Spin-orbit coupling adjusting topological superfluid of mass-imbalanced Fermi gas

Topological superfluid state is different from the normal superfluid one due to the excitation energy gap on the boundary. How to obtain the topological superfluid state by using spin-orbit coupling to control the s-waves paired mass-imbalanced Fermi gas is a recent novel topic. In this paper, we study the topological superfluid phase diagram of two-dimensional mass-imbalanced Fermi gas with Rashba spin-orbit coupling at zero temperature. We find that due to the competition among mass imbalance, pairing interaction and spin-orbit coupling, there is a double-well structure in the thermodynamic potential, which affects the properties of the ground state of the system. We comprehensively give the phase diagrams of the system on the plane of spin-orbit coupling and chemical potential, and the phase diagrams on the plane of the reduced mass ratio and two-body binding energy. This study not only points out the stable region of topological superfluid state of mass-imbalanced Fermi gas, but also provides a detailed theoretical basis for better observation of topological superfluid state in experiments.     

Phase diagram and deformed phase separation for a trapped Fermi gas with population imbalance and BCS pairing interaction

We study the phase separated state of an ultracold atomic Fermi gas confined in a three-dimensional quantum harmonic trap with a BCS pairing interaction. Examining various finite-temperature phase diagrams, we investigate the interplay between the filling of the quantum trap energy levels and the pairing energy. We find that a low (high) filling leads to a large (small) critical population imbalance for the superfluid/normal transition, together with a fully (partially) polarized normal part. We also show that the decrease of the density leads to a changeover of the shape of the superfluid core from an equipotential form to a deformed one. Moreover, we clarify the intrinsic mechanisms that lead to the deformation, providing a unified scenario for phase separation and deformation in a trapped Fermi gas, allowing for a possible interpretation of the apparently controversial experimental findings.     

BCS-BEC crossover in a gas of Fermi atoms with a Feshbach resonance

We discuss the BCS-BEC crossover in a degenerate Fermi gas of two hyperfine states interacting close to a Feshbach resonance. We show that, by including fluctuation contributions to the free energy similar to that considered by Nozières and Schmitt-Rink, the character of the superfluid phase transition continuously changes from the BCS-type to the BEC-type, as the threshold of the quasimolecular band is lowered. In the BEC regime, the superfluid phase transition is interpreted in terms of molecules associated with both the Feshbach resonance and Cooper pairing.     

Low-energy monopole modes of a trapped atomic Fermi gas

We consider the low energy collective monopole modes of a trapped weakly interacting atomic Fermi gas in the collisionless regime. The spectrum is calculated for varying coupling strength and chemical potential. Using an effective Hamiltonian, we derive analytical results that agree well with numerical calculations in various regimes. The onset of superfluidity is shown to lead to effects such as the vanishing of the energy required to create a Cooper molecule at a critical coupling strength and to the emergence of pair vibration excitations. Our analysis suggests ways to experimentally detect the presence of the superfluid phase in trapped atomic Fermi gases.     

Observation of phase separation in a strongly interacting imbalanced fermi gas

We have observed phase separation between the superfluid and the normal component in a strongly interacting Fermi gas with imbalanced spin populations. The in situ distribution of the density difference between two trapped spin components is obtained using phase-contrast imaging and 3D image reconstruction. A shell structure is clearly identified where the superfluid region of equal densities is surrounded by a normal gas of unequal densities. The phase transition induces a dramatic change in the density profiles as excess fermions are expelled from the superfluid.     

Dipole polarizability of a trapped superfluid Fermi gas

The polarization produced by the relative displacement of the potentials trapping two spin species of a dilute Fermi gas with N=N is calculated at unitarity by assuming phase separation between the superfluid and a polarized phase at zero temperature. Because of the energy cost associated with pair breaking, the dipole polarizability is strongly quenched and exhibits important deviations from the ideal gas behavior even for nonlinear displacements of the order of the size of the atomic cloud. The behavior in the presence of different trapping frequencies (monopole polarization) for the two spin species is also discussed. Our results suggest new experimental perspectives to explore the quantum phases of interacting Fermi gases.     

Metastability in spin-polarized Fermi gases

We study the role of particle transport and evaporation on the phase separation of an ultracold, spin-polarized atomic Fermi gas. We show that the previously observed deformation of the superfluid paired core is a result of evaporative depolarization of the superfluid due to a combination of enhanced evaporation at the center of the trap and the inhibition of spin transport at the normal-superfluid phase boundary. These factors contribute to a nonequilibrium jump in the chemical potentials at the phase boundary. Once formed, the deformed state is highly metastable, persisting for times of up to 2?s.     

