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 Quantum Control UP ↑ Chinmay Belthangady, N. Bar-Gill, L. M. Pham, K. Arai, D. Le Sage, P. Cappellaro, R. L. Walsworth "Dressed-State Resonant Coupling between Bright and Dark Spins in Diamond "Phys. Rev. Lett. 110, 157601(2013) [Abstract] [BibTeX] [URL] [DOI] Abstract: Under ambient conditions, spin impurities in solid-state systems are found in thermally-mixed states and are optically "dark", i.e., the spin states cannot be optically controlled. Nitrogen-vacancy (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 spin-resonance techniques, and read out optically, all at room temperature. Here we demonstrate a dressed-state, double-resonance scheme to transfer polarization from bright NV electronic spins to dark substitutional-Nitrogen (P1) electronic spins in diamond. This polarization-transfer mechanism could be used to cool a mesoscopic bath of dark spins to near-zero temperature, thus providing a resource for quantum information and sensing, and aiding studies of quantum effects in many-body spin systems. BibTeX: @article{Belthangady13, author = {Belthangady, C. and Bar-Gill, N. and Pham, L.M. and Arai, K. and Le Sage, D. and Cappellaro, P. and Walsworth, R.L.}, title = {Dressed-State Polarization Transfer between Bright \& Dark Spins in Diamond}, journal = {Phys. Rev. Lett.}, number = {110}, pages = {157601}, doi= {10.1103/PhysRevLett.110.157601}, year = {2013} }  F. Ticozzi, R. Lucchese, P. Cappellaro and L. Viola "Hamiltonian Control of Quantum Dynamical Semigroups: Stabilization and Convergence Speed"IEEE TAC 57, 1931 -1944 (2012) [Abstract] [BibTeX] [DOI] [URL] Abstract: We consider finite-dimensional Markovian open quantum systems, and characterize the extent to which time-independent 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 dissipation-induced 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 quantum-optical systems and nitrogen-vacancy 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} }  C. Altafini, P. Cappellaro and D. Cory "Feedback schemes for radiation damping suppression in NMR: A control-theoretical perspective"Systems & Control Letters 59, 782 - 786 (2010) [Abstract] [BibTeX] [DOI] [URL] Abstract: In Nuclear Magnetic Resonance (NMR) spectroscopy, the measurement of the collective spin magnetization is weakly invasive and its back-action is called radiation damping. The aim of this paper is to provide a control-theoretical analysis of the problem of suppressing radiation damping effects. We show that the various real-time 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 2-degree of freedom control designs, with the exact cancellation as prefeedback. We further show that the formulation in control-theoretical terms naturally leads to devising other possible closed-loop 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 control-theoretical perspective}, journal = {Systems & Control Letters}, year = {2010}, volume = {59}, number = {12}, pages = {782 - 786}, doi = {10.1016/j.sysconle.2010.09.004} }  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 nitrogen-vacancy electronic spin ensembles in diamond"Phys. Rev. B 82, 201201 (2010) [Abstract] [BibTeX] [DOI] [URL] Abstract: We present an experimental and theoretical study of electronic spin decoherence in ensembles of nitrogen-vacancy (NV) color centers in bulk high-purity 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 nuclear-spin bath. The long coherence times and increased signal-to-noise provided by room-temperature 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 nitrogen-vacancy electronic spin ensembles in diamond}, journal = {Phys. Rev. B}, year = {2010}, volume = {82}, pages = {201201}, doi = {10.1103/PhysRevB.82.201201} }  C. Altafini, P. Cappellaro and D. Cory "Feedback schemes for radiation damping suppression in NMR: a control-theoretical perspective" 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] [BibTeX] [DOI] [URL] Abstract: In NMR spectroscopy, the collective measurement is weakly invasive and its back-action is called radiation damping. The aim of this paper is to provide a control-theoretical 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 2-degree 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 