Collective spontaneous emission of two entangled atoms near an oscillating mirror

We consider the cooperative spontaneous emission of a system of two identical atoms, interacting with the electromagnetic field in the vacuum state and in the presence of an oscillating mirror. We assume that the two atoms, one in the ground state and the other in the excited state, are prepared in a correlated (symmetric or antisymmetric) {\em Bell}-type state. We also suppose that the perfectly reflecting plate oscillates adiabatically, with the field modes satisfying the boundary conditions at the mirror surface at any given instant, so that the time-dependence of the interaction Hamiltonian is entirely enclosed in the instantaneous atoms-wall distance. Using time-dependent perturbation theory, we investigate the spectrum of the radiation emitted by the two-atom system, showing how the oscillation of the boundary modifies the features of the emitted spectrum, which exhibits two lateral peaks not present in the case of a static boundary. We also evaluate the transition rate to the collective ground state of the two-atom system in both cases of the superradiant (symmetric) and subradiant (antisymmetric) state. We show that it is modulated in time, and that the presence of the oscillating mirror can enhance or inhibit the decay rate compared to the case of atoms in vacuum space or near a static boundary. Our results thus suggest that a dynamical (i.e. time-modulated) environment can give new possibilities to control and manipulate radiative processes of atoms or molecules nearby, such as the cooperative decay, and strongly indicate a similar possibility for other radiative processes, for example the resonance interaction and the energy transfer between atoms or molecules.