Switchability of multimodal optical phases in a leaky and nonlinear quantum cavity
S. Samimi, Mohammad Mehdi Golshan · Physical Review A · 2021
In the present report, the question of U(1) symmetry breaking in a system of atoms and electromagnetic fields, interacting inside a leaky cavity, filled with a nonlinear medium, is addressed. In particular, the ${Z}_{2}$ discrete symmetry of the system and the emergence of optical phases are fully discussed. For the nonlinearity of a general order, with an electromagnetic field of any number of modes, conditions under which the resulting field-field interactions destroy the U(1) (and ${Z}_{2}$) symmetry are determined. We then apply the theory to the case of a collection of two-level atoms and three electromagnetic modes. Taking one of the fields as a classically adjustable pumping one, it is demonstrated that the quantized field-field coupling profoundly depends upon the pump field strength. The presence of two competing phenomena, namely, the cavity photonic dissipation and nonlinearity, is shown to lead the system towards steady behavior. The steady-state solutions to the atomic population and field quadratures exhibit the normal and superradiant phases, depending on the strengths of pumping field and atom-field couplings. The conditions for the stability of such steady-state solutions are also discussed in detail. A notable result of the present article is that by adjusting the parameters involved in the system one can switch from the normal to electric and/or magnetic superradiant phases.