Two-component Atomic Fermi Gas Research Articles

BCS-BEC crossover of atomic Fermi superfluid in a spherical bubble trap

We present a theory of a two-component atomic Fermi gas with tunable attractive contact interactions on a spherical shell going through the Bardeen-Cooper-Schrieffer (BCS) - Bose Einstein condensation (BEC) crossover, inspired by the realizations of spherical bubble traps for ultracold atoms in microgravity. The derivation follows the BCS-Leggett theory to obtain the gap and number equations. The BCS-BEC crossover can be induced by tuning the interaction, and the properly normalized gap and chemical potential exhibit universal behavior regardless of the planar or spherical geometry. Nevertheless, the spherical-shell geometry introduces another way of inducing the crossover by the curvature. The curvature-induced BCS-BEC crossover is made possible by fixing the particle number and interaction strength while shrinking the sphere, causing a reduction to the ratio of the pairing and kinetic energies and pushing the system towards the BCS limit. The saturation of the superfluid density further confirms the ground state is a Fermi superfluid.

Superfluid Phase Transitions and Effects of Thermal Pairing Fluctuations in Asymmetric Nuclear Matter

We investigate superfluid phase transitions of asymmetric nuclear matter at finite temperature (T) and density (ρ) with a low proton fraction (Yp ≤ 0.2), which is relevant to the inner crust and outer core of neutron stars. A strong-coupling theory developed for two-component atomic Fermi gases is generalized to the four-component case, and is applied to the system of spin-1/2 neutrons and protons. The phase shifts of neutron-neutron (nn), proton-proton (pp) and neutron-proton (np) interactions up to k = 2 fm−1 are described by multi-rank separable potentials. We show that the critical temperature {{boldsymbol{T}}}_{{bf{c}}}^{{bf{n}}{bf{n}}} of the neutron superfluidity at Yp = 0 agrees well with Monte Carlo data at low densities and takes a maximum value {{boldsymbol{T}}}_{{bf{c}}}^{{bf{n}}{bf{n}}}= 1.68 MeV at {boldsymbol{rho }}{boldsymbol{/}}{{boldsymbol{rho }}}_{{bf{0}}}{boldsymbol{=}}{bf{0.14}} with ρ0 = 0.17 fm−3. Also, the critical temperature {{boldsymbol{T}}}_{{bf{c}}}^{{bf{n}}{bf{n}}} of the proton superconductivity for Yp ≤ 0.2 is substantially suppressed at low densities due to np-pairing fluctuations, and starts to dominate over {{boldsymbol{T}}}_{{bf{c}}}^{{bf{n}}{bf{n}}} only above {boldsymbol{rho }}{boldsymbol{/}}{{boldsymbol{rho }}}_{{bf{0}}}{boldsymbol{=}}{bf{0.70}}(0.77) for Yp = 0.1(0.2), and (iii) the deuteron condensation temperature {{boldsymbol{T}}}_{{bf{c}}}^{{bf{d}}} is suppressed at Yp ≤ 0.2 due to a large mismatch of the two Fermi surfaces.

One-dimensional two-component fermions with contact even-wave repulsion and SU(2)-symmetry-breaking near-resonant odd-wave attraction

We consider a one-dimensional (1D) two-component atomic Fermi gas with contact interaction in the even-wave channel (Yang-Gaudin model) and study the effect of an SU(2) symmetry breaking near-resonant odd-wave interaction within one of the components. Starting from the microscopic Hamiltonian, we derive an effective field theory for the spin degrees of freedom using the bosonization technique. It is shown that at a critical value of the odd-wave interaction there is a first-order phase transition from a phase with zero total spin and zero magnetization to the spin-segregated phase where the magnetization locally differs from zero.

