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arXiv:1907.03446 · Physical Review A

Discrete time crystal in a finite chain of Rydberg atoms without disorder

Chu-Hui Fan, Davide Rossini, Han-Xiao Zhang, Jin-Hui Wu, M. Artoni, Giuseppe Carlo La Rocca

Published Jan 13, 2020• 34 citations
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Abstract

We study the collective dynamics of a clean Floquet system of cold atoms, numerically simulating two realistic setups based on a regular chain of interacting Rydberg atoms driven by laser fields. In both cases, the population evolution and its Fourier spectrum display clear signatures of a discrete time crystal (DTC), exhibiting the appearance of a robust subharmonic oscillation which persists on a timescale increasing with the chain size, within a certain range of control parameters. We also characterize how the DTC stability is affected by dissipative processes, typically present in this atomic system even though the Rydberg state is very long lived.

DOI
10.1103/physreva.101.013417

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Communications Physics•Jun 22, 2022•12 citations
We study the collective dynamics of a clean Floquet system of cold atoms, numerically simulating two realistic setups based on a regular chain of interacting Rydberg atoms driven by laser fields. In both cases, the population evolution and its Fourier spectrum display clear signatures of a discrete time crystal (DTC), exhibiting the appearance of a robust subharmonic oscillation which persists on a timescale increasing with the chain size, within a certain range of control parameters. We also characterize how the DTC stability is affected by dissipative processes, typically present in this atomic system even though the Rydberg state is very long lived.
Discrete time crystals (DTCs) represent a nonequilibrium phase of matter characterized by spontaneousbreaking of discrete time-translational symmetry under periodic driving. While Floquet topological phases offer apromising route to stabilizing DTC behavior, their persistence in realistic open quantum systems remains an openproblem. In this work, we numerically investigate a periodically driven one-dimensional Ising chain locally coupledto a dissipative two-level system (TLS) defect, motivated by microscopic defects commonly observed in superconductingcircuit-QED devices. Using Lindblad master-equation simulations implemented in QuTiP, we show that weaklydissipative TLS defects can dynamically synchronize with the Floquet edge mode and inherit its subharmonic oscillations.As the defect coupling and dissipation strength increase, the system undergoes a crossover toward decoherence andFloquet thermalization, accompanied by the suppression of edge-localized period doubling. By combining quasienergyspectroscopy, boundary-condition analysis, rigidity diagnostics, and entropy evolution, we characterize the stabilitylimits of Floquet topological time-crystalline phases in realistic noisy quantum hardware.
Nonequilibrium, strongly interacting systems exhibit rich dynamics even in the presence of strong dissipation. For example, periodic dynamics, such as discrete time crystalline (DTC) phases, can appear. The DTC phase structure can be further enriched using external periodic driving-Floquet driving. In this Letter, we study a photoionization-induced Floquet driving of a DTC phase in a thermal Rydberg gas. We add an additional laser to induce photoelectrons from the cell wall. These electrons are rotated around the magnetic-field vector and collide with the Rydberg atoms, generating a plasma with large electric fields that perturb further Rydberg excitation. This results in a photoionization-induced Floquet driving of the DTC phase. Importantly, we demonstrate experimentally how the DTC phase relies on the emergence of bistability. Simulations of the mean-field Floquet-driven system reproduce the experimental observations. Our Letter fills an experimental gap in our understanding of the relation of multistability and dissipative discrete time crystals, and in this regard, it constitutes a highly controlled platform for exploring exotic nonequilibrium physics in dissipative interacting systems.
Discrete time crystals (DTCs) are non-equilibrium phases of matter that break the discrete time-translation symmetry and is characterized by a robust subharmonic response in periodically driven quantum systems. Here, we explore the DTC in a disorder-free, periodically kicked XXZ spin chain, which is stabilized by the Floquet strong Hilbert space fragmentation. We numerically show the period-doubling response of the conventional DTC order, and uncover a multiple-period response with beating dynamics due to the coherent interplay of multiple πππ-pairs in the Floquet spectrum of small-size systems. The lifetime of the DTC order exhibits independence of the driving frequency and a power-law dependence on the ZZ interaction strength. It also grows exponentially with the system size, as a hallmark of the strong fragmentation inherent to the Floquet model. We analytically reveal the approximate conservation of the magnetization and domain-wall number in the Floquet operator for the emergent strong fragmentation, which is consistent with numerical results of the dimensionality ratio of symmetry subspaces. The rigidity and phase regime of the DTC order are identified through finite-size scaling of the Floquet-spectrum-averaged mutual information, as well as via dynamical probes. Our work establishes the Floquet Hilbert space fragmentation as a disorder-free mechanism for sustaining nontrivial temporal orders in out-of-equilibrium quantum many-body systems.
We describe a general and simple paradigm for discrete time crystals (DTCs), systems with a stable subharmonic response to an external driving field, in a classical thermal setting. We consider, specifically, an Ising model in two dimensions, as a prototypical system with a phase transition into stable phases distinguished by a local order parameter, driven by thermal dynamics and periodically kicked with a noisy protocol. By means of extensive numerical simulations for large sizes-allowed by the classical nature of our model-we show that the system features a true disorder-DTC order phase transition as a function of the noise strength, with a robust DTC phase extending over a wide parameter range. We demonstrate that, when the dynamics is observed stroboscopically, the phase transition to the DTC state appears to be in the equilibrium two-dimensional Ising universality class. However, we explicitly show that the DTC is a genuine nonequilibrium state. More generally, we speculate that systems with thermal phase transitions to multiple competing phases can give rise to DTCs when appropriately driven.
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.
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.