Controlling Local Thermalization Dynamics in a Floquet-Engineered Dipolar Ensemble

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.

Figure 1

Experimental system and Hamiltonian engineering. (a) Black diamond experimental system, consisting of a high density ensemble of NV spins in diamond. Spin initialization and readout are achieved via optical illumination and fluorescence, while spin manipulation is performed via microwave pulses. (b),(c) Representative pulse sequence block and illustration of Hamiltonian engineering concept. By tuning pulse separations in an interaction decoupling sequence, the effective Hamiltonian can be engineered into different forms, such as (b) Heisenberg or (c) $XY$ Hamiltonians. (d) Illustration of accessible $XYZ$ Hamiltonians via Hamiltonian engineering. The accessible Hamiltonians are averages of those obtained via transforming the native Hamiltonian by a $\pi /2$ pulse (squares). Special Hamiltonians of interest are labeled: Ising, purple triangle; Heisenberg, black star; $XY$ Hamiltonian, green diamond.

Figure 2

Measuring global and local spin autocorrelators. (a) Measured coherence decay under an engineered Heisenberg Hamiltonian for global (blue circles) and local (red squares) spin autocorrelators. Fit is a stretched exponential. For reference, we also show the $XY$-8 decay (gray points), which characterizes the decay under the native interaction Hamiltonian. (b) Decay times for normalized global and local spin autocorrelators. Vertical dashed lines denote special Hamiltonians of interest. (c) Disorder-order sequence to measure the decay of local spin autocorrelators for an infinite temperature initial state, which reveals local thermalization. The sequence consists of a $\pi /2$ initialization pulse, a free-evolution duration to encode the local disorder strength into the spin state, a varying number of repetitions of the Hamiltonian engineering sequence, followed by a $\pi$ pulse and free evolution to rephase the spins, and $-\pi /2$ pulse for spin-state readout. The sequence is designed to suppress higher-order corrections (see Supplemental Material [21] for details). (d) Measured normalized spin polarization as a function of disorder unwinding time, showing a revival when the winding and unwinding times are equal. In this example, the Hamiltonian engineering consists of two Floquet cycles of Heisenberg Hamiltonian engineering.

Figure 3

Decay timescale and decay shape for local correlators. (a) Local $X$ (red), $Y$ (yellow), and $Z$ (blue) spin autocorrelator decay timescales, normalized by extrinsic decay and rescaled by Hamiltonian norm. The blue arrow indicates divergent timescales of $Z$ correlators closer to the Ising Hamiltonian [21]. (b) Local spin autocorrelator decay shapes, averaged over $X$, $Y$, as characterized by the stretching exponent. Horizontal dotted line at $d/\alpha =1$ is the naive expectation based on existing arguments in the NMR literature, predicting an exponential decay. A second dashed line at $0.5=d/2\alpha$ is also plotted as the expectation for dynamics that generate Markovian fluctuating fields. Solid line is the prediction from a dynamical mean-field model.

Figure 4

Physical mechanism driving coherence decay. (a) Quantum fluctuations of neighboring spins produce a dynamical mean field that induces decay, and as time progresses, weakly coupled spins at larger distances start to contribute as well. (b) For different Hamiltonians, the correlation time of the dynamical mean field changes, resulting in different rates of phase accumulation over time (ballistic for a static field, diffusive for a Markovian fast-varying field) and leading to different decay shapes at early-to-intermediate times. (c) Illustration of a single spin experiencing the fluctuating magnetic field from its neighbors. (d) Illustration of the additional effect of hybridization between strongly coupled pairs of spins. (e) Ratio between $X$ and $Z$ decay times of local correlators for experimental data and various models. Including local hybridization (blue) improves the agreement with experimental data (red), and exact diagonalization of full quantum dynamics (yellow, 18 spins) agrees best.