Lattice and continuum model for ultra-cold atoms in a crossed-cavity system*

Recent experiments by ETH and MIT groups have reported on the formation of a super-solid, respectively in scalar and spinorial ultra-cold atomic systems, an enigmatic phase of matter that shows superfluidity and solid-like density modulation, simultaneously. In this paper [1], we derive the extended Bose-Hubbard Hamiltonian for a Bose-Einstein condensate loaded in a crossed-cavity set-up. Subsequently, in the continuum limit, we obtain the Gross-Pitaevskii energy functional and the Gross-Pitaevskii equations for the superfluid order parameters for such a super-solid phase and discuss its significance.

[1] Poornima Shakya, Amulya Ratnakar, and Sankalpa Ghosh, to be submitted.