Clean Floquet Time Crystals: Models and Realizations in Cold Atoms

Huang, Biao; Wu, Ying-Hai; Liu, W. Vincent

doi:10.1103/physrevlett.120.110603

Cited by 127 publications

(125 citation statements)

References 77 publications

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“…A crystalline structure in time is related to the periodic dynamics of a system. It has been shown that periodically driven quantum many-body systems can spontaneously self-reorganize their motion and start moving with a period different from the period of the driving [12][13][14] (see also [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]). This kind of spontaneous formation of a new crystalline structure in time is dubbed discrete or Floquet time crystals and has been already realized experimentally [30][31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

Topological time crystals

et al. 2019

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By analogy with the formation of space crystals, crystalline structures can also appear in the time domain. While in the case of space crystals we often ask about periodic arrangements of atoms in space at a moment of a detection, in time crystals the role of space and time is exchanged. That is, we fix a space point and ask if the probability density for detection of a system at this point behaves periodically in time. Here, we show that in periodically driven systems it is possible to realize topological insulators, which can be observed in time. The bulk-edge correspondence is related to the edge in time, where edge states localize. We focus on two examples: Su-Schrieffer-Heeger model in time and Bose Haldane insulator which emerges in the dynamics of a periodically driven many-body system. 5 Note that due to the negative effective mass m eff , the first energy band is the highest in energy. 2 New J. Phys. 21 (2019) 052003 where = ¢ J J i 2and J 2i−1 =J, which is identical to the SSH model [86]. The latter describes spinless fermions hopping on a 1D-lattice with staggered hopping amplitudes. Changing the ratio λ 1 /λ in (1), allows one to control the ratio ¢ J J . This effective Hamiltonian belongs to the BDI class of the periodic table of the topological insulators and superconductors [87] and is characterized by a  topological invariant, the winding number ν. For an infinite system with ¢ > J J ( ¢ < J J ), the system is in a topological (trivial) phase with winding number ν=1 (ν=0). For a finite system, the topological phase exhibits zero energy edge states protected by the topology of the bulk. The SSH model has been experimentally realized in quantum simulators and both the presence of edge states and the winding number have been measured [63][64][65]. Let us emphasize that the Wannier states w i (x, t) of equation (2) are localized wavepackets of the effective SSH Hamiltonian of equation (3). We then discuss how such states allow one to detect the topology of the SSH Hamiltonian. corresponding to quasi-energies closest to zero, see top panel. In the topological phase, these eigenstates have zero quasi-energy and are linear combinations of the edge states localized at the edge of time. That is, in the laboratory frame, a detector is placed close to the oscillating mirror (x≈0) and the probability density of clicking of the detector is shown versus time for different values of the ratio ¢ J J of the tunneling amplitudes in (3). This behavior is repeated with the period 2π/ω. At sωt/(2π)=1 and sωt/(2π)=40 there are edges where the eigenstate localizes if ¢ > J J 1. The results correspond to ω=0.067, λ=0.06 in (1) and are obtained within the quantum secular approach [84], see the appendix.

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Section: Introductionmentioning

confidence: 99%

Topological time crystals

et al. 2019

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“…The major feature of the described system is a subharmonic response which is stable to drive perturbations [14,16]. As the driven system is prone to heating, it also involves many-body localized unitary evolution, although later this condition was relaxed if the finite time scale is considered [17][18][19]. The successful theoretical prediction of time-periodic structures in driven systems was followed by its experimental observation in trapped ions [20], silicon vacancy-based [21] quantum simulators, superfluid helium-3 [22], NMR systems [23,24].…”

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confidence: 99%

Quantum Time Crystals from Hamiltonians with Long-Range Interactions

2019

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Time crystals correspond to a phase of matter where time-translational symmetry (TTS) is broken. Up to date, they are well studied in open quantum systems, where external drive allows to break discrete TTS, ultimately leading to Floquet time crystals. At the same time, genuine time crystals for closed quantum systems are believed to be impossible. In this study we propose a form of a Hamiltonian for which the unitary dynamics exhibits the time crystalline behavior and breaks continuous TTS. This is based on spin-1/2 many-body Hamiltonian which has long-range multispin interactions in the form of spin strings, thus bypassing previously known no-go theorems. We show that quantum time crystals are stable to local perturbations at zero temperature. Finally, we reveal the intrinsic connection between continuous and discrete TTS, thus linking the two realms.

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“…Similar to the spatial crystal, spontaneously breaking of the discrete time translation symmetry leads to the concept of DTC [5][6][7]. Taken an open quantum system as an example, the broken of time translation symmetry requires the existence of a physical observableÔ that acts as an order parameter…”

Section: Definition Of Dtcmentioning

confidence: 99%

“…possesses a fixed oscillation period without fine-tuned system parameters; (C) persistence: the non-trivial oscillation with the fixed period must persist for infinitely long time in the thermodynamic limit. Such a definition of DTC can be regarded as an open system generalization of the definition in closed system [7].…”

Section: Definition Of Dtcmentioning

confidence: 99%

See 1 more Smart Citation

Discrete time-crystalline order in Bose–Hubbard model with dissipation

Dai

2020

New J. Phys.

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Periodically driven quantum systems manifest various non-equilibrium features which are absent at equilibrium. For example, discrete time-translation symmetry can be broken in periodically driven quantum systems leading to an exotic phase of matter, called discrete time crystal (DTC). For open quantum systems, previous studies showed that DTC can be found only when there exists a metastable state in the undriven system. However, by investigating the simplest Bose-Hubbard model with dissipation and time periodically tunneling, we find in this paper that a 2T DTC can appear even when the meta-stable state is absent in the undriven system. This observation extends the understanding of DTC and shed more light on the physics behind the DTC. Besides, by the detailed analysis of simplest two-sites model, we show further that the two-sites model can be used as basic building blocks to construct large rings in which a nT DTC might appear. These results might find applications into engineering exotic phases in driven open quantum systems.

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Clean Floquet Time Crystals: Models and Realizations in Cold Atoms

Cited by 127 publications

References 77 publications

Topological time crystals

Topological time crystals

Quantum Time Crystals from Hamiltonians with Long-Range Interactions

Discrete time-crystalline order in Bose–Hubbard model with dissipation

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