We theoretically investigate one-dimensional three-component spin-orbit-coupled Fermi gases in the presence of Zeeman field. By solving the Bogoliubov-de-Gennes equations, we obtain the phase diagram at given chemical potential and order parameter. W
e show that the system undergoes a phase transition from Bardeen-Cooper-Schrieffer superfluid to topological superfluid as increasing the intensity of Zeeman field. By comparing to the two-component system, we find, besides the topological phase transition from the trivial superfluid to nontrivial topological superfluid, the system can always be in a nontrivial topological superfluid, and there are two Majorana zero energy regions while increasing the magnetic field. We find the three-component spin-orbit-coupled Fermi gases in certain parameter range is more optimizing for experimental realization due to the smaller magnetic field needed. We therefore propose a promising candidate for realizing topological superfluid.
We theoretically investigate the control of a magnetic Feshbach resonance using a bound-to-bound molecular transition driven by spatially modulated laser light. Due to the spatially periodic coupling between the ground and excited molecular states, t
here exists a band structure of bound states, which can uniquely be characterized by some extra bumps in radio-frequency spectroscopy. With the increasing of coupling strength, the series of bound states will cross zero energy and directly result in a number of scattering resonances, whose position and width can be conveniently tuned by the coupling strength of the laser light and the applied magnetic field (i.e., the detuning of the ground molecular state). In the presence of the modulated laser light, universal two-body bound states near zero-energy threshold still exist. However, compared with the case without modulation, the regime for such universal states is usually small. An unified formula which embodies the influence of the modulated coupling on the resonance width is given. The spatially modulated coupling also implies a local spatially varying interaction between atoms. Our work proposes a practical way of optically controlling interatomic interactions with high spatial resolution and negligible atomic loss.
We present a systematic comparison of the most recent thermodynamic measurements of a trapped Fermi gas at unitarity with predictions from strong coupling theories and quantum Monte Carlo (MC) simulations. The accuracy of the experimental data, of th
e order of a few percent, allows a precise test of different many-body approaches. We find that a Nozieres and Schmitt-Rink treatment of fluctuations is in excellent agreement with the experimental data and available MC calculations at unitarity.
We investigate the finite temperature properties of an ultracold atomic Fermi gas with spin population imbalance in a highly elongated harmonic trap. Previous studies at zero temperature showed that the gas stays in an exotic spatially inhomogeneous
Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid state at the trap center; while moving to the edge, the system changes into either a non-polarized Bardeen-Cooper-Schriffer superfluid ($P<P_c$) or a fully polarized normal gas ($P>P_c$), depending on the smallness of the spin polarization $P$, relative to a critical value $P_c$. In this work, we show how these two phase-separation phases evolve with increasing temperature, and thereby construct a finite temperature phase diagram. For typical interactions, we find that the exotic FFLO phase survives below one-tenth of Fermi degeneracy temperature, which seems to be accessible in the current experiment. The density profile, equation of state, and specific heat of the polarized system have been calculated and discussed in detail. Our results are useful for the on-going experiment at Rice University on the search for FFLO states in quasi-one-dimensional polarized Fermi gases.
We develop a variational approach to calculate the density response function at finite temperatures of the lowest-lying two-fluid modes in a trapped two-component Fermi superfluid close to a Feshbach resonance. The out-of-phase oscillations, which ar
e the analogue in trapped gases of second sound in uniform superfluids, have so far not been observed in cold-atom experiments. At unitarity, we show that these modes are observable at finite temperatures via two-photon Bragg scattering, whose spectrum is related to the imaginary part of density response function. This provides direct evidence for superfluidity and a promising way to test microscopic results for thermodynamics at unitarity.
We present the results of a variational calculation of the frequencies of the low-lying Landau two-fluid hydrodynamic modes in a trapped Fermi superfluid gas at unitarity. Landaus two-fluid hydrodynamics is expected to be the correct theory of Fermi
superfluids at finite temperatures close to unitarity, where strong interactions give rise to collisional hydrodynamics. Two-fluid hydrodynamics predicts the existence of in-phase modes in which the superfluid and normal fluid components oscillate together, as well as out-of-phase modes where the two components move against each other. We prove that at unitarity, the dipole and breathing in-phase modes are locally isentropic. Their frequencies are independent of temperature and are the same above and below the superfluid transition. The out-of-phase modes, in contrast, are strongly dependent on temperature and hence, can be used to test the thermodynamic properties and superfluid density of a Fermi gas at unitarity. We give numerical results for the frequencies of these new modes as function of temperature in an isotropic trap at unitarity.
