Abstract Prethermal discrete time crystals are non-equilibrium states of matter with long-range spatiotemporal order and a subharmonic response stabilized by many-body interactions under periodic driving. The robustness of time-crystalline order to perturbations in the drive protocol makes these systems attractive for quantum sensing. Here we exploit the sensitivity of prethermal discrete time crystal order to deviations in its order parameter to implement the frequency-selective detection of time-varying magnetic fields in a system of strongly driven, dipolar-coupled 13 C nuclear spins in a diamond. Incorporating an oscillating field into the time crystal dynamics extends its lifetime exponentially, producing a sharp resonant response in the order parameter. The sensor linewidth is set by the time crystal lifetime alone, as strong interspin interactions help stabilize the time-crystalline order. The device operates in the 0.5–50-kHz range—a challenging frequency regime for sensors based on atomic vapour or electronic spins—and achieves competitive sensitivity. The sensing principle we demonstrate is robust to drive errors and sample inhomogeneities, and is applicable across a range of physical platforms including superconducting circuits, neutral atoms and trapped ions.
Abstract Prethermal discrete time crystals are non-equilibrium states of matter with long-range spatiotemporal order and a subharmonic response stabilized by many-body interactions under periodic driving. The robustness of time-crystalline order to perturbations in the drive protocol makes these systems attractive for quantum sensing. Here we exploit the sensitivity of prethermal discrete time crystal order to deviations in its order parameter to implement the frequency-selective detection of time-varying magnetic fields in a system of strongly driven, dipolar-coupled 13 C nuclear spins in a diamond. Incorporating an oscillating field into the time crystal dynamics extends its lifetime exponentially, producing a sharp resonant response in the order parameter. The sensor linewidth is set by the time crystal lifetime alone, as strong interspin interactions help stabilize the time-crystalline order. The device operates in the 0.5–50-kHz range—a challenging frequency regime for sensors based on atomic vapour or electronic spins—and achieves competitive sensitivity. The sensing principle we demonstrate is robust to drive errors and sample inhomogeneities, and is applicable across a range of physical platforms including superconducting circuits, neutral atoms and trapped ions.
We analyze the quantum dynamics of periodically driven, disordered systems in the presence of long-range interactions. Focusing on the stability of discrete time crystalline (DTC) order in such systems, we use a perturbative procedure to evaluate its lifetime. For 3D systems with dipolar interactions, we show that the corresponding decay is parametrically slow, implying that robust, long-lived DTC order can be obtained. We further predict a sharp crossover from the stable DTC regime into a regime where DTC order is lost, reminiscent of a phase transition. These results are in good agreement with the recent experiments utilizing a dense, dipolar spin ensemble in diamond [Nature (London) 543, 221 (2017)NATUAS0028-083610.1038/nature21426]. They demonstrate the existence of a novel, critical DTC regime that is stabilized not by many-body localization but rather by slow, critical dynamics. Our analysis shows that the DTC response can be used as a sensitive probe of nonequilibrium quantum matter.
Discrete time crystals are non-equilibrium phases of matter in periodically driven systems, characterized by robust subharmonic oscillations and broken discrete time-translation symmetry. Their long-lived coherent dynamics and resilience to imperfections make them promising resources for quantum sensing. A disorder-free discrete-time crystal probe can provide the quantum-enhanced estimation of the coupling parameter. Here, we extend this sensing mechanism to nonlinear interactions and show that this nonlinear profile strongly enhances the sensing precision by increasing the system-size scaling exponent of the quantum Fisher information. Our analytical discussion separates a rigorous seminorm upper bound from the physically relevant scaling realized by product-state probes in the time crystal regime. Numerically, we find that the quantum Fisher information retains its quadratic long-time growth with the number of Floquet cycles, while its system-size exponent increases approximately linearly with the nonlinearity exponent, identifying nonlinearity as a resource for quantum-enhanced sensitivity. We further show that stronger nonlinearities shrink the time crystal stability window, making the probe more sensitive to small deviations from the resonant condition. We also analyze the effect of imperfect pulses and show that such imperfections can enhance, rather than suppress, the information encoded in the evolved state. Finally, we discuss a digital implementation of the nonlinear DTC sensing protocol using superconducting qubits.
