A comparison of Positive-P and truncated Wigner methods for the dynamics of a minimal atom-cavity model

Abstract

We investigate various phase-space methods for simulating the Dicke model. One such phase-space method is the positive-P representation. This method is implemented by transforming the Hamiltonian using the Schwinger boson representation. The resulting differential equations for the positive-P representation yield a nondiagonal diffusion matrix. Compared to dissipative discrete truncated Wigner method, the positive-P representation applied to the Dicke model produces divergent results, signalling the breakdown of the method, at relatively early times. Lastly, we compare the dynamics for collective and individual spins.