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 ^{13}C 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 multiphoton 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.
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 ^{13}C 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 multiphoton 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.
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.
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.
We study the non-equilibrium dynamics of a disordered periodically driven quantum spin chain, with the competition between the interaction, disorder, and Floquet driving being of particular interest. We study dynamics of entanglement entropy, energy absorption to characterize dynamical regimes of the system whether it stays in the Floquet-MBL(many-body localization) region or thermalized region. Starting with a product state in the computational basis, followed by reduced density matrix which in turn gives rise to the entanglement entropy density. With the strength of the interaction, the transverse field, the parallel field, the disorder strength W and the driving frequency, we discover the distinct behaviors of fast delocalization and logarithmic entanglement growth and long-lasting memory of the initial state, indicative of localized or prethermal Floquet regimes. We observe that strong disorder arrests transport and enables slow entanglement dynamics, whereas strong driving frequency arrests energy absorption and creates a long-lived non-equilibrium state. Conversely, weak disorder or low driving frequency leads to delocalization. The outcomes show strong support for non-equilibrium phases in driven many-body systems.
Periodic driving underlies many forms of quantum control, including spin-based quantum sensing. However, in an ensemble sensor, one waveform must act on spins with different detunings, drive amplitudes, hyperfine environments, and local fields. Existing robust-control approaches to such disorder are usually framed in terms of coherence, effective Hamiltonians, filter functions, or refocusing. Here we identify a complementary geometric requirement for collective ensemble Floquet control: disorder realizations must share a common Floquet eigenframe. When this condition is met, initialization, protection, signal coupling, and readout are defined in one dressed basis, so the ensemble responds as a collective Floquet sensor rather than as an average over inequivalent driven members. We make this condition measurable with an eigenvector-based synchronization order parameter and a complementary fragmentation metric that quantify the alignment and spread of Floquet quantization axes across the ensemble. As one realization of this framework, we use a continuous counterdiabatic Floquet drive to derive synchronization criteria and predict resonance-governed breakdown at the first two low-order commensurabilities between the engineered Floquet gap and the drive modulation, with detuning and amplitude disorder producing distinct breakdown channels. Experiments on a nitrogen-vacancy (NV) ensemble in diamond verify the synchronized regime through long-lived collective oscillations, a two-dimensional disorder-robustness map, and breakdown resonances that shift with the modulation rate. Finally, we demonstrate a harmonic-free continuous-drive AC magnetometry protocol whose collective single-tone response is enabled by the synchronized Floquet eigenframe. These results establish Floquet eigenframe synchronization as a measurable condition for disorder-resilient collective control and quantum sensing.
This work presents a theoretical investigation of dynamic stabilization in interacting quantum many-body systems via high-frequency periodic driving. Using Floquet theory and the Magnus expansion, we derive the effective time-independent Hamiltonian governing the slow dynamics of a driven spin chain. We show that the external field induces a parametric renormalization of the transverse tunneling terms through a zeroth-order Bessel function dependence, leading to a critical drive amplitude at which transport is strongly suppressed. This suppression of the lowest-order hopping term gives rise to a long-lived prethermal regime in which many-body thermalization is significantly delayed. The resulting dynamics exhibit a sharp reduction in the short-to-intermediate time entanglement entropy growth rate. The framework is consistent with known results in Floquet engineering and coherent destruction of tunneling, and provides a unified interpretation of transport suppression and delayed scrambling in periodically driven systems. A falsifiable experimental protocol using ultracold atoms in optical lattices is proposed to validate the predicted threshold behavior and prethermal stabilization mechanism.
Non-equilibrium dynamics of strongly and rapidly driven quantum many-body systems is poorly understood beyond periodic driving, where heating is exponentially slow in the drive frequency (Floquet Prethermalization). In contrast, non-periodic drives were found to exhibit widely different heating scalings with no unifying principle. This work identifies a resonance-suppression principle governing slow heating up to a prethermal lifetime τ∗: When the drive's spectral arithmetic structure restricts multiphoton resonances, τ∗ is controlled by low-frequency spectral suppression. The principle distinguishes (i) Single-photon suppression, quantified by a low-frequency suppression law f(Ω) for the drive's Fourier Transform weight near Ω=0, from (ii) Multi-photon suppression, where nested commutators remain controlled if exceptional arithmetic structure satisfies a subadditive property. Remarkably, if multi-photon suppression holds, τ∗ scaling with drive speed λ is governed by f(Ω). This law of τ∗ is found through a small-divisor mechanism in this work's iterative rotating frame scheme. Multi-photon suppression breakdown separates λ-scaling of τ∗ in linear response and non-perturbative theory, shown by a case study of Quasi-Floquet driving. The principle is applied to (i) Resolve inconsistencies in literature on non-periodic driving, and (ii) Provide design principles for engineering prethermal phases of matter in programmable quantum simulators, exemplified by new non-periodic `Factorial' drives with tunable τ∗.