Unconventional Bose-Einstein condensation in a system with two species of bosons in the p-orbital bands in an optical 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. An 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 nonequivalent 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 checkerboardlike spin-density wave state with a real-valued condensate wave function. The influence of lattice asymmetry on the quantum phase transition is addressed. Finally, we present a phase-sensitive measurement scheme for experimentally detecting the unconventional Bose-Einstein condensation in our model.