Space-Time Crystals of Trapped Ions

Li, Tongcang; Gong, Zhe Xuan; Yin, Zhang; Quan, H. T.; Yin, Xiaobo; Zhang, Peng; Duan, L.-M.; Zhang, Xiang

doi:10.1103/physrevlett.109.163001

Cited by 186 publications

(201 citation statements)

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“…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].…”

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confidence: 99%

“…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].…”

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confidence: 99%

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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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“…1. Two different systems have been proposed: a bright soliton formed by attractively interacting particles on an Aharonov-Bohm ring [6] and ions on a ring in the presence of an external magnetic field [7] (see also [8][9][10][11][12]). These proposals triggered debate in the literature whether time crystal formation is possible.…”

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“…These proposals triggered debate in the literature whether time crystal formation is possible. It seems that different assumptions can lead to contradictory conclusions [13][14][15][16][17][18][19][20][21][22].…”

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confidence: 99%

Modeling spontaneous breaking of time-translation symmetry

2015

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We show that an ultra-cold atomic cloud bouncing on an oscillating mirror can reveal spontaneous breaking of a discrete time translation symmetry. In many-body simulations we illustrate the process of the symmetry breaking that can be induced by atomic losses or by a measurement of particle positions. The results pave the way for understanding and realization of the time crystal idea where crystalline structures form in the time domain due to spontaneous breaking of continuous time translation symmetry. 03.75.Lm, Symmetries of a quantum many-body Hamiltonian are reflected by properties of its eigenstates. However, there are systems whose eigenstates are extremely vulnerable to any symmetry breaking perturbation. Bose gas in a symmetric double well potential, with attractive particle interactions, is a simple example [1][2][3][4][5]. The ground state of the system reflects the symmetry of the external potential but it cannot be easily prepared in an experiment because it is a macroscopic superposition of two Bose-Einstein condensates (BEC) located in different potential wells. Loss of a particle is sufficient to break the symmetry and accumulate all remaining particles in one of the wells. Breaking of a symmetry due to an infinitesimally weak perturbation is called spontaneous symmetry breaking phenomenon.Spontaneous breaking of continuous spatial translation symmetry to discrete spatial translation symmetry is responsible for formation of space crystals. Recently it has been proposed that similar phenomenon can also occur in the time domain [6,7]. That is, it is possible to invent systems where the ground state of a time-independent Hamiltonian reveals spatially homogeneous flow of particles which under any symmetry breaking perturbation changes spontaneously to periodic motion of spatially inhomogeneous structures. Such a spontaneous breaking of continuous time translation symmetry to a discrete one is termed time crystal formation, see Fig. 1. Two different systems have been proposed: a bright soliton formed by attractively interacting particles on an Aharonov-Bohm ring [6] and ions on a ring in the presence of an external magnetic field [7] (see also [8][9][10][11][12]). These proposals triggered debate in the literature whether time crystal formation is possible. It seems that different assumptions can lead to contradictory conclusions [13][14][15][16][17][18][19][20][21][22].In the present paper we consider a periodically driven many-body system whose description can be reduced to a Hilbert space spanned by two periodically evolving modes. As in the case of a Bose gas in a double well potential [1-5], a spontaneous symmetry breaking process occurs. In our example, eigenstates of the system pos- sess discrete time translation symmetry which is spontaneously broken to another discrete translation symmetry but with a longer period, see Fig. 1. The spontaneous symmetry breaking that is predicted within the mean field approach, can be analyzed in full many-body simulations. Moreover it can be realized in ultra-...

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“…Tongcang Li et al [4] have suggested a method for actually creating such space-time crystals, by confining ions in a ring-shaped trapping potential with a static magnetic field. They propose that the resultant ion crystal will rotate persistently, with no loss of energy.…”

Section: Testing the Theorymentioning

confidence: 99%

Is “Time” Speeding up?

Biegeleisen¹

2016

OALib

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This article considers the possibility that there might be a plausible scientific explanation for the 900-year lifespans of the characters in the beginning of the biblical book of Genesis. The explanation is based upon the hypothesis that there may be two different forms of "time". The first form would be "astronomical" time, which is based upon the quasi-perpetual rotational and revolutionary motions of heavenly bodies. The rates of these processes, which ideally consume no energy, have been, to a first approximation, relatively invariant, at least within the brief temporal framework of recorded human history. The second form of time would be "thermodynamic" time, the measurement of which is based upon the movements of clocks, whose reported rates of passage of time are linked inextricably to a decrease in the free energy of the system. This second form of time is the form generally employed to measure the rates of progress of physical phenomena, such as chemical reactions. If the underlying rate of passage of thermodynamic time had changed at some point in history, both the chemical reactions and the clocks used to measure their progress, would have changed together, which change might therefore have gone unnoticed. The effects of a changing thermodynamic clock on human perception of the world, and upon the perceived speed of light, are discussed.

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Space-Time Crystals of Trapped Ions

Cited by 186 publications

References 38 publications

Discrete Time Crystals: Rigidity, Criticality, and Realizations

Discrete Time Crystals: Rigidity, Criticality, and Realizations

Modeling spontaneous breaking of time-translation symmetry

Is “Time” Speeding up?

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