control-theoretical 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} }  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"Phys. Rev. Lett. 102, 210502 (2009) [Abstract] [BibTeX] [DOI] [URL] Abstract: We consider a protocol for the control of few-qubit 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 solid-state 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 nitrogen-vacancy 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} }  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"Phys. Rev. B 79, 041302 (2009) [Abstract] [BibTeX] [DOI] [URL] Abstract: We describe a technique that enables a strong coherent coupling between a single electronic spin qubit associated with a nitrogen-vacancy 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 nuclear-spin bath. In combination with optical pumping techniques, the coherent exchange between spin and motional excitations enables ground-state 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} }  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"Phys. Rev. Lett. 100, 073001 (2008) [Abstract] [BibTeX] [DOI] [URL] 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 nitrogen-vacancy (N-V) center is being interrogated by optical radiation. The resulting nuclear spin dynamics are governed by time-dependent hyperfine interaction associated with rapid electronic transitions, which can be described by a spin-fluctuator 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} }  P. Cappellaro, J. S. Hodges, T. F. Havel and D. G. Cory "Control of qubits encoded in decoherence-free subspaces"Las. Phys. 17, 545-551 (2007) [Abstract] [BibTeX] [DOI] [URL] Abstract: Decoherence-free 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 multi-qubit 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 built-in, 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 liquid-state NMR, we have found the task of operating on quantum information encoded in decoherence-free 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{Cappellaro07, author = {Cappellaro, P. and Hodges, J.~S. and Havel, T.~F. and Cory, D.~G.}, title = {Control of qubits encoded in decoherence-free subspaces}, journal = {Las. Phys.}, year = {2007}, volume = {17}, pages = {545-551}, doi = {10.1134/S1054660X0704038X} }  P. Cappellaro, J. S. Hodges, T. F. Havel and D. G. Cory "Subsystem pseudopure states"Phys. Rev. A 75, 042321 (2007) [Abstract] [BibTeX] [DOI] [URL] 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 error-correcting codes, noiseless subsystems, and decoherence-free subspaces. These encodings lead to the promise of fault-tolerant 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 liquid-state NMR. The method of subsystem pseudopure states will allow the study of decoherence control schemes on up to six logical qubits using liquid-state NMR implementations. BibTeX: @article{Cappellaro07b, 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} }  M. Henry, A. Gorshkov, Y. Weinstein, P. Cappellaro, J. Emerson, N. Boulant, J. Hodges, C. Ramanathan, T. Havel, R. Martinez and D. Cory "Signatures of Incoherence in a Quantum Information Processor"Quantum Information Processing 6, 431-444 (2007) [Abstract] [BibTeX] [URL] Abstract: Incoherent noise is manifest in measurements of expectation values when the underlying ensemble evolves under a classical distribution of unitary processes. While many incoherent processes appear decoherent, there are important differences. The distribution functions underlying incoherent processes are either static or slowly varying with respect to control operations and so the errors introduced by these distributions are refocusable. The observation and control of incoherence in small Hilbert spaces is well known. Here we explore incoherence during an entangling operation, such as is relevant in quantum information processing. As expected, it is more difficult to separate incoherence and decoherence over such processes. However, by studying the fidelity decay under a cyclic entangling map we are able to identify distinctive experimental signatures of incoherence. This is demonstrated both through numerical simulations and experimentally in a three qubit nuclear magnetic resonance implementation. BibTeX: @article{Henry07, author = {Henry, Michael and Gorshkov, Alexey and Weinstein, Yaakov and Cappellaro, Paola and Emerson, Joseph and Boulant, Nicolas and Hodges, Jonathan and Ramanathan, Chandrasekhar and Havel, Timothy and Martinez, Rudy and Cory, David}, title = {Signatures of Incoherence in a Quantum Information Processor}, journal = {Quantum Information Processing}, publisher = {Springer Netherlands}, year = {2007}, volume = {6}, pages = {431-444} }  J. S. Hodges, P. Cappellaro, T. F. Havel, R. Martinez and D. G. Cory "Experimental implementation of a logical Bell state encoding"Phys. Rev. A 75, 042320 (2007) [Abstract] [BibTeX] [DOI] [URL] Abstract: Liquid-phase NMR is a general-purpose 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 decoherence-free 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} }  P. Cappellaro, J. S. Hodges, T. F. Havel and D. G. Cory "Principles of Control for Decoherence-Free Subsystems"J. Chem. Phys. 125, 044514 (2006) [Abstract] [BibTeX] [DOI] [URL] Abstract: Decoherence-free 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 high-fidelity 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 Decoherence-Free Subsystems}, journal = {J. Chem. Phys.}, year = {2006}, volume = {125}, pages = {044514}, doi = {10.1063/1.2216702} }  P. Cappellaro "Quantum Information Processing in Multi-Spin Systems"Thesis at: Massachusetts Institute of Technology, Department of Nuclear Science and Engineering (2006) [Abstract] [BibTeX] [URL] Abstract: Coherence and entanglement in multi-spin systems are valuable resources for quantum information processing. In this thesis, I explore the manipulation of quantum information in complex multi-spin 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 multi-spin coherent states provides a hedge against the noise, via the encoding of information in logical degrees of freedom distributed over several spins. Manipulating multi-spin 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 many-body 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 closed-system limit. Entanglement and multi-spin 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 multi-spin states as a tool to explore many-body 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 multi-spin 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{CappellaroPhd, author = {Paola Cappellaro}, title = {Quantum Information Processing in Multi-Spin Systems}, school = {Massachusetts Institute of Technology}, year = {2006} }  H. J. Cho, P. Cappellaro, D. G. Cory and C. Ramanathan "Decay of highly correlated spin states in a dipolar-coupled solid: NMR study of CaF[sub 2]"Phys. Rev. B 74, 224434 (2006) [Abstract] [BibTeX] [DOI] [URL] 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 pseudo-one-dimensional 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 one-dimensional 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 dipolar-coupled solid: NMR study of CaF[sub 2]}, journal = {Phys. Rev. B}, year = {2006}, volume = {74}, number = {22}, pages = {224434}, doi = {10.1103/PhysRevB.74.224434} }  J. Hodges, P. Cappellaro, T. Havel and D. Cory "Quantum Control of Nuclear Spins" In Decision and Control, 2006 45th IEEE Conference on , 2488 -2494 (2006) [Abstract] [BibTeX] [DOI] [URL] Abstract: Nuclear magnetic resonance (NMR) spectroscopy has proven to be a facile means of achieving small-scale 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 open-loop 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 real-time control, these developments relied upon our ability to simulate the evolution of the system under the action of radio-frequency 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 on-going 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} }  T. Havel, P. Cappellaro, C. Ramanathan and D. Cory "Quantum Information Processing with Nuclear Spin-Based Devices" In Technical Proceedings of the 2005 NSTI Nanotechnology Conference and Trade Show 3, 161 - 164 (2005) [Abstract] [BibTeX] [URL] 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 Spin-Based Devices}, booktitle = {Technical Proceedings of the 2005 NSTI Nanotechnology Conference and Trade Show}, year = {2005}, volume = {3}, pages = {161 - 164} }  G. S. Boutis, P. Cappellaro, H. Cho, C. Ramanathan and D. G. Cory "Pulse error compensating symmetric magic-echo trains"J. Mag. Res. 161, 132-137 (2003) [Abstract] [BibTeX] [DOI] [URL] Abstract: We present improved line-narrowing sequences for dipolar coupled spin systems, based on a train of magic-echoes 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 time-suspension magic-echo cycle, the highest level of line-narrowing 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 = {G. S. Boutis and P. Cappellaro and H. Cho and C. Ramanathan and D. G. Cory}, title = {Pulse error compensating symmetric magic-echo trains}, journal = {J. Mag. Res.