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arXiv:2402.12378 · Reports on Progress in Physics

Observation of a phase transition from a continuous to a discrete time crystal

Phatthamon Kongkhambut, Jayson G. Cosme, Jim Skulte, Michelle A. Moreno-Armijos, Ludwig Mathey, Andreas Hemmerich, Hans Keßler

Published Jul 19, 2024• 14 citations
arXivHTMLPDF

Abstract

Discrete (DTCs) and continuous time crystals (CTCs) are novel dynamical many-body states, that are characterized by robust self-sustained oscillations, emerging via spontaneous breaking of discrete or continuous time translation symmetry. DTCs are periodically driven systems that oscillate with a subharmonic of the external drive, while CTCs are continuously driven and oscillate with a frequency intrinsic to the system. Here, we explore a phase transition from a continuous time crystal to a discrete time crystal. A CTC with a characteristic oscillation frequencyωCTCis prepared in a continuously pumped atom-cavity system. Modulating the pump intensity of the CTC with a frequencyωdrclose to2ωCTCleads to robust locking ofωCTCtoωdr/2, and hence a DTC arises. This phase transition in a quantum many-body system is related to subharmonic injection locking of non-linear mechanical and electronic oscillators or lasers.

DOI
10.1088/1361-6633/ad6585

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Discrete (DTCs) and continuous time crystals (CTCs) are novel dynamical many-body states, that are characterized by robust self-sustained oscillations, emerging via spontaneous breaking of discrete or continuous time translation symmetry. DTCs are periodically driven systems that oscillate with a subharmonic of the external drive, while CTCs are continuously driven and oscillate with a frequency intrinsic to the system. Here, we explore a phase transition from a continuous time crystal to a discrete time crystal. A CTC with a characteristic oscillation frequencyωCTCis prepared in a continuously pumped atom-cavity system. Modulating the pump intensity of the CTC with a frequencyωdrclose to2ωCTCleads to robust locking ofωCTCtoωdr/2, and hence a DTC arises. This phase transition in a quantum many-body system is related to subharmonic injection locking of non-linear mechanical and electronic oscillators or lasers.
Time crystals are classified as discrete or continuous depending on whether they spontaneously break discrete or continuous time translation symmetry. Although discrete time crystals have been extensively studied in periodically driven systems, the experimental realization of a continuous time crystal is still pending. We report the observation of a limit cycle phase in a continuously pumped dissipative atom-cavity system that is characterized by emergent oscillations in the intracavity photon number. The phase of the oscillation was found to be random for different realizations, and hence, this dynamical many-body state breaks continuous time translation symmetry spontaneously. Furthermore, the observed limit cycles are robust against temporal perturbations and therefore demonstrate the realization of a continuous time crystal.
Periodically driven quantum systems host a range of non-equilibrium phenomena which are unrealizable at equilibrium. Discrete time-translational symmetry in a periodically driven many-body system can be spontaneously broken to form a discrete time crystal, a putative quantum phase of matter. We present the observation of discrete time crystalline order in a driven system of paramagnetic PPP -donor impurities in isotopically enriched 28Si^{28}Si28Si cooled below 101010 K. The observations exhibit a stable subharmonic peak at half the drive frequency which remains pinned even in the presence of pulse error, a signature of DTC order. We propose a theoretical model based on the paradigmatic central spin model which is in good agreement with experimental observations, and investigate the role of dissipation in the stabilisation of the DTC. Both experiment and theory indicate that the order in this system is primarily a dissipative effect, and which persists in the presence of spin-spin interactions. We present a theoretical phase diagram as a function of interactions and dissipation for the central spin model which is consistent with the experiments. This opens up questions about the interplay of coherent interaction and dissipation for time-translation symmetry breaking in many-body Floquet systems.
Abstract Time crystals represent temporal analogues of the spatial self-ordering exhibited by atomic or molecular building blocks of solid-state crystals. The pursuit of discrete time crystals (DTCs) in periodically forced Floquet closed systems has revealed how they can evade thermalization and loss of temporal order. Recently, it has been shown that even with coupling to the ambient and its concomitant noise, some states maintain their time crystalline order, formingdissipativeDTCs. Here, we introduce a scheme for the realization and state control of dissipative DTCs hinging on pumping a Kerr optical resonator with a phase-modulated continuous-wave laser. We show the possible symmetry breaking states possess temporal long-range order and analyze the phase noise of the accompanying signature radio frequency (RF) subharmonic. Besides offering a technique for generating high-spectral-purity RF signals, this versatile platform empowers controlled switching between various DTC states through accessible experimental knobs, hence facilitating the future study of DTC phase transitions.
Continuous time crystals (CTCs) are characterized by sustained oscillations that break the time-translation symmetry. Since the ruling out of equilibrium CTCs by no-go theorems, the emergence of such dynamical phases has been observed in various driven-dissipative quantum platforms. The current understanding of CTCs is mainly based on mean-field theories, which fail to address the problem of whether the continuous time-translation symmetry can be broken in noisy, spatially extended systems absent in all-to-all couplings. Here, we propose a CTC realized in a quantum contact model through self-organized bistability. The CTCs stem from the interplay between collective dissipation induced by the first-order absorbing phase transitions and slow constant driving provided by an incoherent pump. The stability of such oscillatory phases in finite dimensions under the action of intrinsic quantum fluctuations is scrutinized by the functional renormalization group method and numerical simulations. Occurring at the edge of many-body synchronization, the CTC phase exhibits an inherent period and amplitude with a coherence time linearly diverging with system size, thus also constituting a boundary time crystal. Our results serve as a solid route towards self-protected CTCs in strongly interacting open systems. Published by the American Physical Society 2024
Time crystals are classified into discrete time crystals and continuous time crystals based on whether they spontaneously break time-translation symmetry. Continuous-time crystals do not require external driving. By introducing AdS/CFT duality to time crystals, we derive their thermodynamic limit and find that in strongly correlated many-body systems such as a 3D optical lattice(ions or tweezer in supplemental materials), cooperative many-body tunneling enables time crystals to oscillate spontaneously. In strongly correlated quantum systems driven by many-body cooperative tunneling, we discover a universal scaling law governing the time-crystalline phase transition at a critical temperature.
Non-equilibrium Rydberg gases exhibit exotic many-body phases stabilized by the interplay of coherent interactions and dissipation. Strong Rydberg interactions drive sustained limit cycle oscillations, whose robustness, long-range temporal order, and spontaneous time-translation symmetry breaking establish a dissipative time crystal (DTC). Collective self-entrainment in driven ensembles leads to global synchronization and a dominant oscillation frequency. Here, injection locking of a Rydberg DTC is demonstrated using a radio-frequency (RF) electric field that gradually pulls the intrinsic oscillation toward the injected frequency. Above a critical threshold, full synchronization occurs, with the locking bandwidth scaling linearly with RF amplitude. This includes synchronization of higher-order harmonics, revealing entrainment of the system's nonlinear temporal dynamics. The phenomenon parallels injection locking in classical nonlinear systems, but emerges here in a strongly interacting quantum medium. This approach establishes a new method for stabilizing and controlling time-crystalline temporal order, with applications in precision sensing, quantum metrology, and timekeeping.