Unconventional Bose-Einstein Condensation in a System of Two-species Bosons in the p-orbital Bands of a Bipartite Lattice

In the context of Gross-Pitaevskii theory, we investigate the unconventional Bose-Einstein condensations in the two-species mixture with $p$-wave symmetry in the second band of a bipartite optical lattice. A new imaginary-time propagation method is developed to numerically determine the $p$-orbital condensation. Different from the single-species case, the two-species boson mixture exhibits two non-equivalent complex condensates in the intraspecies-interaction-dominating regime, exhibiting the vortex-antivortex lattice configuration in the charge and spin channels, respectively. When the interspecies interaction is tuned across the SU(2) invariant point, the system undergoes a quantum phase transition toward a checkerboard-like spin density wave state with a real-valued condensate wavefunction. The influence of lattice asymmetry on the quantum phase transition is addressed. Finally, we present a phase-sensitive measurement scheme for experimentally detecting the UBEC in our model.