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arXiv:2307.14188 · Physical Review Research

Understanding the dynamics of randomly positioned dipolar spin ensembles

Timo Gräßer, Kristine Rezai, Alexander O. Sushkov, Götz Silvester Uhrig

Published Dec 1, 2023• 7 citations
arXivHTMLPDF

Abstract

Dipolar spin ensembles with random spin positions are attracting much attention because they help us to understand decoherence as it occurs in solid-state quantum bits in contact with spin baths. Also, these ensembles are systems which may show many-body localization, at least in the sense of very slow spin dynamics. We present measurements of the autocorrelations of spins on diamond surfaces at infinite temperature in a doubly rotating frame which eliminates local disorder. Strikingly, the timescales in the longitudinal and the transversal channel differ by more than one order of magnitude, which is a factor much greater than one would have expected from simulations of spins on lattices. A previously developed dynamic mean-field theory for spins (spinDMFT) fails to explain this phenomenon. Thus, we improve it by extending it to clusters (CspinDMFT). This theory does capture the striking mismatch up to two orders of magnitude for random ensembles. Without positional disorder, however, the mismatch is only moderate with a factor below 4. The pivotal role of positional disorder suggests that the strong mismatch is linked to precursors of many-body localization.

DOI
10.1103/physrevresearch.5.043191

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Dipolar spin ensembles with random spin positions are attracting much attention because they help us to understand decoherence as it occurs in solid-state quantum bits in contact with spin baths. Also, these ensembles are systems which may show many-body localization, at least in the sense of very slow spin dynamics. We present measurements of the autocorrelations of spins on diamond surfaces at infinite temperature in a doubly rotating frame which eliminates local disorder. Strikingly, the timescales in the longitudinal and the transversal channel differ by more than one order of magnitude, which is a factor much greater than one would have expected from simulations of spins on lattices. A previously developed dynamic mean-field theory for spins (spinDMFT) fails to explain this phenomenon. Thus, we improve it by extending it to clusters (CspinDMFT). This theory does capture the striking mismatch up to two orders of magnitude for random ensembles. Without positional disorder, however, the mismatch is only moderate with a factor below 4. The pivotal role of positional disorder suggests that the strong mismatch is linked to precursors of many-body localization.
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.
Spin squeezed entanglement enables metrological precision beyond the classical limit. Understood through the lens of continuous symmetry breaking, dipolar spin systems exhibit the remarkable ability to generate spin squeezing via their intrinsic quench dynamics. To date, this understanding has primarily focused on lattice spin systems; in practice however, dipolar spin systems$\unicode{x2014}$ranging from ultracold molecules to nuclear spin ensembles and solid-state color centers$\unicode{x2014}$often exhibit significant amounts of positional disorder. Here, we develop a theory for scalable spin squeezing in a two-dimensional randomly diluted lattice of quantum dipoles, which naturally realize a dipolar XXZ model. Via extensive quantum Monte Carlo simulations, we map out the phase diagram for finite-temperature XY order, and by extension scalable spin squeezing, as a function of both disorder and Ising anisotropy. As the disorder increases, we find that scalable spin squeezing survives only near the Heisenberg point. We show that this behavior is due to the presence of rare tightly-coupled dimers, which effectively heat the system post-quench. In the case of strongly-interacting nitrogen-vacancy centers in diamond, we demonstrate that an experimentally feasible strategy to decouple the problematic dimers from the dynamics is sufficient to enable scalable spin squeezing.
A dynamic mean-field theory for spin ensembles (spinDMFT) at infinite temperatures on arbitrary lattices is established. The approach is introduced for an isotropic Heisenberg model with S=12S=\frac{1}{2}S=21​ and external field. For large coordination numbers, it is shown that the effect of the environment of each spin is captured by a classical time-dependent random mean field which is normally distributed. Expectation values are calculated by averaging over these mean fields, i.e., by a path integral over the normal distributions. A self-consistency condition is derived by linking the moments defining the normal distributions to spin autocorrelations. In this framework, we explicitly show how the rotating-wave approximation becomes a valid description for increasing magnetic field. We also demonstrate that the approach can easily be extended. Exemplarily, we employ it to reach a quantitative understanding of a dense ensemble of spins with dipolar interaction which are distributed randomly on a plane including static Gaussian noise as well.
The dynamics of disordered nuclear spin ensembles are the subject of nuclear magnetic resonance studies. Due to the through-space long-range dipolar interaction generically many spins are involved in the time evolution, so that exact brute force calculations are impossible. The recently established spin dynamic mean-field theory (spinDMFT) represents an efficient and unbiased alternative to overcome this challenge. The approach only requires the dipolar couplings as input and the only prerequisite for its applicability is that each spin interacts with a large number of other spins. In this article, we show that spinDMFT can be used to describe spectral spin diffusion in static samples and to simulate zero-quantum line shapes which eluded an efficient quantitative simulation so far to the best of our knowledge. We perform benchmarks for two test substances that establish an excellent match with published experimental data. As spinDMFT combines low computational effort with high accuracy, we strongly suggest to use it for large-scale simulations of spin diffusion, which are important in various areas of magnetic resonance.
Dimensionality plays a central role in determining the collective behavior of interacting quantum systems. Engineering strongly interacting ensembles of solid-state spin defects in reduced dimensions remains a significant challenge at the interface between the applied and fundamental sciences. Here, we create and characterize a positionally disordered, quasi-one-dimensional spin chain in diamond, consisting of optically dark substitutional nitrogen defects (P1 centers) and optically addressable probe nitrogen-vacancy (NV) centers. Our approach exploits the preferential incorporation of nitrogen along step bunches formed during chemical vapor deposition to achieve both lateral and vertical confinement. Combining spatially resolved materials characterization with nanoscale quantum sensing, we establish the one-dimensional character of the optically dark, unpolarized P1 spin ensemble. We then use correlation spectroscopy to probe local spin autocorrelations and investigate infinite-temperature dipolar spin transport. Our results establish a materials-based route for engineering low-dimensional quantum spin systems.