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Physical review. E

Scaling of thermal hysteretic behavior in a parametrically modulated cold atomic system

Wanhee Lee, Ji-Hyoun Kim, Jong Geun Hwang, Heung‐Ryoul Noh, Wonho Jhe

Published Sep 30, 2016• 9 citations
Publisher

Abstract

We observe the hysteresis of a spontaneous symmetry breaking (SSB) transition in a parametrically modulated magneto-optical trap by sweeping the total number of atoms and study thermal hysteretic behavior in the system by measuring the scaling exponent of hysteresis. It is shown that the relaxation time of the order parameter in the SSB transition becomes larger near the critical number. The scaling exponent of the hysteresis area with number sweeping rate is found to be 0.64±0.04, which is consistent with the value in the mean-field model.

DOI
10.1103/physreve.94.032141

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We have observed spontaneous symmetry breaking of the population of Brownian particles between two moving potentials in the spatiotemporally symmetric system. Cold atoms preferentially occupy one of the dynamic double-well potentials, produced in the parametrically driven dissipative magneto-optical trap far from equilibrium, above a critical number of atoms. We find that the population asymmetry, which may be interpreted as the biased Brownian motion, can be qualitatively described by the mean-field Ising-class phase transition. This in situ study may be useful for investigation of dynamic phase transition or temporal behavior of critical phenomena.
This chapter describes the experimental and theoretical studies of a spontaneous time-translation symmetry breaking transition in a non-equilibrium cold atom system. Such studies prepare two vibrating atomic clouds by periodically modulating the laser intensity in a magneto-optical trap (MOT). For a comparatively small total number of trapped atoms the clouds have equal populations, a consequence of fluctuation-induced inter-cloud transitions. As the total number of atoms is increased, spontaneous breaking of the discrete time-translation symmetry is observed with respect to the modulation period. The measured critical exponents and the frequency dispersion of the response show an ideal mean-field transition behaviour. The symmetry breaking is due to the modification of fluctuational dynamics by the interatomic interaction. The chapter provides a theoretical model based on the activation energy and master equation which explains the experimental results well. The enhancement of the fluctuation which cannot be described by the mean-field model, is also discussed.
We realize an ideal mean-field transition of time-translation symmetry in a periodically-driven atomic system. The symmetry in steady-state oscillatory atomic motions spontaneously changes with the total number of atoms due to the interplay between inter-atomic interactions which originate from the attenuation effects in the trapping laser light and thermal fluctuations. A large separation of the time scales governing the transition suppresses the spatial dependence of the system dynamics, leading to a mean-field behavior even close to the transition point.
We have studied in this paper,by performing the Monte Carlo numerical simulation,both the hysteretic scaling and the dynamical phase transition of a three-dimen sional,(3D) classical X-Y model driven by an sinusoidally oscillating external m agnetic field.A scaling formula has been worked out which relates the hysteresis loop area with the amplitude h0 and frequency ω of the external fie ld as wel l as the reduced temperature T/Tc of the system in the form:Area～hα0ωβ(1-T/Tc)γ.The best-fit expo nents are α=0.57,β=0.34 and γ=0.9.The 3D X- Y model also characterizes a distinctive discrepancy in dynamical transition fea ture after short and long term evolution of magnetization,respectively.Our simul ation disclosed that the short-term evolution of magnetization (period number≤1 0) attains the symmetry-breaking of system with a nonzero dynamical order parame ter (Q≠0) at a either critical amplitude h0c or frequency ωc.The symme try-breaking in short term,however,evolves steadily into a symmetric disorder st ate (Q=0) after a longer term relaxation of system.The specific relaxation times at which the Q value becomes zero from nonzero increase evidently as the temper ature of system drops.