Rev. Mod. Phys.:Protecting quantum information against environmental noise

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Colloquium: Protecting quantum information against environmental noise

Dieter Suter and Gonzalo A. Álvarez
Rev. Mod. Phys. 88, 041001 (2016)
Published 10 October 2016

RevModPhys.88.041001Quantum-mechanical systems retain their properties so long as the phase of quantum superpositions evolve stably over time. Contact with an environment can disrupt this phase evolution. But for environments that do not exchange energy with the quantum system, strategies exist where the controlled driving of the system can recover or maintain the quantum phase. This Colloquium surveys the host of techniques that are available to “refocus” the phase when disturbed by various forms of classical or quantum environment. While the first such techniques were developed long ago, ideas from quantum information theory have introduced new strategies for accomplishing this goal.

Source: Reviews of Modern Physics – Volume 88 Issue 4

Phys. Rev. Applied: Maximizing Information on the Environment by Dynamically Controlled Qubit Probes

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Maximizing Information on the Environment by Dynamically Controlled Qubit Probes

Analia Zwick, Gonzalo A. Álvarez, and Gershon Kurizki
Phys. Rev. Applied 5, 014007 (2016)
Published 25 January 2016

PhysRevApplied.5.014007-2From computers to medicine, miniaturization approaches the atomic scale, where device operation can be dominated by quantum effects that are strongly coupled to the local environment. These influences may be seen not as a nuisance, but rather a nearly untapped source of information about physical or biochemical processes playing out nearby. How can one extract maximum information from such fluctuations with an atomic probe, under typical experimental constraints? The authors use quantum estimation theory to outline a general strategy for dynamical measurement of a broad class of environmental processes.

Source: Physical Review Applied – Volume 5 Issue 1

 

Simulation of an experimental real-time adaptive-estimation protocol for realistic conditions with a NVC spin probe. (a),(b) Convergence of the real-time adaptive-estimation protocol to the theoretically predicted values for estimating τc. Free evolution of the probe (blue circles) is contrasted with that of a dynamically controlled probe under a CPMG (green square) sequence with N=8 pulses in the presence of an Ornstein-Uhlenbeck process with Lorentzian spectrum with τc=10μs, a coupling with the environment g=1 MHz consistently with the spectral density of a HPHT diamond sample. The simulated curves derived from exact analytical results are averaged over 600 realizations. In (a), the optimal measurement time tm as a function of the number of measurements Nm converges to the optimal value to perform the measurements t^{opt} for the CPMG case. Similar curves converging to the corresponding t^{opt} are observed for other controls and free evolution. In (b), the minimal relative error ϵ(τc,t^{opt}) converges to the (Cramer-Rao) bound. Under free evolution, the regime where ϵ∝(1/√Nm) is attained for Nm≫100. The ultimate bound (ϵ0/√Nm dashed line, α=β−1) is attained only by optimal control. (c) Convergence to the minimal relative error ϵ(g,t^{opt}) to the (Cramer-Rao) bound for estimating g by N=500 consecutive projective measurements in the Zeno regime (green triangle) compared to the estimation under free evolution (blue circle). In this case, G_{β=2}(g=0.03 MHz,ω), with τc=10 μs, consistently with the spectral density of a 12C diamond sample. Here too the ultimate bound (ϵ0/2√Nm dashed line, α=2) is attained only by optimal control. (d) Proposed scheme for using a NVC as a qubit probe for its environment. The ms=0 (|0⟩) state is fully populated by laser irradiation (dashed curly arrow). Microwave (MW) pulses are selectively applied between the states with ms=0 and −1 (|0⟩ and |−1⟩) of the electronic ground states to initialize the spin probe in a |+⟩=(1/√2)(|0⟩+|−1⟩) state and effect the π pulse CPMG sequence for estimating τc. For estimating g, projective measurements are emulated by combining MW π/2 pulses on the 0↔−1 transition and laser-induced relaxation between the ground and exited electronic states that conserve the spin components (solid curly arrows). The readout is done at the end of the N-pulse sequence by detecting the laser-induced fluorescence signal.
Simulation of an experimental real-time adaptive-estimation protocol for realistic conditions with a NVC spin probe. (a),(b) Convergence of the real-time adaptive-estimation protocol to the theoretically predicted values for estimating τc. Free evolution of the probe (blue circles) is contrasted with that of a dynamically controlled probe under a CPMG (green square) sequence with N=8 pulses in the presence of an Ornstein-Uhlenbeck process with Lorentzian spectrum with τc=10μs, a coupling with the environment g=1 MHz consistently with the spectral density of a HPHT diamond sample. The simulated curves derived from exact analytical results are averaged over 600 realizations. In (a), the optimal measurement time tm as a function of the number of measurements Nm converges to the optimal value to perform the measurements t^{opt} for the CPMG case. Similar curves converging to the corresponding t^{opt} are observed for other controls and free evolution. In (b), the minimal relative error ϵ(τc,t^{opt}) converges to the (Cramer-Rao) bound. Under free evolution, the regime where ϵ∝(1/√Nm) is attained for Nm≫100. The ultimate bound (ϵ0/√Nm dashed line, α=β−1) is attained only by optimal control. (c) Convergence to the minimal relative error ϵ(g,t^{opt}) to the (Cramer-Rao) bound for estimating g by N=500 consecutive projective measurements in the Zeno regime (green triangle) compared to the estimation under free evolution (blue circle). In this case, G_{β=2}(g=0.03 MHz,ω), with τc=10 μs, consistently with the spectral density of a 12C diamond sample. Here too the ultimate bound (ϵ0/2√Nm dashed line, α=2) is attained only by optimal control. (d) Proposed scheme for using a NVC as a qubit probe for its environment. The ms=0 (|0⟩) state is fully populated by laser irradiation (dashed curly arrow). Microwave (MW) pulses are selectively applied between the states with ms=0 and −1 (|0⟩ and |−1⟩) of the electronic ground states to initialize the spin probe in a |+⟩=(1/√2)(|0⟩+|−1⟩) state and effect the π pulse CPMG sequence for estimating τc. For estimating g, projective measurements are emulated by combining MW π/2 pulses on the 0↔−1 transition and laser-induced relaxation between the ground and exited electronic states that conserve the spin components (solid curly arrows). The readout is done at the end of the N-pulse sequence by detecting the laser-induced fluorescence signal.

