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arXiv:2012.08885 · Physical Review Letters

Observation of a Dissipative Time Crystal

Hans Keßler, Phatthamon Kongkhambut, Christoph Georges, Ludwig Mathey, Jayson G. Cosme, Andreas Hemmerich

Published Jul 19, 2021• 236 citations
arXivHTMLPDF

Abstract

We present the first experimental realization of a time crystal stabilized by dissipation. The central signature in our implementation in a driven open atom-cavity system is a period doubled switching between distinct checkerboard density wave patterns, induced by the interplay between controlled cavity dissipation, cavity-mediated interactions, and external driving. We demonstrate the robustness of this dynamical phase against system parameter changes and temporal perturbations of the driving.

DOI
10.1103/physrevlett.127.043602

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We present the first experimental realization of a time crystal stabilized by dissipation. The central signature in our implementation in a driven open atom-cavity system is a period doubled switching between distinct checkerboard density wave patterns, induced by the interplay between controlled cavity dissipation, cavity-mediated interactions, and external driving. We demonstrate the robustness of this dynamical phase against system parameter changes and temporal perturbations of the driving.
We demonstrate the emergence of a time crystal of atoms in a high-finesse optical cavity driven by a phase-modulated transverse pump field, resulting in a shaken lattice. This shaken system exhibits macroscopic oscillations in the number of cavity photons and order parameters at noninteger multiples of the driving period, which signals the appearance of an incommensurate time crystal. The subharmonic oscillatory motion corresponds to dynamical switching between symmetry-broken states, which are nonequilibrium bond ordered density wave states. Employing a semiclassical phase-space representation for the driven-dissipative quantum dynamics, we confirm the rigidity and persistence of the time crystalline phase. We identify experimentally relevant parameter regimes for which the time crystal phase is long lived, and map out the dynamical phase diagram. We compare and contrast the incommensurate time crystal with the commensurate Dicke time crystal in the amplitude-modulated case.
Continuous time crystals represent a novel state in many-body systems that can self-organize into timeperiodic oscillations without external periodic driving. Recent experiments have achieved such systems in dissipative solid-state materials, where persistent temporal order is autonomously sustained. A decisive characteristic of time crystals is their robustness, meaning that despite various disturbances, including fluctuations in internal parameters and external noise, they can still maintain rhythmic behavior, which has scientific value and echnological application potential. Although previous studies have shown that specific experimental parameters have robustness, thare is a lack of a systematic framework for quantifying and predicting their resilience to disturbances, and the underlying physics of this robustnessis still not fully understood. The key unresolved problems include how nonlinear interactions and feedback mechanisms contribute to stability, and what the critical thresholds are for parameter variations beyond which temporal order collapses. This work addresses these gaps by systematically analyzing how internal parameters and external influences affect the oscillation period and overall stability. Internally, the dynamics are determined by dipole-dipole interactions and atomic transition strengths, which define the temporal symmetry breaking that occurs in the system. Externally, the response of the system is controlled by the strength of the optical driving field and the energy dissipation rate. A key finding is the determination of an intrinsic feedback mechanism for a dynamically stabile time crystal. This mechanism plays a role in restoring force, correcting deviations caused by minor disturbances, and maintaining the coherence of oscillatory phase. Moreover, the system displays nonlinear dynamical behavior, characterized by two different states: one is stable oscillation continuing under moderate disturbance, and the other is stronger disturbance causing dynamical phase transition, resulting in switching between disordered or dynamically unstable state and stable state. These results provide a comprehensive understanding of the various behaviors observed in continuous time crystals and lay an important theoretical foundation for utilizing their unique properties in advanced applications such as quantum information processing and precision metrology.
Periodic driving of strongly correlated systems has led to outstanding discoveries from light-induced superconductivity to time crystals. To gain insights into the fundamental nature of these phenomena, we have recently studied the effects of an external periodic driving in a well-controlled yet simple many-body platform consisting of a Bose-Einstein condensate inside a high-finesse optical cavity. This system hosts a competition between a homogeneous condensate phase and a self-organized density wave phase, which manifests in a superradiant phase transition as the intensity of a transverse pump beam is increased. We demonstrate dynamical control of this phase transition by periodic driving of the pump laser. Furthermore, we discover the emergence of genuine dynamical phases, namely a discrete time crystalline phase and nonequilibrium density wave orders. Accompanying experimental results confirm our theoretical predictions about light-induced control in the atom-cavity system.
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.
A time crystal is an exotic phase of matter where time-translational symmetry is broken; this phase differs from the spatial symmetry breaking induced in conventional crystals. Lots of experiments report the transition from a thermal equilibrium phase to a time crystal phase. However, there is no experimental method to probe the bifurcation effect of distinct continuous time crystals in quantum many-body systems. Here, in a driven and dissipative many-body Rydberg atom system, we observe multiple continuous dissipative time crystals and emergence of more complex temporal symmetries beyond the single time crystal phase. Bifurcation of time crystals in strongly interacting Rydberg atoms is observed; the process manifests as a transition from a time crystal of long periodicity to a time crystal of short periodicity, or vice versa. By manipulating the driving field parameters, we observe the time crystal’s bistability and a hysteresis loop. These investigations indicate new possibilities for control and manipulation of the temporal symmetries of non-equilibrium systems. The time crystal is an exotic phase of matter where time-translational symmetry is broken. Here, the authors observe multiple continuous dissipative time crystals and bifurcation of time crystals in driven and dissipative Rydberg atomic gas.
A time crystal is an exotic phase of matter where time-translational symmetry is broken; this phase differs from the spatial symmetry breaking induced in crystals in space. Lots of experiments report the transition from a thermal equilibrium phase to time crystal phase. However, there is no experimental method to probe the bifurcation effect of distinct time crystals in quantum many-body systems. Here, in a driven and dissipative many-body Rydberg atom system, we observe multiple continuous dissipative time crystals and emergence of more complex temporal symmetries beyond the single time crystal phase. Bifurcation of time crystals in strongly interacting Rydberg atoms is observed; the process manifests as a transition from a time crystal state of long temporal order to one of short temporal order, or vice versa. By manipulating the driving field parameters, we observe the time crystal's bistability and a hysteresis loop. These investigations indicate new possibilities for control and manipulation of the temporal symmetries of non-equilibrium systems.