Polarized Fermi Gas Research Articles

Topological Fulde–Ferrell–Larkin–Ovchinnikov states in spin–orbit-coupled Fermi gases

Pairing in an attractively interacting two-component Fermi gas in the absence of time-reversal symmetry or inversion symmetry may give rise to exotic superfluid states. Notable examples range from the Fulde-Ferrell-Larkin-Ovchinnikov state with a finite centre-of-mass momentum in a polarized Fermi gas to the topological superfluid (TSF) state in a two-dimensional (2D) Fermi gas under Rashba spin-orbit coupling and an out-of-plane Zeeman field. Here we show that a TSF state with a single-component nonzero centre-of-mass momentum, called a topological Fulde-Ferrell (tFF) state, can be stabilized in a 2D Fermi gas with Rashba spin-orbit coupling and both in-plane and out-of-plane Zeeman fields. The tFF state features a non-trivial Berry phase, along with unique properties that may be detected using existing experimental techniques.

Tunneling of polarized fermions in 3D double wells

We study the tunneling of a spin polarized Fermi gas in a three-dimensional double-well potential, focusing on the time dynamics starting from an initial state in which there is an imbalance in the number of particles in the two wells. Although fermions in different doublets of the double well tunnel with different frequencies, we point out that (incoherent) oscillations of a large number of particles can arise, as a consequence of the presence of transverse degrees of freedom. Estimates of the doublet structure and of the occupation of transverse eigenstates for a realistic experimental setup are provided.

Energy and Contact of the One-Dimensional Fermi Polaron at Zero and Finite Temperature

We use the T-matrix approach for studying highly polarized homogeneous Fermi gases in one dimension with repulsive or attractive contact interactions. Using this approach, we compute ground state energies and values for the contact parameter that show excellent agreement with exact and other numerical methods at zero temperature, even in the strongly interacting regime. Furthermore, we derive an exact expression for the value of the contact parameter in one dimension at zero temperature. The model is then extended and used for studying the temperature dependence of ground state energies and the contact parameter.

Meissner-like effect on normal-superfluid interface of imbalanced Fermi gas

We examine the N-SF interface of a polarized Fermi gas with two spin species a and b, in the presence of a weak external magnetic field. In our analysis we shall, therefore, consider the possibility of the Meissner effect too. We use perturbation theory to solve the Bogoliubov equations and obtain the wave functions. We consider the various scattering regions of the BCS regime and analytically obtain the transmission coefficients and the heat conductivity across the interface. We describe how the heat conductivity is affected by the Meissner effect and the species imbalance. It suffices to remark that the leading order term in transmission coefficients are independent of energy E. Also the additional heat conductivity is found to be proportional to λ2 (λ is penetration depth). The corresponding graphs is also plotted and discussed.

Highly polarized Fermi gases in two dimensions

We investigate the highly polarized limit of a two-dimensional (2D) Fermi gas, where we effectively have a single spin-down impurity atom immersed in a spin-up Fermi sea. By constructing variational wave functions for the impurity, we map out the ground state phase diagram as a function of mass ratio M/m and interaction strength. In particular, we determine when it is favorable for the dressed impurity (polaron) to bind particles from the Fermi sea to form a dimer, trimer or even larger clusters. Similarly to 3D, we find that the Fermi sea favors the trimer state so that it exists for M/m less than the critical mass ratio for trimer formation in the vacuum. We also find a region where dimers have finite momentum in the ground state, a scenario which corresponds to the Fulde-Ferrell-Larkin-Ovchinnikov superfluid state in the limit of large spin imbalance. For equal masses (M=m), we compute rigorous bounds on the polaron-dimer transition, and we show that the polaron energy and residue is well captured by the variational approach, with the former quantity being in good agreement with experiment. When there is a finite density of impurities, we find that this polaron-dimer transition is preempted by a first-order superfluid-normal transition at zero temperature, but it remains an open question what happens at finite temperature.

Dispersion of waves in the two-dimensional ultracold fermi gas of atoms and molecules

System of quantum hydrodynamics equations for the polarized Fermi gas is presented. The short-range interaction is considered to within the third order in the interaction radius. The dispersion of elementary excitations in the two-dimensional Fermi gas of atoms and molecules is investigated. The equations of the evolution of the electric polarization together with the continuity and balance equations for the momentum are used for investigations. The dispersion law is analytically derived. It is demonstrated that two waves can exist in the examined system of particles. Without electric dipole moment, a solution is reduced to the well-known concentration wave. The dynamics of polarization contributes additionally to the dispersion of this wave. In addition, the polarization wave arises. Numerical analysis of the dispersion is presented, and stability of the examined system of particles is analyzed. Cases of wave propagation along the direction of equilibrium polarization and perpendicular to it (when the polarization lies in the gas plane or is perpendicular to it) are considered.