Nat. Commun.: Local and bulk 13C hyperpolarization in nitrogen-vacancy-centred diamonds at variable fields and orientations

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Gonzalo A. Álvarez, Christian O. Bretschneider, Ran Fischer, Paz London, Hisao Kanda, Shinobu Onoda, Junichi Isoya, David Gershoni & Lucio Frydman

Nature Communications 6, 8456 (2015). doi:10.1038/ncomms9456

 

 
Combined Optical and Nuclear Magnetic Resonance (NMR) setup for hyperpolarizing nuclear spins in diamonds at room- temperature. During the polarization transfer phase, the entire single-crystal diamond (red in the picture) is irradiated with green laser light and microwaves underneath the NMR magnet at a low magnetic field. The hyperpolarized diamond is then shuttled into a high field superconducting magnet, for a directly detected NMR experiment on the 13C spins.Polarizing nuclear spins is of fundamental importance in biology, chemistry and physics. Methods for hyperpolarizing 13C nuclei from free electrons in bulk usually demand operation at cryogenic temperatures. Room temperature approaches targeting diamonds with nitrogen-vacancy centres could alleviate this need; however, hitherto proposed strategies lack generality as they demand stringent conditions on the strength and/or alignment of the magnetic field. We report here an approach for achieving efficient electron-13C spin-alignment transfers, compatible with a broad range of magnetic field strengths and field orientations with respect to the diamond crystal. This versatility results from combining coherent microwave- and incoherent laser-induced transitions between selected energy states of the coupled electron–nuclear spin manifold. 13C-detected nuclear magnetic resonance experiments demonstrate that this hyperpolarization can be transferred via first-shell or via distant 13Cs throughout the nuclear bulk ensemble. This method opens new perspectives for applications of diamond nitrogen-vacancy centres in nuclear magnetic resonance, and in quantum information processing.

 

Source: Local and bulk 13C hyperpolarization in nitrogen-vacancy-centred diamonds at variable fields and orientations : Nature Communications : Nature Publishing Group

 

