Nonlinear, nonequilibrium and collective dynamics in a periodically modulated cold atom system

The physics of critical phenomena in a many-body system far from thermal equilibrium is an interesting and important issue to be addressed both experimentally and theoretically. The trapped cold atoms have been actively used as a clean and versatile simulator for classical and quantum-mechanical systems, deepening understanding of the many-body physics behind. Here we review the nonlinear and collective dynamics in a periodically modulated magneto-optically trapped cold atoms. By temporally modulating the intensity of the trapping lasers with the controlled phases, one can realize two kinds of nonlinear oscillators, the parametrically driven oscillator and the resonantly driven Duffing oscillator, which exhibit the dynamical bistable states. Cold atoms behave not only as the single- particle nonlinear oscillators, but also as the coupled oscillators by the light-induced inter-atomic interaction, which leads to the phase transitions far from equilibrium in a way similar to the phase transition in equilibrium. The parametrically driven cold atoms show the ideal mean-field symmetry-breaking transition, and the symmetry is broken with respect to time translation by the modulation period. Such a phase transition results from the cooperation and competition between the inter-particle interaction and the fluctuations, which lead to the nonlinear switching of atoms between the vibrational states, and the experimentally measured critical characteristics prove it as the ideal mean-field transition class. On the other hand, the resonantly driven cold atoms that possess the coexisting periodic attractors exhibit the kinetic phase transition analogous to the discon- tinuous gas–liquid phase transition in equilibrium, and interestingly the global interaction between atoms causes the shift of the phase-transition boundary. We demonstrate that the temporally driven cold atom system serves as a unique and controllable platform suitable for investigating the nonlinear dynamics of many-body cold atoms far from equilibrium and for relating the relevant dynamics to other domains of physics. The results presented in this article may be useful for better understanding of the fundamentals of critical phenomena occurring in a many-body system far from thermal equilibrium, which still demands further studies both experimental and theoretical.