Observation of a Time Quasicrystal and Its Transition to a Superfluid Time Crystal

Autti, S.; Eltsov, V. B.; Volovik, G. E.

doi:10.1103/physrevlett.120.215301

Cited by 159 publications

(130 citation statements)

References 51 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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“…(6). We emphasize that, differently from previous works [36], we believe the presence of two incommensurate frequencies to be a necessary but not sufficient ingredient for the definition of a DTQC [40]. Rather, in analogy with the more established notion of DTC, we judge essential the presence of the robust subharmonic peak, which is a genuine many-body feature.…”

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confidence: 64%

Period- n Discrete Time Crystals and Quasicrystals with Ultracold Bosons

2019

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We investigate the out-of-equilibrium properties of a system of interacting bosons in a ring lattice. We present a Floquet driving that induces clockwise (counterclockwise) circulation of the particles among the odd (even) sites of the ring which can be mapped to a fully connected model of clocks of two counter-rotating species. The clock-like motion of the particles is at the core of a period-n discrete time crystal where L = 2n is the number of lattice sites. In presence of a "staircase-like" on-site potential, we report the emergence of a second characteristic timescale in addition to the period n-tupling. This new timescale depends on the microscopic parameters of the Hamiltonian and is incommensurate with the Floquet period, underpinning a dynamical phase we call 'time quasicrystal'. The rich dynamical phase diagram also features a thermal phase and an oscillatory phase, all of which we investigate and characterize. Our simple, yet rich model can be realized with state-ofthe-art ultracold atoms experiments. arXiv:1907.04703v2 [cond-mat.quant-gas]

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“…This requires that the non-zero Floquet quasi-frequency of the long life modes takes the form q w = m n j Im with integer n=2, 3, K and = ¼ m n 1, 2, , 1. In general, the non-zero Floquet quasifrequency can be incommensurate with the drive, this would lead to the so called time quasi-crystal [26], but this is beyond our scope of study in this work.…”

Section: Floquet Analysis 41 Floquet Basicsmentioning

confidence: 99%

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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Observation of a Time Quasicrystal and Its Transition to a Superfluid Time Crystal

Cited by 159 publications

References 51 publications

Topological time crystals

Topological time crystals

Period- n Discrete Time Crystals and Quasicrystals with Ultracold Bosons

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

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