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We study the Bardeen-Cooper-Shrieffer (BCS) pairing state of a two-component Bose gas with a symmetric spin-orbit coupling. In the dilute limit at low temperatures, this system is essentially a dilute gas of diatomic molecules. We compute the effective mass of the molecule and find that it is anisotropic in momentum space. The critical temperature of the pairing state is about eight times smaller than the Bose-Einstein condensation (BEC) transition temperature of an ideal Bose gas with the same density., Comment: 7 pages, 1 figure

We study a two-component Bose gas with a symmetric spin-orbit coupling, and find that two atoms can form a bound state with any intra- or inter-species scattering length. Consequently, in the dilute limit, the Bardeen-Cooper-Shrieffer (BCS) pairing state of bosons can be formed with weakly-attractive inter-species and repulsive intra-species interactions. The quasiparticle excitation energies are anisotropic due to spin-orbit coupling. This BCS paring state is energetically favored over Bose-Einstein condensation (BEC) of atoms at low densities. As the density increases, there is a first-order transition from the BCS to BEC states., Comment: 6 pages, 3 figures, a few corrections and changes

We studied the atomic momentum distribution for a superposition of Bloch states spreading in the lowest band of an optical lattice after the action of the standing wave pulse. By designing the imposing pulse on this superposed state, an atomic momentum pattern appears with narrower interval between the adjacent peaks that can be far less than the double recoil momentum. The patterns with narrower interval come from the superposition of the action of the designed pulse on many Bloch states with quasi-momenta over the first Brillouin zone, where for each quasi-momentum there is an interference among several lowest bands. Our experimental result of narrow interval peaks is consistent with the theoretical simulation. The patterns of multi modes with different quasi-momenta are helpful for precise measurement and atomic manipulation., Comment: 6 pages, 5 figures

We study fermions and hardcore bosons with long range dipolar interactions at fractional fillings in a topological checkerboard lattice with short-range hoppings up to next-next-nearest neighbors \cite{Neupert2011}. We consider the case that the dipoles are aligned in the perpendicular direction by an external field without the complication of anisotropic interaction. Using exact diagonalization, we find clear signatures of fractional quantum Hall (FQH) states at filling factors 1/3 and 1/5 for fermions (1/2 and 1/4 for bosons) in the lowest Chern band with a robust spectrum gap at moderate dipolar interaction strength. The robustness of these FQH states against long-range interaction tail and band flatness is investigated. When the dipolar interaction decreases, the fermionic FQH states turn into normal states, and the bosonic 1/4-FQH state turns into a superfluid state. The bosonic 1/2-FQH state survives even in the absence of the dipolar interaction, but vanishes when the hard core becomes a soft core with a critical onsite repulsion. In the thin torus limit, the static density structure factors indicates that the FQH state turns into a commensurate charge density wave (CDW) state., Comment: 8 pages, 8 figures

Weyl superconductivity or superfluidity, a fascinating topological state of matter, features novel phenomena such as emergent Weyl fermionic excitations and anomalies. Here we report that an anisotropic Weyl superfluid state can arise as a low temperature stable phase in a 3D dipolar Fermi gas. A crucial ingredient of our model is a rotating external field that generates a direction-dependent two-body effective attraction. Experimental signatures are predicted for cold gases in radio-frequency spectroscopy. The finite temperature phase diagram of this system is studied and the transition temperature of the Weyl superfluidity is found to be within the experimental scope for atomic dipolar Fermi gases., Comment: 6 pages, 5 figures, presentation improved, version as accepted by Phys. Rev. Lett

We study the phase diagram of a dipolar fermi gas at half-filling in a cubic optical lattice with dipole moments aligned along the z-axis. The anisotropic dipole-dipole interaction leads to the competition between pz-wave superfluid and nematic charge-density-wave (CDW) orders at low temperatures. We find that the superfluid phase survives with weak interactions and the CDW phase dominates with strong interactions. In between, the supersolid phase appears as a balance between superfluid and CDW orders. The superfluid density is anisotropic in the supersolid and superfluid phases. In the CDW phase, there is a semimetal to insulator transition with increase of the interaction strength. Experimental implications are discussed., Comment: 12 pages, 4 figures, published version

We show that in a two-component Bose gas with Rashba spin-orbit coupling (SOC) two atoms can form bound states (Rashbons) with any intra-species scattering length. At zero center-of-mass momentum there are two degenerate Rashbons due to time-reversal symmetry, but the degeneracy is lifted at finite in-plane momentum with two different effective masses. A stable Rashbon condensation can be created in a dilute system with weakly attractive intra-species and repulsive inter-species interactions. The critical temperature of Rashbon condensation is about six times smaller than the BEC transition temperature of an ideal Bose gas. Due Rashba SOC, excitations in the Rashbon condensation phase are anisotropic in momentum space., Comment: 13 pages, 3 figures, text and figures updated

