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arXiv:2505.04991 · Physical Review Applied

Discrete time crystal for periodic-field sensing with quantum-enhanced precision

Rozhin Yousefjani, Saif M. Al-Kuwari, Abolfazl Bayat

Published Nov 17, 2025• 3 citations
arXivHTMLPDF

Abstract

Sensing periodic fields using quantum sensors has been an active field of research. In many of these scenarios, the quantum state of the probe is flipped regularly by the application of $\ensuremath{\pi}$ pulses to accumulate information about the target periodic field. The emergence of a discrete time crystalline phase, as a nonequilibrium phase of matter, naturally provides oscillations in a many-body system with an inherent controllable frequency. They benefit from long coherence time and robustness against imperfections, which makes them excellent potential quantum sensors. In this paper, through theoretical and numerical analysis, we show that a disorder-free discrete time crystal probe can reach the ultimate achievable precision for sensing a periodic field. As the amplitude of the periodic field increases, the discrete time crystalline order diminishes, and the performance of the probe decreases remarkably. Nevertheless, the obtained quantum enhancement in the discrete time crystal phase, which is experimentally accessible using standard projective measurements, shows robustness against different imperfections and dephasing noise in the protocol. Finally, we propose the implementation of our protocol in ultracold atoms in optical lattices.

DOI
10.1103/7m63-lnb8

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Sensing periodic fields using quantum sensors has been an active field of research. In many of these scenarios, the quantum state of the probe is flipped regularly by the application of \ensuremathπ\ensuremath{\pi}\ensuremathπ pulses to accumulate information about the target periodic field. The emergence of a discrete time crystalline phase, as a nonequilibrium phase of matter, naturally provides oscillations in a many-body system with an inherent controllable frequency. They benefit from long coherence time and robustness against imperfections, which makes them excellent potential quantum sensors. In this paper, through theoretical and numerical analysis, we show that a disorder-free discrete time crystal probe can reach the ultimate achievable precision for sensing a periodic field. As the amplitude of the periodic field increases, the discrete time crystalline order diminishes, and the performance of the probe decreases remarkably. Nevertheless, the obtained quantum enhancement in the discrete time crystal phase, which is experimentally accessible using standard projective measurements, shows robustness against different imperfections and dephasing noise in the protocol. Finally, we propose the implementation of our protocol in ultracold atoms in optical lattices.
Discrete time crystals are a special phase of matter in which time translational symmetry is broken through a periodic driving pulse. Here, we first propose and characterize an effective mechanism to generate a stable discrete time crystal phase in a disorder-free many-body system with indefinite persistent oscillations even in finite-size systems. Then we explore the sensing capability of this system to measure the spin exchange coupling. The results show strong quantum-enhanced sensitivity throughout the time crystal phase. As the spin exchange coupling varies, the system goes through a sharp phase transition and enters a non-time-crystal phase in which the performance of the probe considerably decreases. We characterize this phase transition as a second-order type and determine its critical properties through a comprehensive finite-size scaling analysis. The performance is independent of the initial states and may even benefit from imperfections in the driving pulse. A simple set of projective measurements can capture the quantum-enhanced sensitivity.
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.
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.
Discrete time crystals (DTCs) are non-equilibrium phases in periodically driven systems that exhibit spontaneous breaking of discrete time-translation symmetry. The stabilization of most DTC phases is achieved via the disorder-induced many-body localization. In this work, we propose an experimental scheme to realize disorder-free DTCs in a periodically driven Rydberg atom array. Our scheme utilizes a linear potential in the atomic detuning to enhance the DTC order, without being tired to (Stark) many-body localization. We numerically demonstrate that the Stark potential enhances the robustness of the DTC against the flip imperfections and extends its lifetime, which are independent of initial states. Thus, our scheme provides a promising way to explore DTCs in Rydberg atom arrays without disorder averaging and special state preparation.
The long range spatial and temporal ordering displayed by discrete time crystals, can become advantageous properties when used for sensing extremely weak signals. Here, we investigate their performance as quantum sensors of weak AC-fields and demonstrate, using the quantum Fisher information measure, that they can overcome the shot noise limit while allowing long interrogation times. In such systems, collective interactions stabilize their dynamics against noise making them robust enough to protocol imperfections.
Time crystals are nonequilibrium phases of matter characterized by the emergence of temporal ordering, in which an interacting many-body system develops robust structure in its time evolution that is not trivially dictated by the external driving or environment. While related phenomena have long been studied in classical nonlinear systems, their realization in entangled quantum matter represents a distinct frontier. The theoretical understanding of discrete time crystals has substantially advanced, yet recent experiments using modern quantum devices and quantum processors reveal regimes beyond established paradigms. These developments call for an extended classification of time-crystalline phases according to both their stabilization mechanisms and their physical character, including discrete and continuous, closed and open, critical, topological, quasiperiodic, and controlled realizations. We review recent implementations of time crystals on quantum platforms and propose such a classification framework, identifying promising directions for the discovery of novel time-crystalline phases of matter.