The control of many-body quantum dynamics in complex systems is a key challenge in the quest to reliably produce and manipulate large-scale quantum entangled states. Recently, quench experiments in Rydberg atom arrays [Bluvstein et al. Science 371, 1355 (2021)SCIEAS0036-807510.1126/science.abg2530] demonstrated that coherent revivals associated with quantum many-body scars can be stabilized by periodic driving, generating stable subharmonic responses over a wide parameter regime. We analyze a simple, related model where these phenomena originate from spatiotemporal ordering in an effective Floquet unitary, corresponding to discrete time-crystalline behavior in a prethermal regime. Unlike conventional discrete time crystals, the subharmonic response exists only for Néel-like initial states, associated with quantum scars. We predict robustness to perturbations and identify emergent timescales that could be observed in future experiments. Our results suggest a route to controlling entanglement in interacting quantum systems by combining periodic driving with many-body scars.
A time crystal is a state of periodically driven matter that breaks discrete time-translation symmetry.Time crystals have been demonstrated experimentally in various programmable quantum simulators, and they exemplify how nonequilibrium, driven quantum systems can exhibit intriguing and robust properties absent in systems at equilibrium.These robust driven states need to be stabilized by some mechanism, with the preeminent candidates being many-body localization and prethermalization.This introduces additional constraints that make it challenging to experimentally observe time crystallinity in naturally occurring systems.Recent theoretical work has developed the notion of prethermalization without temperature, expanding the class of time-crystal systems to explain time-crystalline observations at (or near) infinite temperature.In this work, we conclusively observe the emergence of a prethermal Uð1Þ time-crystalline state at quasi-infinite temperature in a solid-state NMR quantum emulator by verifying the requisites of prethermalization without temperature.In addition to observing the signature period-doubling behavior, we show the existence of a long-lived prethermal regime whose lifetime is significantly enhanced by strengthening an emergent Uð1Þ conservation law.Not only do we measure this enhancement through the global magnetization, but we also exploit on-site disorder to measure local observables, ruling out the possibility of many-body localization and confirming the emergence of long-range correlations.
Discrete time crystals are periodically driven systems characterized by a response with periodicity nT, with T the period of the drive and n > 1. Typically, n is an integer and bounded from above by the dimension of the local (or single particle) Hilbert space, the most prominent example being spin-1/2 systems with n restricted to 2. Here, we show that a clean spin-1/2 system in the presence of long-range interactions and transverse field can sustain a huge variety of different 'higher-order' discrete time crystals with integer and, surprisingly, even fractional n > 2. We characterize these (arguably prethermal) non-equilibrium phases of matter thoroughly using a combination of exact diagonalization, semiclassical methods, and spin-wave approximations, which enable us to establish their stability in the presence of competing long- and short-range interactions. Remarkably, these phases emerge in a model with continous driving and time-independent interactions, convenient for experimental implementations with ultracold atoms or trapped ions.
Prethermal discrete time crystals (DTCs) are a novel phase of periodically driven matter that exhibits robust subharmonic oscillations without requiring disorder. However, previous realizations of prethermal DTCs have relied on the presence of polarization, either spontaneous or induced. Here we introduce a class of prethermal DTCs termed ``unpolarized prethermal discrete time crystals'' (UPDTCs) that arise without any uniform or staggered polarization and propose an experiment to observe them in current trapped-ion quantum simulators. By studying a model of trapped ions using a quantum circuit simulator, we demonstrate that robust period-doubled dynamics can persist in the autocorrelation function of the staggered magnetization, even though its expectation value does not exhibit such dynamics. The period-doubled dynamics is not explained by the classical picture of flipping spins but by quantum fluctuations. We establish that UPDTCs are exponentially long-lived in the high-frequency driving regime, a hallmark of prethermalization. These results expand the known phenomenology and mechanism of prethermal time crystals and underscore the role of quantum effects in stabilizing novel nonequilibrium phases.