}, year = {2003}, volume = {161}, pages = {132-137}, doi = {10.1016/S1090-7807(03)00010-7} }  C. Ramanathan, H. Cho, P. Cappellaro, G. S. Boutis and D. G. Cory "Encoding multiple quantum coherences in non-commuting bases"Chem. Phys. Lett. 369, 311 (2003) [Abstract] [BibTeX] [DOI] [URL] 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 non-commuting 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 non-commuting bases}, journal = {Chem. Phys. Lett.}, year = {2003}, volume = {369}, pages = {311}, doi = {10.1016/S0009-2614(02)02020-1} }  P. G. B. C. Ramanathan H. Cho and D. Cory "Exploring large nuclear spin systems in the solid state using NMR" In Proceedings of the 6th International Conference on Quantum Communication, Measurement and Computing. , 267-270 (2003) [BibTeX] [URL] 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 = {267-270} }  Quantum Metrology UP ↑ E. Magesan and P. Cappellaro "Experimentally efficient methods for estimating the performance of quantum measurements"ArXiv:1301.5037 (2013) [BibTeX] [URL] BibTeX: @article{Magesan13x, author = {Magesan, E. and Cappellaro, P.}, title = {Experimentally efficient methods for estimating the performance of quantum measurements}, journal = {ArXiv:1301.5037}, year = {2013} }  C. D. Aiello, M. Hirose and P. Cappellaro "Composite-pulse magnetometry with a solid-state quantum sensor"Nat Commun. 4, 1419 (2013) [Abstract] [BibTeX] [DOI] [URL] 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 rotary-echo yields a flexible magnetometry scheme, mitigating both driving power imperfections and decoherence. A suitable choice of rotary-echo 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 room-temperature implementation, based on a single electronic spin in diamond, composite-pulse magnetometry provides a tunable trade-off between sensitivities in the uTHz−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 = {Composite-pulse magnetometry with a solid-state quantum sensor}, journal = {Nat Commun}, year = {2013}, volume = {4}, pages = {1419--}, doi = {10.1038/ncomms2375}, url = {http://dx.doi.org/10.1038/ncomms2375} }  A. Ajoy and P. Cappellaro "Stable three-axis nuclear-spin gyroscope in diamond"Phys. Rev. A 86, 062104 (2012) [Abstract] [BibTeX] [DOI] [URL] Abstract: Gyroscopes find wide applications in everyday life from navigation and inertial sensing to rotation sensors in hand-held devices and automobiles. Current devices, based on either atomic or solid-state systems, impose a choice between long-time stability and high sensitivity in a miniaturized system. Here, we introduce a quantum sensor that overcomes these limitations by providing a sensitive and stable three-axis gyroscope in the solid state. We achieve high sensitivity by exploiting the long coherence time of the 14N nuclear spin associated with the nitrogen-vacancy 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 long-time drifts. Such a sensor can achieve a sensitivity of \eta~0.5 (mdeg s-1)/\sqrt{Hz mm3} while offering enhanced stability in a small footprint. In addition, we exploit the four axes of delocalization of the nitrogen-vacancy center to measure not only the rate of rotation, but also its direction, thus obtaining a compact three-axis gyroscope. BibTeX: @article{Ajoy12g, author = {Ajoy, Ashok and Cappellaro, Paola}, title = {Stable three-axis nuclear-spin gyroscope in diamond}, journal = {Phys. Rev. A}, year = {2012}, volume = {86}, pages = {062104}, doi = {10.1103/PhysRevA.86.062104} }  M. Hirose, C. D. Aiello and P. Cappellaro "Continuous dynamical decoupling magnetometry"Phys. Rev. A 86, 062320 (2012) [Abstract] [BibTeX] [DOI] [URL] Abstract: Solid-state 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} }  N. Bar-Gill, L. Pham, C. Belthangady, D. Le Sage, P. Cappellaro, J. Maze, M. Lukin, A. Yacoby and R. Walsworth "Suppression of spin-bath dynamics for improved coherence of multi-spin-qubit systems"Nat. Commun. 