We experimentally demonstrate vibration phase reversal transition in a discrete time-translational symmetry broken cold atomic system by the application of a pulsed bias-field opposite to the existing phase of the symmetry broken vibrational state. The reversal transition depends on the strength hp and the duration Δt of the applied pulse. Consequently, we obtain a hp − Δt phase boundary with a divergent relaxation time τ due to the critical slowdown behavior. Interestingly, the dependence of the dynamic phase boundary and relaxation time on the noise-induced switching rate implies that the system is out of equilibrium, though not so in the Ising model of a spin system.

We discuss the collective and nonequilibrium phenomena that occur in the periodically driven cold atom system with the specific interparticle interaction and the thermal fluctuations. One can deal with the time evolution of the system using the fluctuation-induced switching of particles between the dynamics attractors caused by the thermal fluctuations. Although the corresponding theory looks similar to the classical reaction rate theory represented by the Kramers’ seminal work, one still needs completely new approaches because the systems of our interest are not in thermal equilibrium. The novel methods have been indeed employed to investigate the driven nonlinear oscillators in the presence of fluctuations such as the Josephson junctions, the nano-magnetic oscillators and the microwave cavities. We have analyzed the driven cold atoms using the similar approaches and we have observed, in particular, the unique collective phenomena that result from the competitive and cooperative interplays between the fluctuations and the atom–atom interactions.