π-phase and Spontaneous Supercurrent induced by Pseudo-ferromagnetic Junction in a Spin-polarized Superfluid Fermi Gas

We theoretically investigate a possible spontaneous current state in a polarized superfluid Fermi gas confined in a toroidal trap. When one puts a weak nonmagnetic potential barrier in this system, this barrier is known to be magnetized in the sense that some of excess ↑-spin atoms are localized around it (where the ↑-spin describes the majority component of the polarized Fermi gas). Using this unique property, we show that this magnetized barrier, or the pseudo-ferromagnetic junction, induces a spontaneous current circulating along the toroidal trap. While the ordinary supercurrent state appears as a metastable state, this spontaneous current state is realized as the most stable state, originating from the phase twist of the superfluid order parameter by the magnetized potential barrier.

Spin susceptibility and fluctuation corrections in the BCS-BEC crossover regime of an ultracold Fermi gas

We investigate magnetic properties and effects of pairing fluctuations in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover regime of an ultracold Fermi gas. Recently, Liu and Hu, and Parish, pointed out that the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink (NSR), which has been extensively used to successfully clarify various physical properties of cold Fermi gases, unphysically gives negative spin susceptibility in the BCS-BEC crossover region. The same problem is found to also exist in the ordinary non-self-consistent T-matrix approximation. In this paper, we clarify that this serious problem comes from incomplete treatment in term of pseudogap phenomena originating from strong pairing fluctuations, as well as effects of spin fluctuations on the spin susceptibility. Including these two key issues, we construct an extended T-matrix theory which can overcome this problem. The resulting positive spin susceptibility agrees well with the recent experiment on a 6Li Fermi gas done by Sanner and co-workers. We also apply our theory to a polarized Fermi gas to examine the superfluid phase transition temperature Tc, as a function of the polarization rate. Since the spin susceptibility is an important physical quantity, especially in singlet Fermi superfluids, our results would be useful in considering how singlet pairs appear above and below Tc in the BCS-BEC crossover regime of cold Fermi gases.

Molecule and Polaron in a Highly Polarized Two-Dimensional Fermi Gas with Spin-Orbit Coupling

We show that spin-orbit coupling (SOC) gives rise to pairing instability in a highly polarized two-dimensional Fermi gas for an arbitrary interaction strength. The pairing instability can lead to a Fulde-Ferrell-Larkin-Ovchinnikov-like molecular state, which undergoes a first-order transition into a pairing state with zero center-of-mass momentum as the parameters are tuned. These pairing states are metastable against a polaron state dressed by particle-hole fluctuations for small SOC. At large SOC, a polaron-molecule transition exists, which suggests a phase transition between the topological superfluid state and the normal state for a highly polarized Fermi gas in the thermodynamic limit. As polarization in a Fermi gas with SOC is induced by the effective Zeeman field, we also discuss the influences of the effective Zeeman field on the ground state of the system. Our findings may be tested directly in future experiments.

Expansion of 1D Polarized Superfluids: The Fulde-Ferrell-Larkin-Ovchinnikov State Reveals Itself

We study the expansion dynamics of a one-dimensional polarized Fermi gas after its sudden release from confinement using both the mean-field Bogoliubov-deGennes and the numerically unbiased time-evolving block decimation methods. Our results show that experimentally observable spin density modulations, directly related to the presence of a Fulde-Ferrell-Larkin-Ovchinnikov state, develop during the expansion of the cloud. Our work therefore provides a robust theoretical proposal for the detection of this long-sought state.

Highly polarized Fermi gases across a narrow Feshbach resonance

We address the phase of a highly polarized Fermi gas across a narrow Feshbach resonance starting from the problem of a single down spin fermion immersed in a Fermi sea of up spins. Both polaron and pairing states are considered using the variational wave function approach, and we find that the polaron to pairing transition will take place at the BCS side of the resonance, strongly in contrast to a wide resonance where the transition is located at the BEC side. For pairing phase, we find out the critical strength of repulsive interaction between pairs above which the mixture of pairs and fermions will not phase separate. Therefore, nearby a narrow resonance, it is quite likely that magnetism can coexist with s-wave BCS superfluidity at large Zeeman field, which is a remarkable property absent in conventional BCS superconductors (or fermion pair superfluids).

Polarons in extremely polarized Fermi gases: The strongly interacting6Li-40K mixture

We study the extremely polarized two-component Fermi gas with a mass imbalance in the strongly interacting regime. Specifically we focus on the experimentally available mixture of ${}^{6}$Li and ${}^{40}$K atoms. In this regime spin polarons, i.e., dressed minority atoms, form. We consider the spectral function for the minority atoms, from which the lifetime and the effective mass of the spin polaron can be determined. Moreover, we predict the radio-frequency (rf) spectrum and the momentum distribution for the spin polarons for experiments with ${}^{6}$Li and ${}^{40}$K atoms. Subsequently we study the relaxation of the motion of the Fermi polaron due to spin drag.

Phase diagram of a uniform two-dimensional Fermi gas with spin-orbit coupling

We investigate the ground state of a uniform two-dimensional polarized Fermi gas with Rashba spin-orbit coupling at zero temperature. We construct the phase diagram by comparing the thermodynamic potential of superfluid and phase-separated states in detail. Due to the competition between polarization and spin-orbit coupling, we find that phase-separated states in the phase diagram can be topologically trivial and nontrivial. These two topologically distinct phase-separated states can not be connected without topological phase transition. The spin-orbit coupling reduces the effect of the population imbalance. Therefore, the phase-separated states are unstable to the superfluid phases for a large spin-orbit coupling.

