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arXiv:2209.12408

Non-equilibrium dynamics of ultracold lattice bosons inside a cavity

Huan Wang, Xiayao He, Shuai Li, Hongrong Li, Bo Liu

Published Sep 26, 2022• 0 citations
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Abstract

We study the non-equilibrium quench dynamics crossing a continuous phase transition between the charge density wave (CDW) and supersolid (SS) phases of a bosonic lattice gas with cavity-mediated interactions. When changing the hopping amplitude in the Hamiltonian as a function of time, we investigate the scaling behavior of the correlation length and vortex density with respect to the quench time and find that there is a threshold of the quench rate separating two distinct scaling regimes. When slowly varying the system below that threshold, we find a power-law scaling as predicted by the Kibble-Zurek mechanism (KZM). While considering fast quench above that threshold, a deviation from the KZM prediction occurs, manifested by a saturation of the defect density. We further show that such distinct scaling behaviors during different dynamic procedures can be understood through comparing the relaxation time and the quench rate.

DOI
10.48550/arxiv.2209.12408

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We study the non-equilibrium quench dynamics crossing a continuous phase transition between the charge density wave (CDW) and supersolid (SS) phases of a bosonic lattice gas with cavity-mediated interactions. When changing the hopping amplitude in the Hamiltonian as a function of time, we investigate the scaling behavior of the correlation length and vortex density with respect to the quench time and find that there is a threshold of the quench rate separating two distinct scaling regimes. When slowly varying the system below that threshold, we find a power-law scaling as predicted by the Kibble-Zurek mechanism (KZM). While considering fast quench above that threshold, a deviation from the KZM prediction occurs, manifested by a saturation of the defect density. We further show that such distinct scaling behaviors during different dynamic procedures can be understood through comparing the relaxation time and the quench rate.
We investigate the quench dynamics of the dipolar bosons in two dimensional optical lattice of square geometry using the time dependent Gutzwiller method. The system exhibits different density orders like the checkerboard and the striped pattern, depending upon the polarization angle of the dipoles. We quench the hopping parameter across the striped density wave (SDW) to striped supersolid (SSS) phase transition, and obtain the scaling laws for the correlation length and topological vortex density, as function of the quench rate. The results are reminiscent of the Kibble-Zurek mechanism (KZM). We also investigate the dynamics from the striped supersolid phase to the checkerboard supersolid phase, obtained by quenching the dipole tilt angle θθθ. This is a first order structural quantum phase transition, and we study the non-equilibrium dynamics from the perspective of the KZM. In particular, we find the number of the domains with checkerboard order follows a power law scaling with the quench rate. This indicates the applicability of the KZM to this first order quantum phase transition.
Universal scaling laws govern the density of topological defects generated while crossing an equilibrium continuous phase transition. The Kibble-Zurek mechanism (KZM) predicts the dependence on the quench time for slow quenches. By contrast, for fast quenches, the defect density scales universally with the amplitude of the quench. We show that universal scaling laws apply to dynamic phase transitions driven by an oscillating external field. The difference in the energy response of the system to a periodic potential field leads to energy absorption, spontaneous breaking of symmetry, and its restoration. We verify the associated universal scaling laws, providing evidence that the critical behavior of nonequilibrium phase transitions can be described by time-average critical exponents combined with the KZM. Our results demonstrate that the universality of critical dynamics extends beyond equilibrium criticality, facilitating the understanding of complex nonequilibrium systems.
In this work, we study the quench dynamics of quantum phases of ultracold neutral bosons trapped in optical lattices. We investigate the validity of the Kibble-Zurek (KZ) scaling laws with the single-site Gutzwiller mean-field (SGMF) and cluster Gutzwiller mean-field (CGMF) theory. With CGMF, we note the evolution of the dynamical wavefunction in the ``impulse" regime of the Kibble-Zurek mechanism. We obtain the power law scalings for the crossover time and defect density with the quench rate predicted by KZ scaling laws. The critical exponents obtained from dynamics are close to their equilibrium values. Furthermore, it is observed that the obtained dynamical critical exponent zzz improves towards the equilibrium value with increasing cluster sizes in CGMF.
The Kibble-Zurek (KZ) hypothesis identifies the relevant time scales in out-of-equilibrium dynamics of critical systems employing concepts valid at equilibrium: It predicts the scaling of the defect formation immediately after quenches across classical and quantum phase transitions as a function of the quench speed. Here we study the crossover between the scaling dictated by a slow quench, which is ruled by the critical properties of the quantum phase transition, and the excitations due to a faster quench, where the dynamics is often well described by the classical model. We estimate the value of the quench rate that separates the two regimes and support our argument using numerical simulations of the out-of-equilibrium many-body dynamics. For the specific case of a ϕ4\phi^4ϕ4 model we demonstrate that the two regimes exhibit two different power-law scalings, which are in agreement with the KZ theory when applied to the quantum and to the classical case. This result contributes to extending the prediction power of the Kibble-Zurek mechanism and to provide insight into recent experimental observations in systems of cold atoms and ions.
The crossing of a continuous phase transition gives rise to the formation of topological defects described by the Kibble-Zurek mechanism (KZM) in the limit of slow quenches. The KZM predicts a universal power-law scaling of the defect density as a function of the quench time. We focus on the deviations from KZM experimentally observed in rapid quenches and establish their universality. While KZM scaling holds below a critical quench rate, for faster quenches the defect density and the freeze-out time become independent of the quench rate and exhibit a universal power-law scaling with the final value of the control parameter. These predictions are verified in several paradigmatic scenarios in both the classical and quantum domains.
In this paper, we study the dynamics of the Bose-Hubbard model with the nearest-neighbor repulsion by using time-dependent Gutzwiller methods. Near the unit filling, the phase diagram of the model contains density wave (DW), supersolid (SS), and superfluid (SF). The three phases are separated by two second-order phase transitions. We study ``slow-quench'' dynamics by varying the hopping parameter in the Hamiltonian as a function of time. In the phase transitions from the DW to SS and from the DW to SF, we focus on how the SF order forms and study scaling laws of the SF correlation length, vortex density, etc. The results are compared with the Kibble-Zurek scaling. On the other hand from the SF to DW, we study how the DW order evolves with generation of the domain walls and vortices. Measurement of first-order SF coherence reveals interesting behavior in the DW regime.