Classical Dynamics of a Two-species Bose-Einstein Condensate in the Presence of Nonlinear Maser Processes

Abstract

The stability analysis of a generalized Dicke model, in the semi-classical limit, describing the interaction of a two-species Bose-Einstein condensate driven by a quantized field in the presence of Kerr and spontaneous parametric processes is presented. The transitions from Rabi to Josephson dynamics are identified depending on the relative value of the involved parameters. Symmetry-breaking dynamics are shown for both types of coherent oscillations due to the quantized field and nonlinear optical processes. IntroductionA great deal of attention has been granted to research about unifying concepts in classical and quantum physics through experimental demonstrations involving Bose-Einstein Condensates (BECs) at a macroscopic scale [1]. For example, by considering BECs loaded in a double-well potential, the quantum tunnelling between two trapped condensates provides a possibility to study and understand symmetry-breaking, self-trapping, and Josephson oscillation; all of them are fundamental problems in quantum physics. Macroscopic quantum self-trapping [2] and bosonic Josephson junction [3] have been demonstrated recently, and successfully described by a mean-field approach. The realization of these macroscopic quantum self-trapped modes opens up new avenues for research; e.g., generation of squeezed atomic states [4] and atomic interferometry [5].

The exact solution of generalized Dicke models via Susskind–Glogower operators

“…Furthermore, the general Hamiltonian (2) and its reductions are experimentally feasible in cavity-and circuit-QED as well as trapped ions. It may also be possible to realize some of these models with two-mode Bose-Einstein condensates coupled to radiation fields [15,[23][24][25][26].…”