How to Create a Time Crystal

Abstract

Despite being forbidden in equilibrium, spontaneous breaking of time translation symmetry can occur in periodically driven, Floquet systems with discrete time-translation symmetry. The period of the resulting discrete time crystal is quantized to an integer multiple of the drive period, arising from a combination of collective synchronization and many body localization. Here, we consider a simple model for a onedimensional discrete time crystal which explicitly reveals the rigidity of the emergent oscillations as the drive is varied. We numerically map out its phase diagram and compute the properties of the dynamical phase transition where the time crystal melts into a trivial Floquet insulator. Moreover, we demonstrate that the model can be realized with current experimental technologies and propose a blueprint based upon a one dimensional chain of trapped ions. Using experimental parameters (featuring long-range interactions), we identify the phase boundaries of the ion-time-crystal and propose a measurable signature of the symmetry breaking phase transition. DOI: 10.1103/PhysRevLett.118.030401 Spontaneous symmetry breaking-where a quantum state breaks an underlying symmetry of its parent Hamiltonianrepresents a unifying concept in modern physics [1,2]. Its ubiquity spans from condensed matter and atomic physics to high energy particle physics; indeed, examples of the phenomenon abound in nature: superconductors, Bose-Einstein condensates, (anti)ferromagnets, any crystal, and Higgs mass generation for fundamental particles. This diversity seems to suggest that almost any symmetry can be broken.Spurred by this notion, and the analogy to spatial crystals, Wilczek proposed the intriguing concept of a "time crystal"-a state which spontaneously breaks continuous time translation symmetry [3][4][5]. Subsequent work developed more precise definitions of such time translation symmetry breaking (TTSB) [6][7][8] and ultimately, led to a proof of the "absence of (equilibrium) quantum time crystals" [9]. However, this proof leaves the door open to TTSB in [10,11] has demonstrated that quantum systems subject to periodic driving can indeed exhibit discrete TTSB [10-13]; such systems develop persistent macroscopic oscillations at an integer multiple of the driving period, manifesting in a subharmonic response for physical observables.An important constraint on symmetry breaking in manybody Floquet systems is the need for disorder and localization [10][11][12][13][14][15][16][17]. In the translation-invariant setting, Floquet eigenstates are short-range correlated and resemble infinite temperature states which cannot exhibit symmetry breaking [15,18,19]. Under certain conditions, however, prethermal time-crystal-like dynamics can persist for long times [20,21] even in the absence of localization before ultimately being destroyed by thermalization [17,22].In this Letter, we present three main results. First, by exploring the interplay between entanglement, many body localization and TTSB, we produce a phase diagram for a d...

Photonic time crystals

“…Whereas, our research focused on the permittivity and permeability of photonic time crystal varying with time periodically. Borzdov studied electromagnetic space-time crystal of a quantum version 24 , 25 , however, all physically observable properties of quantum systems are time independent in equilibrium, so no time-periodic behavior can manifest itself 11 .…”

“…They found that the time crystal exists again in non-equilibrium Floquet systems because of a loophole 6 – 17 . Under the condition of periodical-driven, the discrete time crystal (or Floquet time crystal) in non-equilibrium Floquet systems could form which broke time translation symmetry 8 , the period of discrete time crystal is the integer multiple of the drive period 10 , 11 . Meanwhile, utilizing completely different quantum system, Choi et al .…”

Route to Extend the Lifetime of a Discrete Time Crystal in a Finite Spin Chain without Disorder

“…A time crystal is an intriguing non-equilibrium phase of matter that is expected to be a very useful platform for performing precision measurements [84,85] and quantum simulation [86]. In this paper, we have described a scheme to extend the lifetime of a DTC in a periodically driven finite Ising spin chain with nearest-neighbor interactions and no disorder.…”

Route to Extend the Lifetime of a Discrete Time Crystal in a Finite Spin Chain Without Disorder

“…A time crystal is an intriguing non-equilibrium phase of matter, that is expected to be a very useful platform for performing precision measurements [84,85] and quantum simulation [86]. In this paper, we have described a scheme to extend the lifetime of a DTC in a periodically driven finite Ising spin chain with nearestneighbor interactions and no disorder.…”