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Physical Review A

Effect of dipole-dipole interaction on unpolarized ultracold fermionic gases in a two-dimensional optical lattice

Takayuki Watanabe

Published Nov 23, 2009• 8 citations
Publisher

Abstract

We study effects of the dipole-dipole interaction on fermionic cold atomic gases in two-dimensional optical lattice. We calculate spin and density correlation functions within the random-phase approximation. It is shown that the spin-correlation functions of spin components perpendicular to the lattice plane show a characteristic peak structure different from that of the parallel component. We study $s$-wave and $d$-wave superfluidity induced by the spin and density correlations and show that the dipole-dipole interaction assists the $d$-wave superfluidity.

DOI
10.1103/physreva.80.053621

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We study effects of the dipole-dipole interaction on fermionic cold atomic gases in two-dimensional optical lattice. We calculate spin and density correlation functions within the random-phase approximation. It is shown that the spin-correlation functions of spin components perpendicular to the lattice plane show a characteristic peak structure different from that of the parallel component. We study sss-wave and ddd-wave superfluidity induced by the spin and density correlations and show that the dipole-dipole interaction assists the ddd-wave superfluidity.
Many-body effects on superfluidity and transition temperatures are calculated for optical lattices and uniform systems with ultracold multi-component Fermi gases. The induced interactions depend sensitively on the interactions between the multi-components and their densities. The s- and d-wave pairing gaps and critical temperatures are calculated for optical lattices at low (dilute) filling as well as near half filling to leading orders in the interaction strength with and without induced interactions. They can deviate strongly from dilute two-component systems and affect the phase diagram. In two dimensional optical lattices the induced interactions are singular at half filling and strongly affect s- and d-wave superfluidity.
We investigate two-component ultracold fermionic atoms with attractive interactions trapped in a two-dimensional optical lattice at zero temperature. By introducing a superfluid trial state with spatially modulated order parameters, we perform the variational Monte Carlo simulations to treat the correlation effects beyond mean-field treatments. It is shown that there appears a strong tendency to the formation of a density wave state in the regions with specific values of local atom density. We then analyze two kinds of perturbations to the superfluid state and show that a coexisting state of superfluid and density wave ordering, a sort of supersolid state, can be stabilized. It is discussed how the trap potential and the resulting spatial modulation of the superfluid state affect the momentum distributions and the noise correlation functions.
We investigate effects of optical lattice potential in one- and two-dimensional two-component trapped Fermi gases with population imbalances. Using the exact diagonalization and the density matrix renormalization group methods complementarily, we calculate the atom-density profile from the ground state many-body wave function as a function of attractive interaction strength for various population imbalances. The numerical results reveal that although a phase separation between the superfluid core and the shell cloud of excess atoms occurs as observed in experiments without the optical lattice, the population imbalance generally remains in the core region in contrast to the nonlattice cases. The essence of the numerical results in a strong attractive regime can be explained by an effective model composed of Cooper pairs and excess major fermions.
We model a system of ultracold fermionic dipolar molecules on a two-dimensional square lattice. Assuming that the molecules are in their nondegenerate hyperfine ground state, and that the dipole moment is polarized perpendicular to the plane (as in the recent experiments on 40K^{40}\mathrm{K}40K-87Rb^{87}\mathrm{Rb}87Rb molecules), we approximate these molecules as spinless fermions with long-range repulsive dipolar interactions. We use mean-field theory to obtain the restricted phase diagram as a function of the filling, the strength of interaction, and the temperature. We find a number of ordered density-wave phases in the system, as well as phase separation between these phases. A Monte Carlo analysis shows that the higher-period phases are usually suppressed in the exact solution.
We study a system of ultracold fermionic polar molecules in a two-dimensional square lattice interacting via both the long-range dipole-dipole interaction and a short-range on-site attractive interaction. Singlet-superfluid, change density wave, and supersolid phases are found to exist in the system. We map out the zero-temperature phase diagram and find that the supersolid phase is considerably stabilized by the dipole-dipole interaction and thus can exist over a large region of filling factors. We study the melting of the supersolid phase with increasing temperature, map out a finite-temperature phase diagram of the system at fixed filling, and determine the parameter region where the supersolid phase can possibly be observed in experiments.
The density-density correlations of ultracold Bosons released from a two-dimensional square optical lattice are investigated based on the quantum phase field U (1) rotor field. With the effects of the particle number fluctuations and the phase degrees of freedom taken into consideration, the theory can be used to describe the cold atom system with strong interaction. Using this theory, the characteristics of ultracold atom gas in the process in which the superfluid state of optical lattice transits to insulating state, are well described. The results show that in the patterns of the density-density correlations, the continuous diagonal lines gradually transit to scattered peaks. The results match the experimental ones. In addition, the effects of the quantum depletion on the density-density correlation are also included in the result, and the relevant conclusions are also consistent with the existing theoretical and experimental results.