Collective excitations and supersolid behavior of bosonic atoms inside two crossed optical cavities

Abstract

We discuss the nature of symmetry breaking and the associated collective excitations for a system of bosons coupled to the electromagnetic field of two optical cavities. For the specific configuration realized in a recent experiment at ETH [ 1 , 2 ], we show that, in absence of direct intercavity scattering and for parameters chosen such that the atoms couple symmetrically to both cavities, the system possesses an approximate U (1) symmetry which holds asymptotically for vanishing cavity field intensity. It corresponds to the invariance with respect to redistributing the total intensity $I={I}_{1}+{I}_{2}$ between the two cavities. The spontaneous breaking of this symmetry gives rise to a broken continuous translation-invariance for the atoms, creating a supersolid-like order in the presence of a Bose–Einstein condensate. In particular, we show that atom-mediated scattering between the two cavities, which favors the state with equal light intensities ${I}_{1}={I}_{2}$ and reduces the symmetry to ${{\bf{Z}}}_{2}\otimes {{\bf{Z}}}_{2}$ , gives rise to a finite value $\sim \sqrt{I}$ of the effective Goldstone mass. For strong atom driving, this low energy mode is clearly separated from an effective Higgs excitation associated with changes of the total intensity I . In addition, we compute the spectral distribution of the cavity light field and show that both the Higgs and Goldstone mode acquire a finite lifetime due to Landau damping at non-zero temperature.

Keywords

• symmetry breaking
• superradiance
• Goldstone mode
• supersolidity
• cavity QED
• ultracold atoms