Acquiring ensemble 13C polarization spectra for varying NV orientations with respect to B0. (a) Opto-NMR set-up and (b) detection sequence used in these experiments. During the polarization transfer phase, the entire single-crystal diamond is irradiated with laser light and MW underneath the NMR magnet at a low B0. The hyperpolarized diamond is then shuttled (in <1 s) into a 4.7-T superconducting magnet to directly detect its macroscopic 13C magnetization via a spin-echo sequence. The low B0 magnetic field is aligned to one of the nitrogen-vacancy-centre orientations (in red), while the other three orientations (in blue) subtend an angle of ≈109° with respect to the field. (c) Typical 13C polarization enhancement patterns observed by NMR as a function of the MW frequency ω with signals normalized with respect to the thermal 13C response at 4.7 T (inset). The left part of the plot corresponds the nuclear polarization generated by MW transitions for the aligned orientation (red circles), while the right part corresponds to nuclear polarization enhanced via the three non-aligned, equivalent orientations (blue circles). The ≈1:3 intensity ratio reflects the relative abundances of aligned and non-aligned sites in the diamond’s tetrahedral structure. In each of the patterns, the central peaks represent bulk nuclear hyperpolarization pumped via 13C spins coupled with hyperfine interactions lower than 20 MHz, while the outer peaks originate from first-shell 13Cs whose hyperfine splitting is ≈130 MHz (refs 26, 29). The antiphase structure of each of these peaks corresponds to the MW transitions and at one side of the central peaks, and to the state at the other side. The inset shows NMR spectra obtained for a thermally polarized sample, and at the maxima of the central peaks for the aligned and non-aligned orientations. p.p.m. refers to parts-per-million of the high-field NMR 13C resonance frequency, which in our case is 50.5 MHz.
Acquiring ensemble 13C polarization spectra for varying NV orientations with respect to B0. (a) Opto-NMR set-up and (b) detection sequence used in these experiments. During the polarization transfer phase, the entire single-crystal diamond is irradiated with laser light and MW underneath the NMR magnet at a low B0. The hyperpolarized diamond is then shuttled (in <1 s) into a 4.7-T superconducting magnet to directly detect its macroscopic 13C magnetization via a spin-echo sequence. The low B0 magnetic field is aligned to one of the nitrogen-vacancy-centre orientations (in red), while the other three orientations (in blue) subtend an angle of ≈109° with respect to the field. (c) Typical 13C polarization enhancement patterns observed by NMR as a function of the MW frequency ω with signals normalized with respect to the thermal 13C response at 4.7 T (inset). The left part of the plot corresponds the nuclear polarization generated by MW transitions for the aligned orientation (red circles), while the right part corresponds to nuclear polarization enhanced via the three non-aligned, equivalent orientations (blue circles). The ≈1:3 intensity ratio reflects the relative abundances of aligned and non-aligned sites in the diamond’s tetrahedral structure. In each of the patterns, the central peaks represent bulk nuclear hyperpolarization pumped via 13C spins coupled with hyperfine interactions lower than 20 MHz, while the outer peaks originate from first-shell 13Cs whose hyperfine splitting is ≈130 MHz. The inset shows NMR spectra obtained for a thermally polarized sample, and at the maxima of the central peaks for the aligned and non-aligned orientations. p.p.m. refers to parts-per-million of the high-field NMR 13C resonance frequency, which in our case is 50.5 MHz.

Quanten-Computer löst Quanten-Problem :: pro-physik.de

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Quanten-Computer löst Quanten-Problem

Einfluss von Störungen auf das Ausbreiten eines Quantensystems untersucht.

Source: :: Quanten-Computer löst Quanten-Problem :: pro-physik.de

Science: Localization-delocalization transition in the dynamics of dipolar-coupled nuclear spins

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Nonequilibrium dynamics of many-body systems are important in many scientific fields. Here, we report the experimental observation of a phase transition of the quantum coherent dynamics of a three-dimensional many-spin system with dipolar interactions. Using nuclear magnetic resonance (NMR) on a solid-state system of spins at room-temperature, we quench the interaction Hamiltonian to drive the evolution of the system. Depending on the quench strength, we then observe either localized or extended dynamics of the system coherence. We extract the critical exponents for the localized cluster size of correlated spins and diffusion coefficient around the phase transition separating the localized from the delocalized dynamical regime. These results show that NMR techniques are well suited to studying the nonequilibrium dynamics of complex many-body systems.

 

Gonzalo A. Álvarez (1), Dieter Suter (2), Robin Kaiser (3)

(1) Department of Chemical Physics, Weizmann Institute of Science, 76100, Rehovot, Israel.
(2) Fakultät Physik, Technische Universität Dortmund, D-44221, Dortmund, Germany.
(3) Institut Non-Linéaire de Nice, CNRS, Université de Nice Sophia Antipolis, 06560, Valbonne, France.

Science 349, 846 (2015)

DOI: 10.1126/science.1261160

 

scaling_localization-delocalization_transition
Time evolution of the cluster size of correlated spins K for different quench strengths (1-p) and finite-time scaling procedure. (A) Cluster-size K as a function of the time t after the quench. The unperturbed quenched evolution (black squares) shows a cluster-size K that grows as ∼t^(4.3) at long times (dashed line is a guide to the eye). The solid symbols show the points used for a finite-time scaling analysis, while the empty symbols do not belong to the long time regime (t < 0.3 ms). For the largest perturbation strengths p to the quench, localization effects are clearly visible by the saturation of the cluster size. (B and C) In these two panels, we present the finite-time scaling procedure. In (B), the rescaled and squared correlation length l^2= K^(2/3) as a function of the evolution time 1=t^(k_2) is plotted. In (C), the curves of (B) are rescaled horizontally by the scaling factor ξ(p) to obtain a universal scaling law.

 

localization-delocalization_transition
Scaling factor and critical exponents. Normalized scaling factor ξ(p) as a function of p (blue triangles). The red solid line is a fit to the blue triangles with a expression ξ(p) proportional to|p − p_c|^nu, the critical exponent is then nu= 0,42. The two insets show the distribution of coherence orders of the density matrix as a function of the evolution time t for two perturbation strengths, which correspond to a delocalized and localized regime, respectively. The corresponding scaling factors are indicated by the arrows.

via Localization-delocalization transition in the dynamics of dipolar-coupled nuclear spins.