Unconventional Pairing States In Ultracold Fermi Gases

The study of unconventional pairing states in ultracold Fermi gases is a new direc-tion that has attracted much recent attention. The concept of pairing states in attractive-ly interacting fermions was first proposed in the BCS theory. The superconductivity is described as the condensation of the so-called Cooper pairs. We usually refer to this pairing state as the conventional pairing state. With the conception of quantum simula-tion put forward by Feiman in 1982, and the Kitaev model proposed in 2001, the study of unconventional pairing states has evolved into a forefront in atomic, molecular and optical physics.Ultracold atomic physics is the research of the atoms maintained at temperatures close to 0 Kelvin. At these temperatures the quantum-mechanical properties would be-come dominating. In recent years, a variety of experimental techniques,which leads to highly tunable parameters, have been implemented in ultracold atomic physics. With the realization of Feshbach resonance, the strength of interaction becomes a control-lable parameter. With the realization of the controlable optical lattice, we can use cold atom physics to simulate many lattice systems and low dimensional systems in con-densed matter physics. With the realization of the synthetic gauge field, such as the spin-orbit coupling, the synthetic magnetic field, the synthetic electric field etc., the dispersion spectrum of atoms becomes another controllable parameter. Based on the above conditions, ultracold atomic gases become an ideal platform for the research of unconventional pairing states.In this thesis, we focus on the properties and relization of unconventional pairing states, based on the experimental methods of ultracold atomic physics. For the zero temperature case, we perform the numerical simulation of the system with mean-field theory. And for the finite temperature case, we use the broken symmetry phase theory.The detailed works are as the follows:1. Significance of dressed molecules in a quasi-two-dimensional Fermi gas with spin-orbit couplingWe study the properties of a spin-orbit coupled quasi-two-dimensional two com-ponent Fermi gas with tunable s-wave interaction. By analyzing the two-body problem,we find that, SOC tends to enhance the two-body binding energy, and when the two-body binding energy approaches or exceeds the axial confinement, the population of the excited states in the tightly-confined axial direction would be significant. Thus,with the finite strength of SOC, the population of the excited states cannot be ignored.Base on the understanding of the two body problem, we propose a two dimensional two channel effective Hamilton, where the dressed molecule in the closed channel in-cludes the fermions in axial excited states and the Feshbach molecule. By comparing the numerical simulation results of single channel model, we find that, both the density distribution and the phase structure in the trap can be significantly modified with the influence of the dressed molecule even in a wide Feshbach resonance. Specifically, the stability region of the topological superfluid phase is increased when we consider the effect of the dressed molecule.2. BCS-BEC crossover and quantum phase transition in an ultracold Fermi gas under spin-orbit couplingMost of the previous studies about the spin-orbit coupled Fermi systems have adopted a single-channel model. But a two-channel model is more appropriate to char-acterize the Feshbach resonance, on a phenomenological level. By analyzing the two-body problem, we find that, the numerical simulation results of the two channel are qualitative different from those of the single channel model. In the two channel model,there are in general two branches of solution under a finite SOC and with a finite back-ground scattering length. But in the single channel model, there is only one branch of solution. For many body cases, tlhese properties still exist. In the upper branch of the many-body solution, we find an interesting phenomenon, that there is a quantum phase transition between normal phase and superfluid phase. And the location of the quantum phase transition can be tuned close to or across the resonance point by choosing a proper resonance with moderate SOC strength. This means that it is possible to observe this phase transition in experiments.3. Unconventional Fulde-Ferrell-Larkin-Ovchinnikov pairing states in a Fermi gas with spin-orbit couplingIn this work, we study the pairing state in the NIST scheme. Because of the anisotropic SOC and effective Zeeman fields in the NIST scheme, we have to intro-duce the degrees of freedom in the center-of-mass momentum of the pairing states.Through the analysis about the expansion of the thermodynamic potential, we find that the ground state is in general the result of the competition between various FFLO states and the normal state. The transverse field makes the bands asymmetric, and the Fermi surface becomes deformed. The interplay of SOC and Fermi surface deformation leads to unconventional FFLO pairing states. We also show the gapless contours in the mo-mentum space, which may define several different types of nodal FFLO states. At the end of this work, we discussed the feasible proposal to observe these interesting features in the experiment.4. Three-component Fulde-Ferrell superfluids in a two-dimensional Fermi gas with spin-orbit couplingIn this work, we demonstrate that exotic FF states can also be stabilized in a three-component Fermi gas where all three hyperfine states are coupled by SOC. We map out the phase diagram of the three-component spin-orbit coupled Fermi gas in two spatial dimensions at zero temperature. In order to characterize the properties of the three-component FF state, we show the gapless contours and the number distributions in the momentum space. We also propose the possible experimental detection schemes for these unconventional FF states.5. The finite temperature behavior of Fermi superfluid with hybridized s- and p-wave pairingsRecently, it has been shown that there are many interesting properties in the Fermi superfluid with hybridized s- and p-wave pairings at zero temperature. From the mean-field level calculation, we find that the behavior of this system at finite temperature would be different from the system at the zero temperature. We use the broken symmetry phase theory to do the numerical simulation of the system at finite temperature. From the critical temperature of s- and p-wave pairings, we find that the competition between s- and p-wave pairings has led to many interesting phenomena in the system, such as the non monotonicity of the critical temperature evolution. These results can help us to understand the finite temperature behavior of the fermion superfluids with multiple partial-wave scatterings in cold atomic gases.