Abstract
We consider a gas of ultracold two-level atoms confined in a cavity, taking account of atomic center-of-mass motion and cavity-mode variations. We use the generalized Dicke model (DM), and analyze separately the cases of a Gaussian, and a standing wave mode shape. Owing to the interplay between external motional energies of the atoms and internal atomic and field energies, the phase-diagrams exhibit novel features not encountered in the standard DM, such as the existence of first- and second-order phase transitions between normal and superradiant phases. Due to the quantum description of atomic motion, internal and external atomic degrees of freedom are highly correlated leading to modified normal and superradiant phases.
Highlights
Generalized Dicke model (DM) and its partition functionWe consider a gas of N ultracold identical two-level atoms, with mass m and energy level separation h , interacting with a single cavity mode with frequency ω
We consider a gas of ultracold two-level atoms confined in a cavity, taking account of atomic center-of-mass motion and cavity-mode variations
We have studied a new regime in the Dicke model (DM)
Summary
We consider a gas of N ultracold identical two-level atoms, with mass m and energy level separation h , interacting with a single cavity mode with frequency ω. Pi and xi are the scaled center-of-mass momentum and position of atom i, respectively, g(x ) the effective position-dependent atom–field coupling and V the mode volume. Provided that the adiabatic potentials do not cross, it is legitimized to perform an adiabatic diagonalization of the internal states [27] In this regime, the single particle Hamiltonian relaxes to two decoupled adiabatic ones h±ad(|α|) =. The single particle Hamiltonian relaxes to two decoupled adiabatic ones h±ad(|α|) = This approximation will be imposed considering a Gaussian mode profile. The justification of the adiabatic approximation applied to the Gaussian mode profile will be discussed at the end of the section Within this regime, the problem has become one of solving for the eigenvalues of two time-independent decoupled Schrödinger equations. It is worth mentioning that the numerics deal with exponentially large numbers, especially for small temperatures, which restrict the analysis to certain ranges
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