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In the context of Gross-Pitaevskii theory, we investigate the unconventionalBose-Einstein condensations in the two-species mixture with $p$-wave symmetryin the second band of a bipartite optical lattice. A new imaginary-timepropagation method is developed to numerically determine the $p$-orbitalcondensation. Different from the single-species case, the two-species bosonmixture exhibits two non-equivalent complex condensates in theintraspecies-interaction-dominating regime, exhibiting the vortex-antivortexlattice configuration in the charge and spin channels, respectively. When theinterspecies interaction is tuned across the SU(2) invariant point, the systemundergoes a quantum phase transition toward a checkerboard-like spin densitywave state with a real-valued condensate wavefunction. The influence of latticeasymmetry on the quantum phase transition is addressed. Finally, we present aphase-sensitive measurement scheme for experimentally detecting the UBEC in ourmodel.

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