3, 858 (2012) [Abstract] [BibTeX] [DOI] [URL] Abstract: Multi-qubit 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 solid-state spin systems, qubit coherence is closely related to fundamental questions of many-body spin dynamics. Here we apply a coherent spectroscopic technique to characterize the dynamics of the composite solid-state spin environment of nitrogen-vacancy colour centres in room temperature diamond. We identify a possible new mechanism in diamond for suppression of electronic spin-bath 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 multi-spin-qubit systems, thus paving the way for applications in quantum information, sensing and metrology. BibTeX: @article{Bar-Gill12, author = {Bar-Gill, 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 spin-bath dynamics for improved coherence of multi-spin-qubit systems}, journal = {Nat. Commun.}, year = {2012}, volume = {3}, pages = {858}, doi = {10.1038/ncomms1856} }  P. Cappellaro "Spin-bath narrowing with adaptive parameter estimation"Phys. Rev. A 85, 030301(R) (2012) [Abstract] [BibTeX] [DOI] [URL] 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 solid-state sensors. Thanks to recent advances in single-shot 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 = {Spin-bath narrowing with adaptive parameter estimation}, journal = {Phys. Rev. A}, year = {2012}, volume = {85}, pages = {030301(R)}, doi = {10.1103/PhysRevA.85.030301} }  P. Cappellaro, G. Goldstein, J. S. Hodges, L. Jiang, J. R. Maze, A. S. Sørensen and M. D. Lukin "Environment-assisted metrology with spin qubits"Phys. Rev. A 85, 032336 (2012) [Abstract] [BibTeX] [DOI] [URL] 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 solid-state 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 echo-based sensing schemes. This figure of merit can be used to engineer optimized samples for high-sensitivity nanoscale magnetic sensing, such as diamond nanocrystals with controlled impurity density. BibTeX: @article{Cappellaro12b, 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 = {Environment-assisted metrology with spin qubits}, journal = {Phys. Rev. A}, year = {2012}, volume = {85}, pages = {032336}, doi = {10.1103/PhysRevA.85.032336} }  L. M. Pham, N. Bar-Gill, C. Belthangady, D. Le Sage, P. Cappellaro, M. D. Lukin, A. Yacoby and R. L. Walsworth "Enhanced solid-state multispin metrology using dynamical decoupling"Phys. Rev. B 86, 045214 (2012) [Abstract] [BibTeX] [DOI] [URL] Abstract: We use multipulse dynamical decoupling to increase the coherence lifetime (T2) of large numbers of nitrogen-vacancy (NV) electronic spins in room temperature diamond, thus enabling scalable applications of multispin quantum information processing and metrology. We realize an order-of-magnitude 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 Bar-Gill, N. and Belthangady, C. and Le Sage, D. and Cappellaro, P. and Lukin, M. D. and Yacoby, A. and Walsworth, R. L.}, title = {Enhanced solid-state multispin metrology using dynamical decoupling}, journal = {Phys. Rev. B}, year = {2012}, volume = {86}, pages = {045214}, doi = {10.1103/PhysRevB.86.045214} }  G. Goldstein, P. Cappellaro, J. R. Maze, J. S. Hodges, L. Jiang, A. S. Sørensen and M. D. Lukin "Environment Assisted Precision Measurement"Phys. Rev. Lett. 106, 140502 (2011) [Abstract] [BibTeX] [DOI] [URL] 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 Heisenberg-limited 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} }  L. M. Pham, D. L. 