborcoupled N spin chain, the dynamics are found to be restricted to a Liouville operator space whose dimension scales only as N 2 , leading to a slow growth of multispin correlations. Even though longrange couplings are present in the real system, we find excellent agreement between the analytical predictions and our experimental results, confirming that leakage out of the restricted Liouville space is slow on the timescales investigated. Our results indicate that the group velocity of the magnetization is6.04 ± 0.38 μ m s −1 , corresponding to a coherent transport over N ≈ 26 spins on the experimental timescale. As the DQ Hamiltonian is related to the standard onedimensional XX Hamiltonian by a similarity transform, our results can be directly extended to XX quantum spin chains, which have been extensively studied in the context of both quantum magnetism and quantum information processing.  
BibTeX:
@article{Ramanathan11, author = {Chandrasekhar Ramanathan and Paola Cappellaro and Lorenza Viola and David G Cory}, title = {Experimental characterization of coherent magnetization transport in a onedimensional spin system}, journal = {New J. Phys.}, year = {2011}, volume = {13}, number = {10}, pages = {103015}, doi = {10.1088/13672630/13/10/103015} } 

Phys. Rev. A 80, 052323 (2009) 

Abstract: The 19F spins in a crystal of fluorapatite have often been used to experimentally approximate a onedimensional spin system. Under suitable multipulse control, the nuclearspin dynamics may be modeled to first approximation by a doublequantum onedimensional Hamiltonian, which is analytically solvable for nearestneighbor couplings. Here, we use solidstate nuclear magnetic resonance techniques to investigate the multiple quantum coherence dynamics of fluorapatite, with an emphasis on understanding the region of validity for such a simplified picture. Using experimental, numerical, and analytical methods, we explore the effects of longrange intrachain couplings, crosschain couplings, as well as couplings to a spin environment, all of which tend to damp the oscillations of the multiple quantum coherence signal at sufficiently long times. Our analysis characterizes the extent to which fluorapatite can faithfully simulate a onedimensional quantum wire.  
BibTeX:
@article{Zhang09, author = {Zhang, Wenxian and Cappellaro, Paola and Antler, Natania and Pepper, Brian and Cory, David G. and Dobrovitski, Viatcheslav V. and Ramanathan, Chandrasekhar and Viola, Lorenza}, title = {NMR multiple quantum coherences in quasionedimensional spin systems: Comparison with ideal spinchain dynamics}, journal = {Phys. Rev. A}, year = {2009}, volume = {80}, number = {5}, pages = {052323}, doi = {10.1103/PhysRevA.80.052323} } 

Phys. Rev. A 76, 032317 (2007) 

Abstract: We study experimentally a system comprised of linear chains of spin1/2 nuclei that provides a test bed for multibody dynamics and quantuminformation processing. This system is a paradigm for a class of quantuminformation processing devices that can perform particular tasks even without universal control of the whole quantum system. We investigate the extent of control achievable on the system with current experimental apparatus and methods to gain information on the system state, when full tomography is not possible and in any case highly inefficient.  
BibTeX:
@article{Cappellaro07a, author = {P. Cappellaro and C. Ramanathan and D. G. Cory}, title = {Dynamics and control of a quasionedimensional spin system}, journal = {Phys. Rev. A}, year = {2007}, volume = {76}, number = {3}, pages = {032317}, doi = {10.1103/PhysRevA.76.032317} } 

Phys. Rev. Lett. 99, 250506 (2007) 

Abstract: Transport of quantum information in linear spin chains has been the subject of much theoretical work. Experimental studies by NMR in solid state spin systems (a natural implementation of such models) is complicated since the dipolar Hamiltonian is not solely comprised of nearestneighbor XYHeisenberg couplings. We present here a similarity transformation between the XY Hamiltonian and the doublequantum Hamiltonian, an interaction which is achievable with the collective control provided by radiofrequency pulses. Not only can this second Hamiltonian simulate the information transport in a spin chain, but it also creates coherent states, whose intensities give an experimental signature of the transport. This scheme makes it possible to study experimentally the transport of polarization beyond exactly solvable models and explore the appearance of quantum coherence and interference effects.  
BibTeX:
@article{Cappellaro07l, author = {P. Cappellaro and C. Ramanathan and D. G. Cory}, title = {Simulations of Information Transport in Spin Chains}, journal = {Phys. Rev. Lett.}, year = {2007}, volume = {99}, number = {25}, pages = {250506}, doi = {10.1103/PhysRevLett.99.250506} } 

UP ↑ 