Comment on “Space-Time Crystals of Trapped Ions”

Bruno, P.

doi:10.1103/physrevlett.111.029301

Cited by 105 publications

(152 citation statements)

References 10 publications

(11 reference statements)

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“…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 an intrinsically out-of-equilibrium setting, and pioneering recent work [10,11] has demonstrated that quantum systems subject to periodic driving can indeed exhibit discrete TTSB [10][11][12][13]; such systems develop persistent macroscopic oscillations at an integer multiple of the driving period, manifesting in a sub-harmonic response for physical observables.…”

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confidence: 99%

Discrete Time Crystals: Rigidity, Criticality, and Realizations

et al. 2017

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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 one dimensional 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. Spontaneous symmetry breaking-where a quantum state breaks an underlying symmetry of its parent Hamiltonian-represents 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 "timecrystal"-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 an intrinsically out-of-equilibrium setting, and pioneering recent work [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 sub-harmonic response for physical observables.An important constraint on symmetry breaking in many-body Floquet systems is the need for disorder and localization [10][11][12][13][14][15][16][17][18]. In the translation-invariant setting, Floquet eigenstates are short-range correlated and resemble infinite temperature states which cannot exhibit symmetry breaking [16,19,20]. Under certain conditions, however, prethermal time-crystal-like dynamics can persist for long times [21,22] even in the absence of localization before ultimately being destroyed by thermalization [18,23].In this Letter, we present three main results.

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Discrete Time Crystals: Rigidity, Criticality, and Realizations

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“…However for thermodynamic equilibrium system, this kind of time crystal could not exist following a no-go theorem 2,3 . Alternately, Sacha first proposed a new strategy using a periodically driven (Floquet) system to simulate the discrete time-translation symmetry breaking 4 .…”

Section: Introductionmentioning

confidence: 99%

Prethermal time crystals in a one-dimensional periodically driven Floquet system

Zeng

Sheng

2017

Phys. Rev. B

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Motivated by experimental observations of time-symmetry breaking behavior in a periodically driven (Floquet) system, we study a one-dimensional spin model to explore the stability of such Floquet discrete time crystals (DTCs) under the interplay between interaction and the microwave driving. For intermediate interactions and high drivings, from the time evolution of both stroboscopic spin polarization and mutual information between two ends, we show that Floquet DTCs can exist in a prethermal time regime without the tuning of strong disorder. For much weak interactions the system is a symmetry-unbroken phase, while for strong interactions it gives its way to a thermal phase. Through analyzing the entanglement dynamics, we show that large driving fields protect the prethermal DTCs from many-body localization and thermalization. Our results suggest that by increasing the spin interaction, one can drive the experimental system into optimal regime for observing a robust prethermal DTC phase.

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“…In contrast to the continuous TTS breaking [27][28][29] that has turned out to be impossible at thermal equilibrium [30,31], the discrete TTS breaking has been theoretically proposed [32][33][34][35][36] and experimentally demonstrated [37,38]. Phases with broken discrete TTS feature discrete time-crystalline (DTC) order characterized by periodic oscillations of physical observables with period nT , where T is the Floquet period and n = 2, 3, · · · .…”

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Discrete Time-Crystalline Order in Cavity and Circuit QED Systems

2018

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Discrete time crystals are a recently proposed and experimentally observed out-of-equilibrium dynamical phase of Floquet systems, where the stroboscopic evolution of a local observable repeats itself at an integer multiple of the driving period. We address this issue in a driven-dissipative setup, focusing on the modulated open Dicke model, which can be implemented by cavity or circuit QED systems. In the thermodynamic limit, we employ semiclassical approaches and find rich dynamical phases on top of the discrete time-crystalline order. In a deep quantum regime with few qubits, we find clear signatures of a transient discrete time-crystalline behavior, which is absent in the isolated counterpart. We establish a phenomenology of dissipative discrete time crystals by generalizing the Landau theory of phase transitions to Floquet open systems.Introduction.-Phases and phase transitions of matter are key concepts for understanding complex many-body physics [1,2]. Recent experimental developments in various quantum simulators, such as ultracold atoms [3,4], trapped ions [5,6] and superconducting qubits [7,8], motivate us to seek for quantum many-body systems out of equilibrium [9][10][11], such as many-body localized phases [12][13][14][15][16][17] and Floquet topological phases [18][19][20][21][22][23][24][25].In recent years, much effort has been devoted to periodically driven (Floquet) quantum many-body systems that break the discrete time-translation symmetry (TTS) [26]. In contrast to the continuous TTS breaking [27][28][29] that has turned out to be impossible at thermal equilibrium [30,31], the discrete TTS breaking has been theoretically proposed [32][33][34][35][36] and experimentally demonstrated [37,38]. Phases with broken discrete TTS feature discrete time-crystalline (DTC) order characterized by periodic oscillations of physical observables with period nT , where T is the Floquet period and n = 2, 3, · · · . The DTC order is expected to be stabilized by many-body interactions against variations of driving parameters. Note that the system is assumed to be in a localized phase [33,34,36,37] or to have long-range interactions [38][39][40]. Otherwise, the DTC order only exists in a prethermalized regime [41,42] since the system will eventually be heated to a featureless infinite-temperature state due to persistent driving [43][44][45].While remarkable progresses are being made concerning the DTC phase, most studies focus on isolated systems. Indeed, as has been experimentally observed [37,38] and theoretically investigated [46], the DTC order in an open system is usually destroyed by decoherence. On the other hand, it is known that dissipation and decoherence can also serve as resources for quantum tasks such as quantum computation [47] and metrology [48]. From this perspective, it is natural to ask whether the DTC order exists and can even be stabilized in open systems [49]. Such a possibility has actually been pointed out in Ref. [41], but neither a detailed theoretical model nor a concrete experimental imp...

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Comment on “Space-Time Crystals of Trapped Ions”

Cited by 105 publications

References 10 publications

Discrete Time Crystals: Rigidity, Criticality, and Realizations

Discrete Time Crystals: Rigidity, Criticality, and Realizations

Prethermal time crystals in a one-dimensional periodically driven Floquet system

Discrete Time-Crystalline Order in Cavity and Circuit QED Systems

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