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Abstract: We theoretically investigate a polarized dipolar Fermi gas in free expansion. The dipolar-dipolar inter-particle interaction deforms phase-space distribution in trap and also in the expansion. We exactly predict the minimal quadrupole deformation in the expansion for the high-temperature Maxwell-Boltzmann (MB) and zero-temperature Thomas-Fermi (TF) gases in the Hartree-Fock and Landau-Vlasov approaches by developing a new deformation ansatz. In conclusion, we reveal a scaling law associated with the Liouville's theorem in the long-time behaviors of the MB and TF gases and also provide a proper theoretical approach to develop

Abstract: We use Thomas-Fermi approximation to investigate the density variations of an interacting three-component normal Fermi gas in a harmonic trap. We consider both attractive and repulsive interactions between different pairs of fermions and study the effect of population imbalance on densities. We find that the density profiles significantly deviate from those of non-interacting profiles and extremely sensitive to the interactions and population imbalance. Unlike two-component Fermi systems, we find density imbalance in the trap even for balanced populations. For some range of parameters, one component completely repels from the trap center giving rise a donut shape density profile.

Abstract: We consider a strongly interacting ${}^{6}$Li-${}^{40}$K mixture, which is imbalanced both in the masses and the densities of the two fermionic species. At present, it is the experimentalist's favorite for reaching the superfluid regime. We construct an effective thermodynamic potential that leads to excellent agreement with Monte Carlo results for the normal state. We use it to determine the universal phase diagram of the mixture in the unitarity limit, where we find, in contrast to the mass-balanced case, the presence of a Lifshitz point. This

Abstract: We investigate one dimensional attractive Fermi gases in spin-dependent optical lattices. Starting from the asymmetric Hubbard model, we show that three-body bound states - ``trimers'' - exist as soon as the two tunneling rates are different. We calculate the binding energy and the effective mass of a single trimer. We then show numerically that for finite commensurate densities $n_\uparrow=n_\downarrow/2$ an energy gap appears, implying that the gas is a one-component Luttinger liquid of trimers with suppressed superfluid ordering. The boun

Abstract: Using mean-field theory, we study the equilibrium properties of boson-fermion mixtures confined in a harmonic pancake-shaped trap at zero temperature. When the modulus of the s-wave scattering lengths are comparable to the mixture thickness, two-dimensional scattering events introduce a logarithmic dependence on density in the coupling constants, greatly modifying the density profiles themselves. We show that for the case of a negative boson-fermion three-dimensional s-wave scattering leng

Abstract: We study the parity effect of the particle number in the interference fringes of a Bose-Einstein condensate released from a double-well potential. For a coherently splitting condensate in the double-well potential, with a decoupled two-mode Bose-Hubbard model, there is well-known phase diffusion because of interatomic interactions. After a specific holding time of the double-well potential, the phase diffusion will make the interference patterns in the density distribution depend strongly on the parity of the total particle number by further overlapping two condensates. This p

Abstract: We propose to probe the quantum ground state of a spin-1 Bose-Einstein condensate with the transmission spectra of an optical cavity. By choosing a circularly polarized cavity mode with an appropriate frequency, we can realize coupling between the cavity mode and the magnetization of the condensate. The cavity transmission spectra then contain information of

Abstract: Starting from the three-dimensional Gross-Pitaevskii equation we derive a 1D generalized nonpolynomial Schrodinger equation, which describes the dynamics of Bose-Einstein condensates under the action of a generic potential in the longitudinal axial direction and of an anisotropic harmonic potential in the transverse radial direction. This equation reduces to the familiar 1D nonpolynomial Schrodinger equation [Phys. Rev. A 65, 043614 (2002)] in the case of isotropic transverse harmonic confinement. In addition, we show that if the longitudinal potential models a periodic optical lattice the 3D GPE can be mapped into a 1D generalized discrete nonpolynomial Schrodinger equation.