Superfluid phase transition in trapped atomic Fermi gas

Superfluid phase transition in an atomic Fermi gas confined to a harmonic trap is studied. The critical transition temperature and the temperature dependence and spatial shape of the order parameter are determined. The spectrum and wave functions of single-particle and collective excitations are obtained for a gas in the superfluid phase. The excitation eigenfrequencies exhibit a pronounced temperature dependence, allowing, e.g., identification of the superfluid phase.     

Resonance superfluidity in a quantum degenerate Fermi gas

We consider the superfluid phase transition that arises when a Feshbach resonance pairing occurs in a dilute Fermi gas. We apply our theory to consider a specific resonance in potassium ((40)K), and find that for achievable experimental conditions, the transition to a superfluid phase is possible at the high critical temperature of about 0.5T(F). Observation of superfluidity in this regime would provide the opportunity to experimentally study the crossover from the superfluid phase of weakly coupled fermions to the Bose-Einstein condensation of strongly bound composite bosons.     

BCS-BEC crossover in 2D Fermi gases with Rashba spin-orbit coupling

We present a systematic theoretical study of the BCS-BEC crossover in two-dimensional Fermi gases with Rashba spin-orbit coupling (SOC). By solving the exact two-body problem in the presence of an attractive short-range interaction we show that the SOC enhances the formation of the bound state: the binding energy E(B) and effective mass m(B) of the bound state grows along with the increase of the SOC. For the many-body problem, even at weak attraction, a dilute Fermi gas can evolve from a BCS superfluid state to a Bose condensation of molecules when the SOC becomes comparable to the Fermi momentum. The ground-state properties and the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature are studied, and analytical results are obtained in various limits. For large SOC, the BKT transition temperature recovers that for a Bose gas with an effective mass m(B). We find that the condensate and superfluid densities have distinct behaviors in the presence of SOC: the condensate density is generally enhanced by the SOC due to the increase of the molecule binding; the superfluid density is suppressed because of the nontrivial molecule effective mass m(B).     

Bose–Fermi mixtures in a three-dimensional optical lattice

Using the dynamical mean-field theory and the Gutzwiller method, we study the Mott transition in Bose–Fermi mixtures confined in a three-dimensional optical lattice and analyze the effect of fermions on the coherence of bosons. We conclude that increasing fermion composition reduces bosonic coherence in the presence of strong Bose–Fermi interactions and under the condition of the integer filling factors for composite fermions, which consist of one fermion and one or more bosonic holes. Various phases of the mixtures have been demonstrated including phase separation of two species, coexisting regions of superfluid bosons and fermionic liquids, and Mott regions in the phase space spanned by the chemical potentials of the bosons and the fermions.     

Unitarity Schrödinger Equation and Ground State Properties of the Finite Trapped Superfluid Fermi Gases in a BCS-BEC Crossover

On the basis of quantum hydrodynamical equations we derive a unitarity Schrödinger equation of a finite trapped superfluid Fermi gas valid in the whole interaction regime from BCS superfluid to BEC. This equation is just the Ginzburg-Laudau-type equation for the fermionic Cooper pairs in the BCS side, the Gross-Pitaevskii-type equation for the bosonic dimers in the BEC side, and a unitarity equation for a strongly interacting Fermi superfluid in the unitarity limit. By taking a modified Gauss-like trial wave function, we solve the unitarity Schrödinger equation, calculate the energy, chemical potential, sizes and profiles of the ground-state condensate, and discuss the properties of the ground state in the entire BCS-BEC crossover regimes.     

Density profile of a trapped strongly interacting Fermi gas with unbalanced spin populations

We present a theoretical study of the density profile of a trapped strongly interacting Fermi gas with unbalanced spin populations. Making the assumption of the existence of a first order phase transition between an unpolarized superfluid phase and a fully polarized normal phase, we show good agreement with a recent experiment presented by Partridge et al.     

