We investigated effects of a Rashba-type spin-orbit coupling (SOC) on the condensed density and superfluid density tensor of a two-component Fermi gas in the BCS-BEC crossover at zero temperature. In anisotropic three dimensions (3D), we found that SOC has an opposite effect on condensation (enhanced) and superfluidity (suppressed in the SOC direction) and this effect becomes most pronounced for very weak interactions and the SOC strength being larger than a characteristic value. Furthermore, as functions of SOC strength, the condensed density changes monotonously for all interaction parameters while the superfluid density has a minimum when the interaction parameter is below a critical value. We also discussed the isotropic two dimensional (2D) case where analytical expressions for the gap and number equations were obtained and the same phenomena was found as that of the 3D case. Motivated by this new progress, effect of SOC on the pairing and superfluid nature of Fermi systems in the BCS-BEC crossover has become a cutting-edge field recently because of its broad interests in condensed matter physics. The spintriplet pairing fields and anisotropic nature of the superfluidity induced by SOC were investigated in [6] and proposal for detecting this phenomenon was given in [7] through measurement of the momentum distribution and single-particle spectral function. On the other hand, SOC significantly enhances the pairing phenomena as was shown by the exact two-body solutions [8] where a new bound state (rashbons) emerges and many-body mean-field calculations [9][10][11].In this Letter, we study the effects of SOC on two fundamental quantities: condensation and superfluidity. Condensation is well described by the concept of off-diagonal-longrange-order [12]. However, Landau's approach of calculation of superfluid density (tensor) is only applicable to systems satisfying Galilean transformation [13]. For systems in the presence of SOC obviously violating Galilean transformation, we gave the general method of calculating the superfluid density tensor. Furthermore, we found that at zero temperature, SOC enhances condensation while suppresses superfluidity in both 3D and 2D. Up to our knowledge, this is the first demonstration of such opposite behaviors of condensation and superfluidity driven by SOC and renews our previous knowledge that

We investigate a dilute Bose gas confined in a tight one-dimensional (1D) optical lattice plus a superimposed random potential at zero temperature. Accordingly, the ground state energy, quantum depletion and superfluid density are calculated. The presence of the lattice introduces a crossover to the quasi-2D regime, where we analyze asymptotically the 2D behavior of the system, particularly the effects of disorder. We thereby offer an analytical expression for the ground state energy of a purely 2D Bose gas in a random potential. The obtained disorder-induced normal fluid density nn and quantum depletion n d both exhibit a characteristic 1/ ln 1/n2Da 2 2D dependence. Their ratio nn/n d increases to 2 compared to the familiar 4/3 in lattice-free 3D geometry, signifying a more pronounced contrast between superfluidity and Bose-Einstein condensation in low dimensions. Conditions for possible experimental realization of our scenario are also proposed.

We investigate the quantum phases of a dipolar Bose-Einstein condensate (BEC) in an optical lattice based on the extended Bose-Hubbard model taking into account the three-body scattering. Accordingly, the phase diagrams from the superfluid state to the Mott-insulator state for such BEC systems are obtained and analyzed, employing both the mean-field approach and the functional-integral method. In particular, we explore the combined effects of three-body interaction and dipole-dipole interaction on the insulating lobes in detail. The experimental scenario is also discussed.