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arXiv:1503.04534 · Physical Review A

Swallowtail structure in Fermi superfluids with periodically modulated interactions

Dongyang Yu, Wei Yi, Wei Zhang

Published Sep 24, 2015• 6 citations
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Abstract

We study the superfluid flow in a quasi-one-dimensional Fermi gas with spatially modulated interactions induced by an optical Feshbach resonance. Due to the competition between the periodicity of the modulated interaction and the nonlinearity of the background interaction, an interesting swallowtail structure emerges in the energy spectrum under appropriate parameters. As the interaction strengths are tuned, the swallowtail structure may disappear, giving rise to various different states on a rich phase diagram. We investigate the spatial distribution of the order parameter and the particle density under various parameters, which are useful for the experimental detection of the interesting phases in these systems.

DOI
10.1103/physreva.92.033623

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We study the superfluid flow in a quasi-one-dimensional Fermi gas with spatially modulated interactions induced by an optical Feshbach resonance. Due to the competition between the periodicity of the modulated interaction and the nonlinearity of the background interaction, an interesting swallowtail structure emerges in the energy spectrum under appropriate parameters. As the interaction strengths are tuned, the swallowtail structure may disappear, giving rise to various different states on a rich phase diagram. We investigate the spatial distribution of the order parameter and the particle density under various parameters, which are useful for the experimental detection of the interesting phases in these systems.
We investigate the energy band structure of the superfluid flow of ultracold dilute Fermi gases in a one-dimensional optical lattice along the BCS to Bose-Einstein condensate (BEC) crossover within a mean-field approach. In each side of the crossover region, a loop structure (swallowtail) appears in the Bloch energy band of the superfluid above a critical value of the interaction strength. The width of the swallowtail is largest near unitarity. Across the critical value of the interaction strength, the profiles of density and pairing field change more drastically in the BCS side than in the BEC side. It is found that along with the appearance of the swallowtail, there exists a narrow band in the quasiparticle energy spectrum close to the chemical potential, and the incompressibility of the Fermi gas consequently experiences a profound dip in the BCS side, unlike in the BEC side.
The system of a cold atomic gas in an optical lattice is governed by two factors: nonlinearity originating from the interparticle interaction, and the periodicity of the system set by the lattice. The high level of controllability associated with such an arrangement allows for the study of the competition and interplay between these two, and gives rise to a whole range of interesting and rich nonlinear effects. This review covers the basic idea and overview of such nonlinear phenomena, especially those corresponding to extended states. This includes “swallowtail” loop structures of the energy band, Bloch states with multiple periodicity, and those in “nonlinear lattices”, i.e., systems with the nonlinear interaction term itself being a periodic function in space.
Optical Feshbach resonance is capable of inducing spatially varying interactions in ultra-cold atoms. Its applications to pancake-shaped clouds of bosons and fermions enable one to study several fresh phenomena. We examine possibilities of inducing counter-intuitive structures such as creating a superfluid enclave inside a Mott insulator for bosons and a normal-gas core enclosed by a superfluid shell for fermions. We discuss feasible experimental setups and signatures of those interesting structures, which can be very different from common structures observed in experiments so far. While a superfluid enclave in a Mott insulator can be useful for constructing atomic devices for atomtronics, superconducting islands observed in scanning-tunneling microscopy of heavily underdoped high-temperature superconductors may be studied with cold Fermi gases with spatially varying attractions.
We study the phase separation of a spin-polarized Fermi gas with spin-orbit coupling near a wide Feshbach resonance. As a result of the competition between spin-orbit coupling and population imbalance, the phase diagram for a uniform gas develops a rich structure of phase separation involving topologically nontrivial gapless superfluid states. We then demonstrate the phase separation induced by an external trapping potential and discuss the optimal parameter region for the experimental observation of the gapless superfluid phases.
We study the superfluid transition in a quasi-two-dimensional Fermi gas with a magnetic field tuning through a Feshbach resonance. Using an effective two-dimensional Hamiltonian with renormalized interaction between atoms and dressed molecules, we investigate the Berezinskii-Kosterlitz-Thouless transition temperature by studying the phase fluctuation effect. We also take into account the trapping potential in the radial plane and discuss the number and superfluid density distributions. These results can be compared to experimental outcomes for gases prepared in one-dimensional optical lattices.
We propose an experimental protocol to study ppp-wave superfluidity in a spin-polarized cold Fermi gas tuned by an sss-wave Feshbach resonance. A crucial ingredient is to add a quasi-one-dimensional optical lattice and tune the fillings of two spins to the sss and ppp band, respectively. The pairing order parameter is confirmed to inherit ppp-wave symmetry in its center-of-mass motion. We find that it can further develop into a state of unexpected $\ensuremath{\pi}$-phase modulation in a broad parameter regime. Experimental signatures are predicted in the momentum distributions, density of states, and spatial densities for a realistic experimental setup with a shallow trap. The $\ensuremath{\pi}$-phase ppp-wave superfluid is reminiscent of the $\ensuremath{\pi}$ state in superconductor-ferromagnet heterostructures but differs in symmetry and physical origin. The spatially varying phases of the superfluid gap provide an approach to synthetic magnetic fields for neutral atoms. It would represent another example of ppp-wave pairing, first discovered in 3He^{3}\mathrm{He}3He liquids.