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The physics of critical phenomena in a many-body system far from thermalequilibrium is an interesting and important issue to be addressed bothexperimentally and theoretically. The trapped cold atoms have been activelyused as a clean and versatile simulator for classical and quantum-mechanicalsystems, deepening understanding of the many-body physics behind. Here wereview the nonlinear and collective dynamics in a periodically modulatedmagneto-optically trapped cold atoms. By temporally modulating the intensity ofthe trapping lasers with the controlled phases, one can realize two kinds ofnonlinear oscillators, the parametrically driven oscillator and the resonantlydriven Duffing oscillator, which exhibit the dynamical bistable states. Coldatoms behave not only as the single-particle nonlinear oscillators, but also asthe coupled oscillators by the light-induced inter-atomic interaction, whichleads to the phase transitions far from equilibrium in a way similar to thephase transition in equilibrium. The parametrically driven cold atoms show theideal mean-field symmetry-breaking transition, and the symmetry is broken withrespect to time translation by the modulation period. Such a phase transitionresults from the cooperation and competition between the inter-particleinteraction and the fluctuations, which lead to the nonlinear switching ofatoms between the vibrational states, and the experimentally measured criticalcharacteristics prove it as the ideal mean-field transition class. On the otherhand, the resonantly driven cold atoms that possess the coexisting periodicattractors exhibit the kinetic phase transition analogous to the discontinuousgas-liquid phase transition in equilibrium, and interestingly the globalinteraction between atoms causes the shift of the phase-transition boundary.

Nonlinear, Nonequilibrium and Collective Dynamics in a Periodically Modulated Cold Atom System