Quality of variational ground states for a two-state system coupled to phonons

Abstract

We generalize the variational approach proposed by Chen, Zhang, and Wu [Phys. Rev. B 40, 11 326 (1989)] to the ground state of a two-level system coupled to a single boson mode. The resulting displaced-squeezed state is compared to the true ground state (calculated numerically), and to further variational states, by computing energy differences and overlaps. These states are able to describe a bifurcation occurring in the ground state of the quantum system as well as in the equilibrium state of its classical limit, and they are excellent approximations to the true ground state.