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arXiv:1807.10161 · Physical Review Letters

Discrete Time Crystals in the Absence of Manifest Symmetries or Disorder in Open Quantum Systems

Filippo Maria Gambetta, Federico Carollo, Matteo Marcuzzi, Juan P. Garrahan, Igor Lesanovsky

Published Jan 8, 2019• 149 citations
arXivHTMLPDF

Abstract

We establish a link between metastability and a discrete time-crystalline phase in a periodically driven open quantum system. The mechanism we highlight requires neither the system to display any microscopic symmetry nor the presence of disorder, but relies instead on the emergence of a metastable regime. We investigate this in detail in an open quantum spin system, which is a canonical model for the exploration of collective phenomena in strongly interacting dissipative Rydberg gases. Here, a semiclassical approach reveals the emergence of a robust discrete time-crystalline phase in the thermodynamic limit in which metastability, dissipation, and interparticle interactions play a crucial role. We perform numerical simulations in order to investigate the dependence on the range of interactions, from all to all to short ranged, and the scaling with system size of the lifetime of the time crystal.

DOI
10.1103/physrevlett.122.015701

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We establish a link between metastability and a discrete time-crystalline phase in a periodically driven open quantum system. The mechanism we highlight requires neither the system to display any microscopic symmetry nor the presence of disorder, but relies instead on the emergence of a metastable regime. We investigate this in detail in an open quantum spin system, which is a canonical model for the exploration of collective phenomena in strongly interacting dissipative Rydberg gases. Here, a semiclassical approach reveals the emergence of a robust discrete time-crystalline phase in the thermodynamic limit in which metastability, dissipation, and interparticle interactions play a crucial role. We perform numerical simulations in order to investigate the dependence on the range of interactions, from all to all to short ranged, and the scaling with system size of the lifetime of the time crystal.
Abstract We study an emergent semiclassical time crystal composed of two interacting driven-dissipative bosonic modes. The system has a discrete Z 2 spatial symmetry which, depending on the strength of the drive, can be broken in the time-crystalline phase or it cannot. An exact semiclassical mean-field analysis, numerical simulations in the quantum regime, and the spectral analysis of the Liouvillian are combined to show the emergence of the time crystal and to prove the robustness of the oscillation period against quantum fluctuations.
Time crystals, as temporal analogs of space crystals, manifest as stable and periodic behavior that breaks time translation symmetry. In an open quantum system, many-body interaction subjected to dissipation allows one to develop the time crystalline order in an unprecedented way, as refer to dissipative time crystals. Here we report the observation of multiple time crystals in the continuously driven-dissipative and strongly interacting Rydberg thermal gases, in which continuous time crystals, sub-harmonic time crystals and high-harmonic time crystals are observed in the same system by manipulating the Rydberg excitation. Our work provides new ways to explore the non-equilibrium phases of matter in open systems. Such time crystals with persistent oscillation rooted in emergent quantum correlations, may emerge as a ubiquitous tool in quantum metrology, for instance, continuous sensing and parameter estimation surpassing the standard quantum limit. The authors observed multiple time crystals in the continuously driven-dissipative and strongly interacting Rydberg thermal gases. This discovery may benefit the field of quantum metrology, such as continuous sensing, potentially surpassing the standard quantum limit, and time crystalline order as a frequency standard.
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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.
We elucidate the role that the dissipation in a bosonic channel plays in the prevalence and stability of time crystals (TCs) in a periodically driven spin-boson system described by the Dicke model. Here, the bosons are represented by photons, and they mediate the infinite-range interactions between the spin systems. For strong dissipation, we study the dynamics using an effective atom-only description and the closed Lipkin-Meshkov-Glick model. By mapping out the phase diagrams for varying dissipation strengths, ranging from zero to infinitely strong, we demonstrate that the area in the phase diagram, where a TC exists, grows with the dissipation strength but only up to an optimal point, beyond which most of the TCs become unstable. We find TCs in both closed-system and dissipative regimes, but dissipative TCs are shown to be more robust against random noise in the drive and are only weakly affected by the choice of initial state. We present the finite-sized behavior and the scaling of the lifetime of the TCs with respect to the number of spins and the interaction strength within a fully quantum mechanical description.
Time crystals in periodically driven systems have initially been studied assuming either the ability to quench the Hamiltonian between different many-body regimes, the presence of disorder or long-range interactions. Here we propose the simplest scheme to observe discrete time crystal dynamics in a one-dimensional driven quantum system of the Ising type with short-range interactions and no disorder. The system is subject only to a periodic kick by a global magnetic field, and no extra Hamiltonian quenching is performed. We analyze the emerging time crystal stabilizing mechanisms via extensive numerics as well as using an analytic approach based on an off-resonant transition model. Due to the simplicity of the driven Ising model, our proposal can be implemented with current experimental platforms including trapped ions, Rydberg atoms, and superconducting circuits.