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Recent experiments with ultracold lanthanide atoms which are characterized by a large magnetic moment have revealed the crucial importance of beyond-mean-field corrections in understanding the dynamics of the gas. We study how the presence of an external optical lattice modifies the structure of the corrections. We find that deep in the superfluid regime the equation of state is well described by introducing an anisotropic effective mass. However, for a deep lattice we find terms with anomalous density dependence which do not arise in free space. For a one-dimensional lattice, the relative orientation of the dipole axis with respect to the lattice plays a crucial role and the beyond-mean-field corrections can be either enhanced or suppressed.
In the previous papers, we studied the bosonic t-J mode and derived an effective field theory, which is a kind of quantum XY model. The bosonic t-J model is expected to be realized by experiments of two-component cold atoms in an optical lattice. In
The recent advances in creating nearly degenerate quantum dipolar gases in optical lattices are opening the doors for the exploration of equilibrium physics of quantum systems with anisotropic and long-range dipolar interactions. In this paper we stu
We study the role of the Dipolar-Induced Resonance (DIR) in a quasi-one-dimensional system of ultracold bosons. We first describe the effect of the DIR on two particles in a harmonic trap. Then, we consider a deep optical lattice loaded with ultracol
We investigate a binary mixture of bosonic atoms loaded into a state-dependent honeycomb lattice. For this system, the emergence of a so-called twisted-superfluid ground state was experimentally observed in [Soltan-Panahi et al., Nat. Phys. 8, 71 (20
We present a detailed beyond-mean-field analysis of a weakly interacting Bose gas in the crossover from three to low dimensions. We find an analytical solution for the energy and provide a clear qualitative picture of the crossover in the case of a b