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arXiv:1806.10169 · Physical Review Letters

Probing Quantum Thermalization of a Disordered Dipolar Spin Ensemble with Discrete Time-Crystalline Order

Joonhee Choi, Hengyun Zhou, Soonwon Choi, Renate Landig, Wen Wei Ho, Junichi Isoya, Fedor Jelezko, Shinobu Onoda, Hitoshi Sumiya, Dmitry A. Abanin, Mikhail D. Lukin

Published Feb 1, 2019• 49 citations
arXivHTMLPDF

Abstract

We investigate thermalization dynamics of a driven dipolar many-body quantum system through the stability of discrete time crystalline order. Using periodic driving of electronic spin impurities in diamond, we realize different types of interactions between spins and demonstrate experimentally that the interplay of disorder, driving, and interactions leads to several qualitatively distinct regimes of thermalization. For short driving periods, the observed dynamics are well described by an effective Hamiltonian which sensitively depends on interaction details. For long driving periods, the system becomes susceptible to energy exchange with the driving field and eventually enters a universal thermalizing regime, where the dynamics can be described by interaction-induced dephasing of individual spins. Our analysis reveals important differences between thermalization of long-range Ising and other dipolar spin models.

DOI
10.1103/physrevlett.122.043603

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We investigate thermalization dynamics of a driven dipolar many-body quantum system through the stability of discrete time crystalline order. Using periodic driving of electronic spin impurities in diamond, we realize different types of interactions between spins and demonstrate experimentally that the interplay of disorder, driving, and interactions leads to several qualitatively distinct regimes of thermalization. For short driving periods, the observed dynamics are well described by an effective Hamiltonian which sensitively depends on interaction details. For long driving periods, the system becomes susceptible to energy exchange with the driving field and eventually enters a universal thermalizing regime, where the dynamics can be described by interaction-induced dephasing of individual spins. Our analysis reveals important differences between thermalization of long-range Ising and other dipolar spin models.
We analyze the quantum dynamics of periodically driven, disordered systems in the presence of long-range interactions. Focusing on the stability of discrete time crystalline (DTC) order in such systems, we use a perturbative procedure to evaluate its lifetime. For 3D systems with dipolar interactions, we show that the corresponding decay is parametrically slow, implying that robust, long-lived DTC order can be obtained. We further predict a sharp crossover from the stable DTC regime into a regime where DTC order is lost, reminiscent of a phase transition. These results are in good agreement with the recent experiments utilizing a dense, dipolar spin ensemble in diamond [Nature (London) 543, 221 (2017)NATUAS0028-083610.1038/nature21426]. They demonstrate the existence of a novel, critical DTC regime that is stabilized not by many-body localization but rather by slow, critical dynamics. Our analysis shows that the DTC response can be used as a sensitive probe of nonequilibrium quantum matter.
A strongly interacting driven spin system can display a variety of interesting many- body quantum phenomena due to the interplay of interaction, disorder and coherent driving. Using a dense electronic spin ensemble of atom-like impurities in diamond, we study non-equilibrium quantum many-body dynamics involving ∼10^6 spins. Specifically, we describe: (1) investigation of thermalization dynamics of a closed quantum system in the presence of long-range interactions and on-site disorder, (2) realization of new non-equilibrium phases of matter, such as discrete time crystals, and (3) probing emergent phase transitions in a driven many-body system. In addition, the high-density spin ensembles in the solid state also show great promise for practical sensing applications. As a practical application of these studies, we demonstrate high sensitivity magnetic-field sensing with fault-tolerant pulsed control. These studies demonstrate that dense electronic spin ensembles in the solid state can be a powerful tool to simulate quantum many-body dynamics, explore new coherent non-equilibrium phenomena and to detect external signals with superior sensitivity and high spectral and spatial resolution.
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One of the central challenges of modern statistical physics is understanding the thermalization dynamics of quantum many-body systems at the microscopic level. In this thesis, we describe an experimental study of individual spin dynamics in a two-dimensional ensemble of electron spins on the surface of a diamond crystal. A near-surface NV center is used as a nanoscale magnetic sensor to probe individual spin correlation dynamics in a dipolar interacting spin ensemble. For each spin, the rate of relaxation of spin projection along the bias magnetic field is consistently much slower than the dipolar interaction strengths with its nearest neighbors and is strongly correlated with the timescale of the local magnetic field fluctuation. We present a quantitative model based on dynamic resonance counting arguments that explains these observations. Furthermore, we use resonant spin-lock driving to control the effective strength of the local magnetic fields and demonstrate the role of dynamical disorder in different regimes. In the regime of suppressed extrinsic disorder, we use dynamic mean field methods to explain our experimental observations. The work presented in this thesis paves the way towards a microscopic study of quantum thermalization in two-dimensional strongly interacting disordered spin ensembles.
Understanding the thermalization dynamics of quantum many-body systems at the microscopic level is among the central challenges of modern statistical physics. Here we experimentally investigate individual spin dynamics in a two-dimensional ensemble of electron spins on the surface of a diamond crystal. We use a near-surface nitrogen-vacancy center as a nanoscale magnetic sensor to probe correlation dynamics of individual spins in a dipolar interacting surface spin ensemble. We observe that the relaxation rate for each spin is significantly slower than the naïve expectation based on independently estimated dipolar interaction strengths with nearest neighbors and is strongly correlated with the timescale of the local magnetic field fluctuation. We show that this anomalously slow relaxation rate is due to the presence of strong dynamical disorder and present a quantitative explanation based on dynamic resonance counting. Finally, we use resonant spin-lock driving to control the effective strength of the local magnetic fields and reveal the role of the dynamical disorder in different regimes. Our work paves the way towards microscopic study and control of quantum thermalization in strongly interacting disordered spin ensembles.
Time crystals in periodically driven systems have initially been studied assuming either the ability to quench the Hamiltonian between different many-body regimes, the presence of disorder or long-range interactions. Here we propose the simplest scheme to observe discrete time crystal dynamics in a one-dimensional driven quantum system of the Ising type with short-range interactions and no disorder. The system is subject only to a periodic kick by a global magnetic field, and no extra Hamiltonian quenching is performed. We analyze the emerging time crystal stabilizing mechanisms via extensive numerics as well as using an analytic approach based on an off-resonant transition model. Due to the simplicity of the driven Ising model, our proposal can be implemented with current experimental platforms including trapped ions, Rydberg atoms, and superconducting circuits.