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 nitrogen-vacancy ensembles"New J. Phys. 13, 045021 (2011) [Abstract] [BibTeX] [DOI] [URL] Abstract: We demonstrate a method of imaging spatially varying magnetic fields using a thin layer of nitrogen-vacancy (NV) centers at the surface of a diamond chip. Fluorescence emitted by the two-dimensional 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 echo-based technique with sub-micron resolution over a 140 μm×140 μm field of view, giving single-pixel sensitivity ##IMG## [http://ej.iop.org/images/1367-2630/13/4/045021/nj378975ieqn1.gif] 00rm nT/rm Hz . We discuss ongoing efforts to further improve the sensitivity, as well as potential bioimaging applications such as real-time imaging of activity in functional, cultured networks of neurons. BibTeX: @article{Pham11, author = {L M Pham and D Le Sage and P L Stanwix and T K Yeung and D Glenn and A Trifonov and P Cappellaro and P R Hemmer and M D Lukin and H Park and A Yacoby and R L Walsworth}, title = {Magnetic field imaging with nitrogen-vacancy ensembles}, journal = {New J. Phys.}, year = {2011}, volume = {13}, number = {4}, pages = {045021}, doi = {10.1088/1367-2630/13/4/045021} }  G. Goldstein, M. D. Lukin and P. Cappellaro "Quantum Limits on Parameter Estimation"ArXiv:1001.4804 (2010) [Abstract] [BibTeX] [URL] Abstract: We present a new proof of the quantum Cramer-Rao bound for precision parameter estimation [1-3] 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 two-level system interacting with a time-independent Hamiltonian. BibTeX: @arxiv{Goldstein10x, author = {Goldstein, G. and Lukin, M.~D. and Cappellaro, P.}, title = {Quantum Limits on Parameter Estimation}, journal = {ArXiv:1001.4804}, year = {2010} }  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"J. Chem. Phys. 133, 124105 (2010) [Abstract] [BibTeX] [DOI] [URL] 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 nitrogen-vacancy 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 signal-to-noise 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, high-resolution 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} }  P. Cappellaro and M. D. Lukin "Quantum correlation in disordered spin systems: Applications to magnetic sensing"Phys. Rev. A 80, 032311 (2009) [Abstract] [BibTeX] [DOI] [URL] Abstract: We propose a strategy to generate a many-body 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 GHZ-like and spin-squeezed 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 nitrogen-vacancy 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} }  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"21st International Conference on Atomic Physics 21, 78 (2009) [Abstract] [BibTeX] [DOI] [URL] 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 bio-imaging. Here we describe an innovative approach to magnetometry that takes advantage of recently developed techniques for coherent control of solid-state spin qubits. We experimentally demonstrate this novel magnetometer employing an individual electronic spin associated with a Nitrogen-Vacancy (NV) center in diamond. Using an ultra-pure diamond sample, we achieve shot-noise-limited 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} }  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"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] [BibTeX] [DOI] [URL] 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 Nitrogen-Vacancy (NV) center in diamond. At room temperature, using an ultra-pure diamond sample, we achieve shot-noise-limited 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} }  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"Nature 455, 644-647 (2008) [Abstract] [BibTeX] [DOI] [URL] 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 nitrogen-vacancy impurity in diamond at room temperature8. Using an ultra-pure 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 Hz-1/2 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 = {644--647}, doi = {10.1038/nature07279} }  J. M. Taylor, P. Cappellaro, L. Childress, L. Jiang, D. Budker, P. R. Hemmer, A. Yacoby, R. Walsworth and M. D. Lukin "High-sensitivity diamond magnetometer with nanoscale resolution"Nature Phys. 4, 810-816 (2008) [Abstract] [BibTeX] [DOI] [URL] 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 solid-state electron spin quantum bits. Specifically, we investigate a magnetic sensor based on nitrogen-vacancy centres in room-temperature diamond. We discuss two important applications of this technique: a nanoscale magnetometer that could potentially detect precession of single nuclear spins and an optical magnetic-field imager combining spatial resolution ranging from micrometres to millimetres with a sensitivity approaching a few fT Hz-1/2. 