In the Mott-insulator regime, two species of ultracold atoms in an optical lattice can exhibit the low-energy counterflow motion. We construct effective Hamiltonians for the three classes of the two-species (fermion-fermion, boson-boson, and boson-fermion-type) insulators and reveal the conditions when the resulting ground state supports super-counter-fluidity (SCF), with the alternative being phase segregation. We emphasize a crucial role of breaking the isotopic symmetry between the species for realizing the SCF phase.
We study a behaviour of mixture of two species of ultracold bosons trapped in optical lattice.Using mean-field approximation, we determine the phase diagram of the system for wide range of parameters.We observe that each of the groups of atoms can condense into superfluid state or localize and form the Mott insulator, which yields that the whole system is either superfluid, the Mott insulator, or a mixed state.It appears that introduction of interaction between different kinds of atoms can strongly renormalise the phase diagram.It can alter the critical behaviour modifying multi-criticality of crossing points and order of phase transitions between mixed and superfluid states.
Motivated by recent experiments [Y. J. Lin et al., Nature (London) 471, 83 (2011)], we study Mott phases and superfluid-insulator (SI) transitions of two-species ultracold bosonic atoms in a two-dimensional square optical lattice with nearest-neighbor hopping amplitude
t and in the presence of a spin-orbit coupling characterized by a tunable strength $\ensuremath{\gamma}$. Using both strong-coupling expansion and Gutzwiller mean-field theory, we chart out the phase diagrams of the bosons in the presence of such spin-orbit interaction. We compute the momentum distribution of the bosons in the Mott phase near the SI transition point and show that it displays precursor peaks whose position in the Brillouin zone can be varied by tuning $\ensuremath{\gamma}$. Our analysis of the critical theory of the transition unravels the presence of unconventional quantum critical points at $t/\ensuremath{\gamma}=0$, which are accompanied by emergence of an additional gapless mode in the critical region. We also study the superfluid phases of the bosons near the SI transition using a Gutzwiller mean-field theory that reveals the existence of a twisted superfluid phase with an anisotropic twist angle which depends on $\ensuremath{\gamma}$. Finally, we compute the collective modes of the bosons and point out the presence of reentrant SI transitions as a function of $\ensuremath{\gamma}$ for nonzero
t. We propose experiments to test our theory.