Phase detection in an ultracold polarized Fermi gas via electromagnetically induced transparency

An optical detection scheme based on electromagnetically induced transparency is proposed to investigate the nature of Fermi pairing in a trapped strongly interacting two-component atomic Fermi gas with population imbalance. We show that valuable information can be acquired from the in situ probe absorption spectrum to identify different phases existing in the system.

Interaction between polarons and analogous effects in polarized Fermi gases

We consider an imbalanced mixture of two different ultracold Fermi gases, which are strongly interacting. Calling spin-down the minority component and spin-up the majority component, the limit of small relative density $x=n\ds /n\us$ is usually considered as a gas of non interacting polarons. This allows to calculate, in the expansion of the total energy of the system in powers of $x$, the terms proportional to $x$ (corresponding to the binding energy of the polaron) and to $x^{5/3}$ (corresponding to the kinetic energy of the polaron Fermi sea). We investigate in this paper terms physically due to an interaction between polarons and which are proportional to $x^2$ and $x^{7/3}$. We find three such terms. A first one corresponds to the overlap between the clouds dressing two polarons. The two other ones are due to the modification of the single polaron binding energy caused by the non-zero density of polarons. The second term is due to the restriction of the polaron momentum by the Fermi sea formed by the other polarons. The last one results from the modification of the spin-up Fermi sea brought by the other polarons. The calculation of all these terms is made at the simplest level of a single particle-hole excitation. It is performed for all the possible interaction strengths within the stability range of the polaron. At unitarity the last two terms give a fairly weak contribution while the first one is strong and leads to a marked disagreement with Monte-Carlo results. The possible origins of this discrepancy are discussed.

Topological superfluid in a trapped two-dimensional polarized Fermi gas with spin-orbit coupling

We study the stability region of the topological superfluid phase in a trapped two-dimensional polarized Fermi gas with spin-orbit coupling and across a BCS-BEC crossover. Due to the competition between polarization, pairing interaction and spin-orbit coupling, the Fermi gas typically phase separates in the trap. Employing a mean field approach that guarantees the ground state solution, we systematically study the structure of the phase separation and investigate in detail the optimal parameter region for the preparation of the topologically non-trivial superfluid phase. We then calculate the momentum space density distribution of the topological superfluid state and demonstrate that the existence of the phase leaves a unique signature in the trap integrated momentum space density distribution which can survive the time-of-flight imaging process.

Linear response of heat conductivity of normal–superfluid interface of a polarized Fermi gas to orbital magnetic field

Using perturbed Bogoliubov equations, we study the linear response to a weak orbital magnetic field of the heat conductivity of the normal–superfluid interface of a polarized Fermi gas at sufficiently low temperature. We consider the various scattering regions of the BCS regime and analytically obtain the transmission coefficients and the heat conductivity across the interface in an arbitrary weak orbital field. For a definite choice of the field, we consider various values of the scattering length in the BCS range and numerically obtain the allowed values of the average and species-imbalance chemical potentials. Thus, taking Andreev reflection into account, we describe how the heat conductivity is affected by the field and the species imbalance. In particular, we show that the additional heat conductivity due to the orbital field increases with the species imbalance, which is more noticeable at higher temperatures. Our results indicate how the heat conductivity may be controlled, which is relevant to sensitive magnetic field sensors/regulators at the interface.

Phase separation in a polarized Fermi gas with spin-orbit coupling

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 gapless superfluid states which are topologically non-trivial. We find that these novel gapless phases can be stabilized by intermediate spin-orbit coupling strengths. 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.

Composite-fermionization of the mixture composed of Tonks gas and Fermi gas

This paper investigates the ground-state properties of the mixture composed of the strongly interacting Tonks—Girardeau gas and spin polarized Fermi gas confined in one-dimensional harmonic traps, where the interaction between the Bose atoms and Fermi atoms is tunable. With a generalized Bose—Fermi transformation the mixture is mapped into a two-component Fermi gas. The homogeneous Fermi gas is exactly solvable by the Bethe-ansatz method and the ground state energy density can be obtained. Combining the ground-state energy function of the homogeneous system with local density approximation it obtains the ground-state density distributions of inhomogeneous mixture. It is shown that with the increase in boson—fermion interaction, the system exhibits composite-fermionization crossover.

Evolution of the pseudogap in a polarized Fermi gas

We calculate the single-particle spectral density of a normal (nonsuperfluid) two-component gas of fermions in the BCS-BEC crossover within a $T$-matrix approximation. We review how noncondensed pairs lead to a spectral density reminiscent of the ordered state, and explore how a gaplike feature in the spectrum evolves as one changes the polarization of the gas. As the gas is polarized, we find that this pseudogap becomes more diffuse and moves away from the Fermi level, reflecting the fact that fewer pairs are present but that they still play an important role in the excitations.