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 = {High-sensitivity diamond magnetometer with nanoscale resolution}, journal = {Nature Phys.}, publisher = {Nature Publishing Group}, year = {2008}, volume = {4}, number = {10}, pages = {810--816}, doi = {10.1038/nphys1075} }  P. Cappellaro, J. Emerson, N. Boulant, C. Ramanathan, S. Lloyd and D. G. Cory "Spin amplifier for single spin measurement" In Quantum Computing in Solid State Systems , 306-312 (2006) [Abstract] [BibTeX] [DOI] [URL] 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 = {306-312}, doi = {10.1007/0-387-31143-2_37} }  C. A. Perez-Delgado, M. Mosca, P. Cappellaro and D. G. Cory "Single Spin Measurement Using Cellular Automata Techniques"Phys. Rev. Lett. 97, 100501 (2006) [Abstract] [BibTeX] [DOI] [URL] Abstract: We analyze a conceptual approach to single-spin 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{pyramidprl, author = {Carlos A. Perez-Delgado 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} }  P. Cappellaro, J. Emerson, N. Boulant, C. Ramanathan, S. Lloyd and D. G. Cory "Entanglement Assisted Metrology"Phys. Rev. Lett. 94, 020502 (2005) [Abstract] [BibTeX] [DOI] [URL] 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 many-body 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} }  C. Birattari, P. Cappellaro, A. Mitaroff and M. Silari "Development of an Extended Range Bonner Sphere Spectrometer" In Advanced Monte Carlo for Radiation Physics, Particle Transport Simulation and Applications , 1157 (2001) [BibTeX] [URL] 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 Information Transport UP ↑ A. Ajoy and P. Cappellaro "Mixed-state quantum transport in correlated spin networks"Phys. Rev. A 85, 042305 (2012) [Abstract] [BibTeX] [DOI] [URL] Abstract: Quantum spin networks can be used to transport information between separated registers in a quantum-information 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 phase-correlate 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 = {Mixed-state quantum transport in correlated spin networks}, journal = {Phys. Rev. A}, year = {2012}, volume = {85}, pages = {042305}, doi = {10.1103/PhysRevA.85.042305} }  A. Ajoy and P. Cappellaro "Perfect quantum transport in arbitrary spin networks"Phys. Rev. B 87, 064303 (2013) [Abstract] [BibTeX] [DOI] [URL] 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} }  A. Ajoy and P. Cappellaro "Quantum simulation via filtered Hamiltonian engineering: application to perfect quantum transport in spin networks"ArXiv:1208.3656 (2012) [Abstract] [BibTeX] [URL] Abstract: We propose a novel Hamiltonian engineering method in spin-based quantum information processing architectures that requires no local control but only relies on collective spin rotations and field gradients. The technique relies on coupling engineering via the time-domain construction of a Bragg grating and a weighting function that modulate the coupling strengths. As an example, we demonstrate how to engineering the optimal Hamiltonian for perfect quantum information transport between two separated nodes of a large spin network. We engineer a spin chain with optimal couplings from a large spin network, such as naturally occurring in crystals, while decoupling all unwanted interactions. We show that for realistic experimental parameters this Hamiltonian engineering method could be used for perfect quantum information transport at room-temperature. BibTeX: @arxiv{Ajoy12x2, author = {Ajoy, A. and Cappellaro, P.}, title = {Quantum simulation via filtered Hamiltonian engineering: application to perfect quantum transport in spin networks}, journal = {ArXiv:1208.3656}, year = {2012} }  G. Kaur and P. Cappellaro "Initialization and readout of spin chains for quantum information transport"New J. Phys. 14, 083005 (2012) [Abstract] [BibTeX] [DOI] [URL] 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 one-dimensional 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 single-spin 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 = {10.1088/1367-2630/14/8/083005} }  P. Cappellaro, L. Viola and C. Ramanathan "Coherent-state transfer via highly mixed quantum spin chains"Phys. Rev. A 83, 032304 (2011) [Abstract] [BibTeX] [DOI] [URL] Abstract: Spin chains