Critical Thermalization of a Disordered Dipolar Spin System in Diamond.

Statistical mechanics underlies our understanding of macroscopic quantum systems. It is based on the assumption that out-of-equilibrium systems rapidly approach their equilibrium states, forgetting any information about their microscopic initial conditions. This fundamental paradigm is challenged by disordered systems, in which a slowdown or even absence of thermalization is expected. We report the observation of critical thermalization in a three dimensional ensemble of ∼10^{6} electronic spins coupled via dipolar interactions. By controlling the spin states of nitrogen vacancy color centers in diamond, we observe slow, subexponential relaxation dynamics and identify a regime of power-law decay with disorder-dependent exponents; this behavior is modified at late times owing to many-body interactions. These observations are quantitatively explained by a resonance counting theory that incorporates the effects of both disorder and interactions.

[1]  O. Yevtushenko,et al.  Lévy flights and multifractality in quantum critical diffusion and in classical random walks on fractals. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  R. Nandkishore,et al.  Many-Body Localization and Thermalization in Quantum Statistical Mechanics , 2014, 1404.0686.

[3]  B. Meier,et al.  Radio-frequency-driven nuclear spin diffusion in solids☆ , 1989 .

[4]  E. Oort,et al.  Electric-field-induced modulation of spin echoes of N-V centers in diamond , 1990 .

[5]  M. Lukin,et al.  Free-standing mechanical and photonic nanostructures in single-crystal diamond. , 2012, Nano letters.

[6]  Entanglement prethermalization: Locally thermal but non-locally non-thermal states in a one-dimensional Bose gas , 2014, 1410.5576.

[7]  Antonio-José Almeida,et al.  NAT , 2019, Springer Reference Medizin.

[8]  Hengyun Zhou,et al.  Observation of discrete time-crystalline order in a disordered dipolar many-body system , 2016, Nature.

[9]  Soonwon Choi,et al.  Dynamical Engineering of Interactions in Qudit Ensembles. , 2017, Physical review letters.

[10]  M. Segev,et al.  Transport and Anderson localization in disordered two-dimensional photonic lattices , 2007, Nature.

[11]  P Cappellaro,et al.  Dressed-state resonant coupling between bright and dark spins in diamond. , 2013, Physical review letters.

[12]  Aaron C. E. Lee,et al.  Many-body localization in a quantum simulator with programmable random disorder , 2015, Nature Physics.

[13]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[14]  D. Longmore.  The principles of magnetic resonance. , 1989, British medical bulletin.

[15]  A. Aspect,et al.  Direct observation of Anderson localization of matter waves in a controlled disorder , 2008, Nature.

[16]  A. J. Vega.  Relaxation in spin-echo and spin-lock experiments , 1985 .

[17]  Chem. , 2020, Catalysis from A to Z.

[18]  N. Yao,et al.  Many-body localization in dipolar systems. , 2013, Physical review letters.

[19]  E. Hahn,et al.  Nuclear Double Resonance in the Rotating Frame , 1962 .

[20]  Gebräuchliche Fertigarzneimittel,et al.  V , 1893, Therapielexikon Neurologie.

[21]  M. Markham,et al.  Ultralong spin coherence time in isotopically engineered diamond. , 2009, Nature materials.

[22]  Igor E. Mazets,et al.  Experimental observation of a generalized Gibbs ensemble , 2014, Science.

[23]  Mikhail D Lukin,et al.  Depolarization Dynamics in a Strongly Interacting Solid-State Spin Ensemble. , 2016, Physical review letters.

[24]  Massimo Inguscio,et al.  Anderson localization of a non-interacting Bose–Einstein condensate , 2008, Nature.

[25]  Shanming Zhang,et al.  Selective polarization inversion and depolarization of 13C in cross relaxation in NMR , 1989 .

[26]  P. Anderson.  Absence of Diffusion in Certain Random Lattices , 1958 .

[27]  B. Meier,et al.  Polarization echoes in NMR. , 1992, Physical review letters.

[28]  M. Schreiber,et al.  Observation of many-body localization of interacting fermions in a quasirandom optical lattice , 2015, Science.

[29]  Transition from localized to extended eigenstates in the ensemble of power-law random banded matrices. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[30]  Levitov.  Delocalization of vibrational modes caused by electric dipole interaction. , 1990, Physical review letters.

[31]  P. W. Hess,et al.  Observation of a discrete time crystal , 2016, Nature.

[32]  S. Hell,et al.  Far-field optical imaging and manipulation of individual spins with nanoscale resolution. , 2010 .

[33]  Peter Zoller,et al.  Measuring multipartite entanglement through dynamic susceptibilities , 2015, Nature Physics.