Period doubling in period-one steady states

Wang, Reuben R. W.; Xing, Bo; Carlo, Gabriel G.; Poletti, Dario

doi:10.1103/physreve.97.020202

Cited by 46 publications

(46 citation statements)

References 31 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 open nature is common to a vast class of modern experimental platforms in quantum science and technology, such as photonic systems [4], ultracold atoms [5-9], optomechanical systems [10][11][12][13] or superconducting circuits [14][15][16], for which driving and losses are omnipresent. Open quantum systems also display emergent physics, in particular dissipative phase transitions and topological phases [40][41][42][43][44][45].Several studies have highlighted the possibility for a continuous-wave driven-dissipative quantum system to reach a non-stationary state in the long time limit in which undamped oscillations arise spontaneously [46][47][48][49][50][51][52]. This phenomenon has been dubbed as boundary or dissipative time crystal (DTC), in analogy with the time crystals in some Hamiltonian systems [53].…”

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Dissipative time crystal in an asymmetric nonlinear photonic dimer

2020

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We investigate the behavior of two coupled non-linear photonic cavities, in presence of inhomogeneous coherent driving and local dissipations. By solving numerically the quantum master equation, either by diagonalizing the Liouvillian superoperator or by using the approximated truncated Wigner approach, we extrapolate the properties of the system in a thermodynamic limit of large photon occupation. When the mean field Gross-Pitaevskii equation predicts a unique parametrically unstable steady-state solution, the open quantum many-body system presents highly non-classical properties and its dynamics exhibits the long lived Josephson-like oscillations typical of dissipative time crystals, as indicated by the presence of purely imaginary eigenvalues in the spectrum of the Liouvillian superoperator in the thermodynamic limit.Open many-body quantum systems [1-3] have become a major field of study over the last decade. The open nature is common to a vast class of modern experimental platforms in quantum science and technology, such as photonic systems [4], ultracold atoms [5-9], optomechanical systems [10][11][12][13] or superconducting circuits [14][15][16], for which driving and losses are omnipresent. Open quantum systems also display emergent physics, in particular dissipative phase transitions and topological phases [40][41][42][43][44][45].Several studies have highlighted the possibility for a continuous-wave driven-dissipative quantum system to reach a non-stationary state in the long time limit in which undamped oscillations arise spontaneously [46][47][48][49][50][51][52]. This phenomenon has been dubbed as boundary or dissipative time crystal (DTC), in analogy with the time crystals in some Hamiltonian systems [53]. Formally, DTCs are associated with the occurrence of multiple eigenvalues of the Liouvillian with vanishing real and finite imaginary part [54][55][56]. The experimental feasibility of DTC has been confirmed by their observation in phosphorousdoped silicon [57]. The research for further platforms showing this phenomenon is very active and important to understand the mechanisms behind the spontaneous breaking of the time-translation symmetry in open quantum many-body systems.One of the main difficulties in the realization of DTCs in real system is related to the fragility of this phase to external perturbations which affect the symmetric structure of the model. Indeed, in most of the cases considered so far, the engineering of the DTCs relies on the exploitation of certain symmetries (either manifest [48,52] or emergent [50]) in the Hamiltonian or in the dissipation mechanism, which can be hard to maintain in real driven-dissipative systems out of equilibrium.In this letter, we show that a DTC can arise in a simple system of two coupled photonic cavities, whose equation of motion does not preserve any symmetry but the timetranslation invariance. In a broad region of the parameter space, the dynamics of this system presents limit cycles associated to parametric instabilities [58], which can be regar...

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“…For meso-and nanoscopic systems, such a steady state can still exhibit significant fluctuations [1]. Beyond the quantum domain, in which such systems have found considerable attention recently, see, e.g., [2][3][4][5][6][7] and refs. therein, colloidal systems provide a major paradigm [8].…”

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Operationally Accessible Bounds on Fluctuations and Entropy Production in Periodically Driven Systems

2019

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For periodically driven systems, we derive a family of inequalities that relate entropy production with experimentally accessible data for the mean, its dependence on driving frequency, and the variance of a large class of observables. With one of these relations, overall entropy production can be bounded by just observing the time spent in a set of states. Among further consequences, the thermodynamic efficiency both of isothermal cyclic engines like molecular motors under a periodic load and of cyclic heat engines can be bounded using experimental data without requiring knowledge of the specific interactions within the system. We illustrate these results for a driven three-level system and for a colloidal Stirling engine. arXiv:1904.08807v1 [cond-mat.stat-mech]

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Period doubling in period-one steady states

Cited by 46 publications

References 31 publications

Topological time crystals

Topological time crystals

Dissipative time crystal in an asymmetric nonlinear photonic dimer

Operationally Accessible Bounds on Fluctuations and Entropy Production in Periodically Driven Systems

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