In a dipolar Fermi gas, the anisotropic interaction between electric dipoles can be turned into an effectively attractive interaction in the presence of a rotating electric field. We show that the topological $p_{x}+ip_{y}$ superfluid phase can be realized in a single-component dipolar Fermi gas trapped in a 2D square optical lattice with this attractive interaction at low temperatures. The $p_{x}+ip_{y}$ superfluid state has potential applications for topological quantum computing. We obtain the phase diagram of this system at zero temperature. In the weak-coupling limit, the p-wave superfluid phase is stable for all filling factors. As the interaction strength increases, it is stable close to filling factors $n=0$ or $n=1$, and phase separation takes place in between. When the interaction strength is above a threshold, the system is phase separated for any $0

We study the normal state of a 3-$d$ homogeneous dipolar Fermi gas beyond the Hartree-Fock approximation. The correlation energy is found of the same order as the Fock energy, unusually strong for a Fermi-liquid system. As a result, the critical density of mechanical collapse is smaller than that estimated in the Hartree-Fock approximation. With the correlation energy included, a new energy functional is proposed for the trapped system, and its property is explored., Comment: 10 pages, 2 figures

In a dipolar Fermi gas, the dipole-dipole interaction between fermions can be turned into a dipolar Ising interaction between pseduospins in the presence of an AC electric field. When trapped in a 2D optical lattice, such a dipolar Fermi gas has a very rich phase diagram at zero temperature, due to the competition between antiferromagnetism and superfluidity. At half filling, the antiferromagnetic state is the favored ground state. The superfluid state appears as the ground state at a smaller filling factor. In between there is a phase-separated region. The order parameter of the superfluid state can display different symmetries depending on the filling factor and interaction strength, including d-wave ($d$), extend s-wave ($xs$), or their linear combination ($xs+i\times d$). The implication for the current experiment is discussed., Comment: 11 pages, 3 figures, references updated

We study the effect of the induced interaction on the superfluidtransition temperature of a spin-polarized Fermi gas. In the BCS limit, the polarization is very small in the superfluid state, and the effect of the induced interaction is almost the same as in the spin-balanced case. The temperature Tt and the polarization Pt of the tricritical point are both reduced from mean-field results by a factor about 2.22. This reduction is also significant beyond the BCS limit. In the unitary limit, we find (Pt,Tt/TF)=(0.42,0.16), in comparison with mean-field and experimental results., Comment: 6 pages, 2 figures

In a half-filled Hubbard model on a square lattice, the next-nearest-neighbor hopping causes spin frustration, and the collinear antiferromagnetic (CAF) state appears as the ground state with suitable parameters. We find that there is a metal-insulator transition in the CAF state at a critical on-site repulsion. When the repulsion is small, the CAF state is metallic, and a van Hove singularity can be close to the Fermi surface, resulting in either a kink or a discontinuity in the magnetic moment. When the on-site repulsion is large, the CAF state is a Mott insulator. A first-order transition from the CAF phase to the antiferromagnetic phase and a second-order phase transition from the CAF phase to the paramagnetic phase are obtained in the phase diagram at zero temperature., Comment: 5 pages, 5 figures, two columns

Bose-Einstein condensation (BEC) of Feshbach molecules in a homogeneous Bose gas is studied at finite temperatures in a single-channel mean-field approach where the Hartree-Fock energy and pairing gap are determined self-consistently. In the molecular-BEC state, the atomic excitation is gapped and the molecular excitation is gapless. The binding energy of Feshbach molecules is shifted from the vacuum value due to many-body effect. When the scattering length $a_s$ of atoms is negative, the system is subject to mechanical collapse due to negative compressibility. The system is stable in most regions with positive scattering lengths. However at low temperatures near the resonance, the molecular-BEC state vanishes, and the coherent mixture of atomic and molecular BEC is subject to mechanical collapse., Comment: 13 pages, 4 figures

We study the effect of the induced interaction on the superfluid transition temperature of a Fermi gas with a BEC-BCS crossover. The Gorkov-Melik-Barkhudarov theory about the induced interaction is extended from the BCS side to the entire crossover, and the pairing fluctuation is treated in the approach by Nozi\`{e}res and Schmitt-Rink. At unitarity, the induced interaction reduces the transition temperature by about twenty percent. In the BCS limit, the transition temperature is reduced by a factor about 2.22, as found by Gorkov and Melik-Barkhudarov. Our result shows that the effect of the induced interaction is important both on the BCS side and in the unitary region., Comment: 11 pages, 3 figures, to be published in PRA

The Ginzburg-Landau theory of a trapped Fermi gas with a BEC-BCS crossover is derived by the path-integral method. In addition to the standard Ginzburg-Landau equation, a second equation describing the total atom density is obtained. These two coupled equations are necessary to describe both homogeneous and inhomogeneous systems. The Ginzburg-Landau theory is valid near the transition temperature $T_c$ on both sides of the crossover. In the weakly-interacting BEC region, it is also accurate at zero temperature where the Ginzburg-Landau equation can be mapped onto the Gross-Pitaevskii (GP) equation. The applicability of GP equation at finite temperature is discussed. On the BEC side, the fluctuation of the order parameter is studied and the renormalization to the molecule coupling constant is obtained., Comment: 16 pages, 2 figures, to be published in PRA