超流费米气体相滑移时的密度分布

当前在冷原子和玻色爱因斯坦凝聚(BEC)领域的一个重要问题是在Feshbach共振附近的冷费米气体如何从BEC态演变到BCS(Bardeen Schrieffer Cooper)态.本文进一步研究在Feshbach共振附近超流态的相滑移现象.通过具体的数值计算，给出了费米气体在相滑移时的粒子数密度的分布，并对不同温度下的相滑移的大小进行了分析.结果表明，相滑移现象可以作为实验上判断系统是否处于超流态的一个可行的判据. 关键词： 超流费米气体 相滑移 Feshbach共振     

Intermediate-temperature superfluidity in an atomic fermi gas with population imbalance

We derive the underlying finite temperature theory which describes Fermi gas superfluidity with population imbalance in a homogeneous system. We compute the pair formation temperature, superfluid transition temperature Tc, and superfluid density in a manner consistent with the standard ground state equations and, thereby, present a complete phase diagram. Finite temperature stabilizes superfluidity, as manifested by two solutions for Tc or by low T instabilities. At unitarity, the polarized state is an "intermediate-temperature superfluid."     

Normal state of a polarized fermi gas at unitarity

We study the Fermi gas at unitarity and at T=0 by assuming that, at high polarizations, it is a normal Fermi liquid composed of weakly interacting quasiparticles associated with the minority spin atoms. With a quantum Monte Carlo approach we calculate their effective mass and binding energy, as well as the full equation of state of the normal phase as a function of the concentration x=n downward arrow/n upward arrow of minority atoms. We predict a first order phase transition from normal to superfluid at x(c)=0.44 corresponding, in the presence of harmonic trapping, to a critical polarization P(c)=(N upward arrow - N downward arrow/(N upward arrow + N downward arrow)=77%. We calculate the radii and the density profiles in the trap and predict that the frequency of the spin dipole mode will be increased by a factor of 1.23 due to interactions.     

Quantum phase transitions across a p-wave Feshbach resonance

We study a single-species polarized Fermi gas tuned across a narrow p-wave Feshbach resonance. We show that in the course of a Bose-Einstein condensation (BEC)-BCS crossover, the system can undergo a magnetic-field-tuned quantum phase transition from a px-wave to a px+ipy-wave superfluid. The latter state, that spontaneously breaks time-reversal symmetry, furthermore undergoes a topological px+ipy to px+ipy transition at zero chemical potential mu. In two dimensions, for mu > 0 it is characterized by a Pfaffian ground state exhibiting topological order and non-Abelian excitations familiar from fractional quantum Hall systems.     

Spin-orbit coupled Fermi gases across a Feshbach resonance

In this Letter we study both ground state properties and the superfluid transition temperature of a spin-1/2 Fermi gas across a Feshbach resonance with a synthetic spin-orbit coupling, using the mean-field theory and the exact solution of two-body problem. We show that a strong spin-orbit coupling can significantly enhance the pairing gap for negative scattering length a(s), due to increased density of state at Fermi surface. Strong spin-orbit coupling can also significantly enhance the superfluid transition temperature Tc to a sizable fraction of Fermi temperature when a(s) ≤ 0, while it suppresses Tc slightly for positive a(s). The interaction energy and pair size at resonance are also discussed.     

Magnetic phase transitions in one-dimensional strongly attractive three-component ultracold fermions

We investigate the nature of trions, pairing, and quantum phase transitions in one-dimensional strongly attractive three-component ultracold fermions in external fields. Exact results for the ground-state energy, critical fields, magnetization and phase diagrams are obtained analytically from the Bethe ansatz solutions. Driven by Zeeman splitting, the system shows exotic phases of trions, bound pairs, a normal Fermi liquid, and four mixtures of these states. Particularly, a smooth phase transition from a trionic phase into a pairing phase occurs as the highest hyperfine level separates from the two lower energy levels. In contrast, there is a smooth phase transition from the trionic phase into a normal Fermi liquid as the lowest level separates from the two higher levels.     

Topological superfluid in a two-dimensional polarized Fermi gas with spin-orbit coupling and adiabatic rotation

We study the properties of superfluid in a two-dimensional(2 D) polarized Fermi gas with spin–orbit coupling and adiabatic rotation which are trapped in a harmonic potential. Due to the competition between polarization, spin–orbit coupling, and adiabatic rotation, the Fermi gas exhibits many intriguing phenomena. By using the Bardeen–Cooper–Schrieffer(BCS) mean-field method with local density approximation, we investigate the dependence of order parameter solution on the spin–orbit coupling strength and the rotation velocity. The energy spectra with different rotation velocities are studied in detail. Besides, the conditions for the zero-energy Majorana fermions in topological superfluid phase to be observed are obtained. By investigating distributions of number density, we find that the rotation has opposite effect on the distribution of number density with different spins, which leads to the enhancement of the polarization of Fermi gas. Here,we focus on the region of BCS pairing and ignore the Fulde–Ferrell–Larkin–Ovchinnikov state.