have been proposed as quantum wires in many quantum-information processing architectures. Coherent transmission of quantum information in spin chains over short distances is enabled by their internal dynamics, which drives the transport of single-spin 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 mixed-state chains and find similarities that enable the experimental study of pure-state transfer via mixed-state chains. We also demonstrate protocols for the perfect transfer of quantum information in these chains. Remarkably, mixed-state chains allow the use of Hamiltonians that do not preserve the total number of single-spin excitations and are more readily obtainable from the naturally occurring magnetic dipolar interaction. We discuss experimental implementations using solid-state nuclear magnetic resonance and defect centers in diamond. BibTeX: @article{Cappellaro11, author = {Cappellaro, Paola and Viola, Lorenza and Ramanathan, Chandrasekhar }, title = {Coherent-state 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} }  C. Ramanathan, P. Cappellaro, L. Viola and D. G. Cory "Experimental characterization of coherent magnetization transport in a one-dimensional spin system"New J. Phys. 13, 103015 (2011) [Abstract] [BibTeX] [DOI] [URL] Abstract: We experimentally characterize the non-equilibrium, room-temperature magnetization dynamics of a spin chain evolving under an effective double-quantum (DQ) Hamiltonian. We show that the Liouville space operators corresponding to the magnetization and the two-spin correlations evolve 90 degrees out of phase with each other, and drive the transport dynamics. For a nearest-neighbor-coupled 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 multi-spin correlations. Even though long-range 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 one-dimensional 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 one-dimensional spin system}, journal = {New J. Phys.}, year = {2011}, volume = {13}, number = {10}, pages = {103015}, doi = {10.1088/1367-2630/13/10/103015} }  W. Zhang, P. Cappellaro, N. Antler, B. Pepper, D. G. Cory, V. V. Dobrovitski, C. Ramanathan and L. Viola "NMR multiple quantum coherences in quasi-one-dimensional spin systems: Comparison with ideal spin-chain dynamics"Phys. Rev. A 80, 052323 (2009) [Abstract] [BibTeX] [DOI] [URL] Abstract: The 19F spins in a crystal of fluorapatite have often been used to experimentally approximate a one-dimensional spin system. Under suitable multipulse control, the nuclear-spin dynamics may be modeled to first approximation by a double-quantum one-dimensional Hamiltonian, which is analytically solvable for nearest-neighbor couplings. Here, we use solid-state 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 long-range intrachain couplings, cross-chain 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 one-dimensional 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 quasi-one-dimensional spin systems: Comparison with ideal spin-chain dynamics}, journal = {Phys. Rev. A}, year = {2009}, volume = {80}, number = {5}, pages = {052323}, doi = {10.1103/PhysRevA.80.052323} }  P. Cappellaro, C. Ramanathan and D. G. Cory "Dynamics and control of a quasi-one-dimensional spin system"Phys. Rev. A 76, 032317 (2007) [Abstract] [BibTeX] [DOI] [URL] Abstract: We study experimentally a system comprised of linear chains of spin-1/2 nuclei that provides a test bed for multibody dynamics and quantum-information processing. This system is a paradigm for a class of quantum-information 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 quasi-one-dimensional spin system}, journal = {Phys. Rev. A}, year = {2007}, volume = {76}, number = {3}, pages = {032317}, doi = {10.1103/PhysRevA.76.032317} }  P. Cappellaro, C. Ramanathan and D. G. Cory "Simulations of Information Transport in Spin Chains"Phys. Rev. Lett. 99, 250506 (2007) [Abstract] [BibTeX] [DOI] [URL] 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 nearest-neighbor XY-Heisenberg couplings. We present here a similarity transformation between the XY Hamiltonian and the double-quantum Hamiltonian, an interaction which is achievable with the collective control provided by radio-frequency 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} }