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arXiv:2207.10688 · Physical Review Letters

Probing Dynamics of a Two-Dimensional Dipolar Spin Ensemble Using Single Qubit Sensor

Kristine Rezai, Soonwon Choi, Mikhail D. Lukin, Alexander O. Sushkov

Published Feb 5, 2025• 8 citations
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Abstract

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.

DOI
10.1103/physrevlett.134.050801

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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.
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.
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.
We study the depolarization dynamics of a dense ensemble of dipolar interacting spins, associated with nitrogen-vacancy centers in diamond. We observe anomalously fast, density-dependent, and nonexponential spin relaxation. To explain these observations, we propose a microscopic model where an interplay of long-range interactions, disorder, and dissipation leads to predictions that are in quantitative agreement with both current and prior experimental results. Our results pave the way for controlled many-body experiments with long-lived and strongly interacting ensembles of solid-state spins.
The most direct approach for characterizing the quantum dynamics of a strongly-interacting system is to measure the time-evolution of its full many-body state. Despite the conceptual simplicity of this approach, it quickly becomes intractable as the system size grows. An alternate framework is to think of the many-body dynamics as generating noise, which can be measured by the decoherence of a probe qubit. Our work centers on the following question: What can the decoherence dynamics of such a probe tell us about the many-body system? In particular, we utilize optically addressable probe spins to experimentally characterize both static and dynamical properties of strongly-interacting magnetic dipoles. Our experimental platform consists of two types of spin defects in diamond: nitrogen-vacancy (NV) color centers (probe spins) and substitutional nitrogen impurities (many-body system). We demonstrate that signatures of the many-body system's dimensionality, dynamics, and disorder are naturally encoded in the functional form of the NV's decoherence profile. Leveraging these insights, we directly characterize the two-dimensional nature of a nitrogen delta-doped diamond sample. In addition, we explore two distinct facets of the many-body dynamics: First, we address a persistent debate about the microscopic nature of spin dynamics in strongly-interacting dipolar systems. Second, we demonstrate direct control over the spectral properties of the many-body system, including its correlation time. Our work opens the door to new directions in both quantum sensing and simulation.
Understanding the microscopic mechanisms of thermalization in closed quantum systems is among the key challenges in modern quantum many-body physics. We demonstrate a method to probe local thermalization in a large-scale many-body system by exploiting its inherent disorder and use this to uncover the thermalization mechanisms in a three-dimensional, dipolar-interacting spin system with tunable interactions. Utilizing advanced Hamiltonian engineering techniques to explore a range of spin Hamiltonians, we observe a striking change in the characteristic shape and timescale of local correlation decay as we vary the engineered exchange anisotropy. We show that these observations originate from the system's intrinsic many-body dynamics and reveal the signatures of conservation laws within localized clusters of spins, which do not readily manifest using global probes. Our method provides an exquisite lens into the tunable nature of local thermalization dynamics and enables detailed studies of scrambling, thermalization, and hydrodynamics in strongly interacting quantum systems.
Understanding the dynamics of a quantum bit's environment is essential for the realization of practical systems for quantum information processing and metrology. We use single nitrogen-vacancy (NV) centers in diamond to study the dynamics of a disordered spin ensemble at the diamond surface. Specifically, we tune the density of "dark" surface spins to interrogate their contribution to the decoherence of shallow NV center spin qubits. When the average surface spin spacing exceeds the NV center depth, we find that the surface spin contribution to the NV center free induction decay can be described by a stretched exponential with variable power n. We show that these observations are consistent with a model in which the spatial positions of the surface spins are fixed for each measurement, but some of them reconfigure between measurements. In particular, we observe a depth-dependent critical time associated with a dynamical transition from Gaussian (n=2) decay to n=2/3, and show that this transition arises from the competition between the small decay contributions of many distant spins and strong coupling to a few proximal spins at the surface. These observations demonstrate the potential of a local sensor for understanding complex systems and elucidate pathways for improving and controlling spin qubits at the surface.