Stability of $p$-orbital Bose-Einstein condensates in optical checkerboard and square lattices

TL;DR

This paper studies the stability of $p$-orbital Bose-Einstein condensates in square and checkerboard optical lattices, revealing that the checkerboard lattice can host dynamically stable $p$-orbital states, unlike the square lattice.

Contribution

It provides the first numerical analysis of $p$-orbital BEC stability in realistic lattice potentials, identifying conditions for dynamical stability in checkerboard lattices.

Findings

Staggered orbital-current state is the lowest-energy state in the $p$ band.

The $p$-orbital state exhibits Landau instability in both lattices.

Dynamical stability is achieved only in the checkerboard lattice.

Abstract

We investigate $p$-orbital Bose-Einstein condensates in both the square and checkerboard lattice by numerically solving the Gross-Pitaevskii equation. The periodic potential for the latter lattice is taken exactly from the recent experiment [Nature Phys. 7, 147 (2011)]. It is confirmed that the staggered orbital-current state is the lowest-energy state in the $p$ band. Our numerical calculation further reveals that for both lattices the staggered $p$-orbital state suffers Landau instability but the situation is remarkably different for dynamical instability. A dynamically stable parameter region is found for the checkerboard lattice, but not for the square.