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arXiv:2410.09028

Anomalously extended Floquet prethermal lifetimes and applications to long-time quantum sensing

Kieren A. Harkins, Cooper Selco, Christian Bengs, Marchiori, David, Leo Joon Il Moon, Zhang, Zhuo-Rui, Yang, Aristotle, Angad Singh, Emanuel Druga, Yi‐Qiao Song, Ashok Ajoy

Published Oct 11, 2024• 2 citations
arXivHTMLPDF

Abstract

Floquet prethermalization is observed in periodically driven quantum many-body systems where the system avoids heating and maintains a stable, non-equilibrium state, for extended periods. Here we introduce a novel quantum control method using off-resonance and short-angle excitation to significantly extend Floquet prethermal lifetimes. This is demonstrated on randomly positioned, dipolar-coupled, 13C nuclear spins in diamond, but the methodology is broadly applicable. We achieve a lifetime $T_2'~800 s at 100 K while tracking the transition to the prethermal state quasi-continuously. This corresponds to a >533,000-fold extension over the bare spin lifetime without prethermalization, and constitutes a new record both in terms of absolute lifetime as well as the total number of Floquet pulses applied (here exceeding 7 million). Using Laplace inversion, we develop a new form of noise spectroscopy that provides insights into the origin of the lifetime extension. Finally, we demonstrate applications of these extended lifetimes in long-time, reinitialization-free quantum sensing of time-varying magnetic fields continuously for ~10 minutes at room temperature. Our work facilitates new opportunities for stabilizing driven quantum systems through Floquet control, and opens novel applications for continuously interrogated, long-time responsive quantum sensors.

