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arXiv:1409.4562 · Science

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

Gonzalo A. Álvarez, Dieter Suter, Robin Kaiser

Published Aug 20, 2015• 144 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1126/science.1261160

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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.
We investigate analytically and numerically the multiple-quantum (MQ) NMR dynamics in systems of nuclear spins 1∕21∕21∕2 coupled by the dipole-dipole interactions in the case of the dipolar ordered initial state. We suggest two different methods of MQ NMR. One of them is based on the measurement of the dipolar temperature in the quasiequilibrium state which is established after the time of order ${\ensuremath{\omega}}_{\mathit{loc}}^{\ensuremath{-}1}$ (${\ensuremath{\omega}}_{\mathit{loc}}$ is the dipolar local field) after the MQ NMR experiment. The other method uses an additional resonance ${(\ensuremath{\pi}∕4)}_{y}$ pulse after the preparation period of the standard MQ NMR experiment in solids. Many-spin clusters and correlations are created faster in such experiments than in the usual MQ NMR experiments and can be used for the investigation of many-spin dynamics of nuclear spins in solids.
We investigate analytically and numerically the multiple-quantum (MQ) NMR dynamics in systems of nuclear spins 1/2 coupled by dipole-dipole interactions in the case of the dipolar-ordered initial state. We suggest a new method of MQ NMR based on the measurement of the dipolar temperature in the quasi-equilibrium state, which establishes after the time of order ω loc −1 (ωloc is the dipolar local field) after the MQ NMR experiment. Manyspin clusters and correlations are created faster in such an experiment than in usual MQ NMR experiments and can be used for the investigation of the many-spin dynamics of nuclear spins in solids.
Characterizing out-of-equilibrium many-body dynamics is a complex but crucial task for quantum applications and understanding fundamental phenomena. A central question is the role of localization in quenching thermalization in many-body systems and whether such localization survives in the presence of interactions. Probing this question in real systems necessitates the development of an experimentally measurable metric that can distinguish between different types of localization. While it is known that the localized phase of interacting systems [many-body localization (MBL)] exhibits a long-time logarithmic growth in entanglement entropy that distinguishes it from the noninteracting case of Anderson localization (AL), entanglement entropy is difficult to measure experimentally. Here, we present a novel correlation metric, capable of distinguishing MBL from AL in high-temperature spin systems. We demonstrate the use of this metric to detect localization in a natural solid-state spin system using nuclear magnetic resonance (NMR). We engineer the natural Hamiltonian to controllably introduce disorder and interactions, and observe the emergence of localization. In particular, while our correlation metric saturates for AL, it slowly keeps increasing for MBL, demonstrating analogous features to entanglement entropy, as we show in simulations. Our results show that our NMR techniques, akin to measuring out-of-time correlations, are well suited for studying localization in spin systems.
We present an experimental study on nonequilibrium dynamics of a spinor condensate after it is quenched across a superfluid to Mott insulator (MI) phase transition in cubic lattices. Intricate dynamics consisting of spin-mixing oscillations at multiple frequencies are observed in time evolutions of the spinor condensate localized in deep lattices after the quantum quench. Similar spin dynamics also appear after spinor gases in the MI phase are suddenly moved away from their ground states via quenching magnetic fields. We confirm these observed spectra of spin-mixing dynamics can be utilized to reveal atom number distributions of an inhomogeneous system, and to study transitions from two-body to many-body dynamics. Our data also imply the nonequilibrium dynamics depend weakly on the quench speed but strongly on the lattice potential. This enables precise measurements of the spin-dependent interaction, a key parameter determining the spinor physics.
Multiple quantum (MQ) nuclear magnetic resonance (NMR) spin dynamics are investigated analytically in infinite one-dimensional (1D) chains of spins 1/2. The representation of spin 1/2 operators with fermion field operators allows to calculate exactly the spin density operator, and hence NMR observables, under a variety of different conditions for 1D spin systems. The exact expressions are valid for all times and for a macroscopic number of coupled spins. The calculations for a 1D spin system initially at thermal equilibrium, and evolving under a 2-quantum/2-spin average dipolar Hamiltonian, in the presence of nearest-neighbor dipolar interactions yield MQ NMR spectra with 0- and 2-quantum coherences only. For a nonequilibrium initial condition with transverse magnetization, the analogous spin dynamics calculations produce MQ NMR spectra with all possible coherences of odd orders. Calculations at the level of perturbation theory, which include next-nearest-neighbor dipolar interactions, generate MQ spectra with higher even order coherences for equilibrium initial condition and evolution under a 2-quantum/2-spin propagator. Consideration of multiple spin correlations, 0-quantum coherences, and rf pulse imperfections are also presented. The relevance and implications of these theoretical results for comparison with the recent MQ NMR experiments of Yesinowski et al. on materials with quasi-one-dimensional distributions of spins, and for MQ NMR of solids in general are discussed.
Quantum measurement can profoundly impact the dynamics of many-body systems, for instance, inducing phase transitions from volume-law chaotic phases to area-law localized phases. While chaotic phases emerge naturally in generic many-body systems, the experimental realization of a fully localized phase driven by measurement remains challenging, primarily owing to the stringent requirement of near-perfect isolation of the system from environmental dissipation. Here we experimentally observe measurement-induced localization phenomena in an interacting 13C^{13}\mathrm{C}13C nuclear spin system in diamond. In contrast to previous circuit-model-based experiments, our well-isolated system evolves under a physical many-body Hamiltonian with measurements intervening at intervals. By implementing either projective measurements on a single spin or global weak measurements on the entire system, we observe substantially prolonged spin autocorrelation times as the measurement frequency increases. Our results, combined with numerical simulations, provide evidence that quantum measurement can drive a many-body system into a localized regime, and lay the groundwork for future experimental investigations into measurement-induced many-body dynamics and related entanglement phenomena.