DOI
10.48550/arxiv.2410.09028

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Floquet prethermalization is observed in periodically driven quantum many-body systems where the system avoids heating and maintains a stable, non-equilibrium state, for extended periods. Here we introduce a novel quantum control method using off-resonance and short-angle excitation to significantly extend Floquet prethermal lifetimes. This is demonstrated on randomly positioned, dipolar-coupled, 13C nuclear spins in diamond, but the methodology is broadly applicable. We achieve a lifetime $T_2'~800 s at 100 K while tracking the transition to the prethermal state quasi-continuously. This corresponds to a >533,000-fold extension over the bare spin lifetime without prethermalization, and constitutes a new record both in terms of absolute lifetime as well as the total number of Floquet pulses applied (here exceeding 7 million). Using Laplace inversion, we develop a new form of noise spectroscopy that provides insights into the origin of the lifetime extension. Finally, we demonstrate applications of these extended lifetimes in long-time, reinitialization-free quantum sensing of time-varying magnetic fields continuously for ~10 minutes at room temperature. Our work facilitates new opportunities for stabilizing driven quantum systems through Floquet control, and opens novel applications for continuously interrogated, long-time responsive quantum sensors.
Periodically driven (Floquet) systems are said to prethermalize when their energy absorption is very slow for a long time. This effect was first discovered in quantum spin models, where the heating rate is exponentially small in the ratio between the driving frequency and the spin bandwidth. Recently, it was shown that prethermalization occurs also in classical systems with an infinite bandwidth. Here, we address the open question of which small parameter controls the lifetime of the prethermal state in these systems. We show that the lifetime is controlled by the temperature of the prethermal state, which is quasiconserved when the heating is slow. We substantiate this finding in systems of periodically driven coupled rotors, by studying the dependence of the prethermal lifetime on both the initial conditions and the connectivity. This result allows us to develop a simple analytical model that describes the crossover from prethermalization to chaos in many-body classical systems.
Floquet prethermalization can endow interacting quantum solids with long-lived, approximately conserved quantities, enabling Hamiltonian engineering and new dynamical probes. Using a hyperpolarized network of dipolar-coupled 13^{13}13C nuclear spins in diamond driven by pulsed spin-locking, we access a rotating-frame prethermal plateau with quasi-conserved transverse magnetization and cycle-resolved inductive readout. Within this prethermal manifold we observe a robust \emph{rotating-frame solid echo}: after an apparent decay of the rotating-frame free-induction signal over a delay τττ, the magnetization revives at time 2τ2τ2τ following a single (α)y(α)_y(α)y​ pulse, with maximum amplitude near α≃π/2α\simeqπ/2α≃π/2. The echo envelope decays as a stretched exponential with characteristic time T2′≈13 T_2'\approx 13\,T2′​≈13ms. Analytical arguments and toy-model simulations attribute the revival to Floquet micromotion that transfers coherences between operator subspaces, so that only a subset of the many-body dephasing dynamics is inverted by the yyy pulse. These results translate classic echo physics into the prethermal rotating frame and point to continuously interrogated prethermal spin ensembles as a versatile platform for high-throughput spectroscopy, Hamiltonian engineering, and long-duration quantum sensing.
Floquet (periodic) driving has recently emerged as a powerful technique for engineering quantum systems and realizing nonequilibrium phases of matter. A central challenge to stabilizing quantum phenomena in such systems is the need to prevent energy absorption from the driving field. Fortunately, when the frequency of the drive is significantly larger than the local energy scales of the many-body system, energy absorption is suppressed. The existence of this so-called prethermal regime depends sensitively on the range of interactions and the presence of multiple driving frequencies. Here, we report the observation of Floquet prethermalization in a strongly interacting dipolar spin ensemble in diamond, where the angular dependence of the dipolar coupling helps to mitigate the long-ranged nature of the interaction. Moreover, we extend our experimental observation to quasi-Floquet drives with multiple incommensurate frequencies. In contrast to a single-frequency drive, we find that the existence of prethermalization is extremely sensitive to the smoothness of the applied field. Our results open the door to stabilizing and characterizing nonequilibrium phenomena in quasiperiodically driven systems.
Prethermalization, by introducing emergent quasiconserved observables, plays a crucial role in protecting periodically driven (Floquet) many-body phases over an exponentially long time, while the ultimate fate of such quasiconserved operators can signal thermalization to infinite temperature. To elucidate the properties of prethermal quasiconservation in many-body Floquet systems, here we systematically analyze infinite-temperature correlations between observables. We numerically show that the late-time behavior of the autocorrelations unambiguously distinguishes quasiconserved observables from nonconserved ones, allowing one to single out a set of linearly independent quasiconserved observables. By investigating two Floquet spin models, we identify two different mechanisms underlying the quasiconservation law. First, we numerically verify energy quasiconservation when the driving frequency is large, so that the system dynamics is approximately described by a static prethermal Hamiltonian. More interestingly, under moderate driving frequency, another quasiconserved observable can still persist if the Floquet driving contains a large global rotation. We show theoretically how to calculate this conserved observable and provide numerical verification. Having systematically identified all quasiconserved observables, we can finally investigate their behavior in the infinite-time limit and thermodynamic limit, using autocorrelations obtained from both numerical simulation and experiments in solid-state nuclear magnetic resonance systems.
We study the emergence of the prethermal Floquet time crystal (pFTC) in disordered chiral multiferroic chains. The model is an extension of the usual periodically driven nearest-neighbor disordered Heisenberg chain, with additional next-nearest-neighbor Heisenberg couplings and Dzyaloshinskii-Moriya interactions due to external magnetic and electric couplings. We derive the phase diagram of the model, characterizing the magnetization, entanglement, and coherence dynamics of the system along the extended interactions. In addition, we explore the application of the pFTC as quantum sensors of AC fields. The sensor performance to estimate small AC fields is quantified through the quantum Fisher information (QFI) measure. The sensor offers several advantages as compared to those composed of noninteracting spins due to its intrinsic robustness, long coherent interrogation time, and many-body correlations. Specifically, the sensor can overcome the standard quantum limit ($\mathrm{SQL}\ensuremath{\sim}{\mathrm{Nt}}^{2}$) during the prethermal regime, reaching an optimum performance at the pFTC lifetime t∗{t}^{*}t∗, where the $\mathrm{QFI}/{\mathrm{Nt}}^{{*}^{2}}\ensuremath{\sim}{\mathrm{N}}^{\ensuremath{\alpha}}$ with $\ensuremath{\alpha}>0$, scaling superlinarly with the number of spins. Different from full FTCs, the prethermal lifetime does not diverge in the thermodynamic limit, nevertheless it can be increasingly long with tuning system parameters.
Periodic (Floquet) driving enables Hamiltonian engineering and nonequilibrium phases, but interacting systems eventually heat by absorbing energy from the drive. Disorder can greatly delay this process, yielding long-lived prethermal plateaus. Here we show that this protection can fail when pulse-train control introduces a second driving frequency and when the disorder fluctuates. Using a natural-abundance 13C nuclear-spin network in diamond, we observe sharp peaks in the late-time heating rate at the double- and triple-spin-flip resonance conditions predicted by bimodal Floquet interference, and track their evolution with drive frequency. A switching-noise model attributes the resonant absorption to stochastic electron-spin dynamics that intermittently tune rare nuclear clusters into multi-photon resonance. Our results reveal a resonance-activated limit for disorder-stabilized Floquet phases and suggest new routes to DC-field quantum sensing based on an abrupt breakdown of prethermalization.