Coherent manipulation of spin correlations in the Hubbard model

We coherently manipulate spin correlations in a two-component atomic Fermi gas loaded into an optical lattice using spatially and time-resolved Ramsey spectroscopy combined with high-resolution \textit{in situ} imaging. This novel technique allows us not only to imprint spin patterns but also to probe the static magnetic structure factor at arbitrary wave vector, in particular the staggered structure factor. From a measurement along the diagonal of the $1^\mathrm{st}$ Brillouin zone of the optical lattice, we determine the magnetic correlation length and the individual spatial spin correlators. At half filling, the staggered magnetic structure factor serves as a sensitive thermometer for the spin temperature, which we employ to study the thermalization of spin and density degrees of freedom during a slow quench of the lattice depth.

Larkin-Ovchinnikov superfluidity in a two-dimensional imbalanced atomic Fermi gas

We present an extensive study of two-dimensional Larkin-Ovchinnikov (LO) superfluidity in a spin-imbalanced two-component atomic Fermi gas. In the context of Fulde-Ferrell-Larkin- Ovchinnikov (FFLO) phase, we explore a wide and generic class of pairing gap functions with ex- plicit spatial dependency. The mean-field theory of such phases is applied through the Bogoliubov-de Gennes equations in which the pairing gap can be determined self-consistently. In order to systemat- ically explore the configuration space we consider both the canonical and grand canonical ensembles where we control the polarization or chemical potentials of the system, respectively. The mean-field calculations enable us to understand the nature of the phase transitions in the fully paired Bardeen- Cooper-Schrieffer (BCS) state, exotic LO phase, and partially polarized free Fermi gas. The order of the phase transitions has been examined and in particular we find a weak first-order phase transition between the exotic inhomogeneous LO phase and the BCS phase. In comparison to the three-dimensional case, where the phase diagram is dominated by a generic separation phase, we predict a broader parameter space for the spatially inhomogeneous LO phase. By computing the superfluid density of the LO phase at different polarization, we show how the superfluidity of the system is suppressed with increasing spin polarization.

Itinerant ferromagnetism in one-dimensional two-component Fermi gases

We study a one-dimensional two-component atomic Fermi gas with an infinite intercomponent contact repulsion. It is found that adding an attractive resonant odd-wave interaction breaking the rotational symmetry one can make the ground state ferromagnetic. A promising system for the observation of this itinerant ferromagnetic state is a 1D gas of $^{40}$K atoms, where 3D $s$-wave and $p$-wave Feshbach resonances are very close to each other and the 1D confinement significantly reduces the inelastic decay.

Ground-state densities of repulsive two-component Fermi gases

We investigate separations of trapped balanced two-component atomic Fermi gases with repulsive contact interaction. Candidates for ground-state densities are obtained from the imaginary-time evolution of a nonlinear pseudo-Schr\"odinger equation in three dimensions, rather than from the cumbersome variational equations. With the underlying hydrodynamical approach, gradient corrections to the Thomas-Fermi approximation are conveniently included and are shown to be vital for reliable density profiles. We provide critical repulsion strengths that mark the onset of phase transitions in a harmonic trap. We present transitions from identical density profiles of the two fermion species towards isotropic and anisotropic separations for various confinements, including harmonic and double-well-type traps. Our proposed method is suited for arbitrary trap geometries and can be straightforwardly extended to study dynamics in the light of ongoing experiments on degenerate Fermi gases.

Mapping the two-component atomic Fermi gas to the nuclear shell-model

The physics of a two-component cold fermi gas is now frequently addressed in laboratories. Usually this is done for large samples of tens to hundreds of thousands of particles. However, it is now possible to produce few-body systems (1-100 particles) in very tight traps where the shell structure of the external potential becomes important. A system of two-species fermionic cold atoms with an attractive zero-range interaction is analogous to a simple model of nucleus in which neutrons and protons interact only through a residual pairing interaction. In this article, we discuss how the problem of a two-component atomic fermi gas in a tight external trap can be mapped to the nuclear shell model so that readily available many-body techniques in nuclear physics, such as the Shell Model Monte Carlo (SMMC) method, can be directly applied to the study of these systems. We demonstrate an application of the SMMC method by estimating the pairing correlations in a small two-component Fermi system with moderate-to-strong short-range two-body interactions in a three-dimensional harmonic external trapping potential.

Superfluidity and collective modes in Rashba spin–orbit coupled Fermi gases

We present a theoretical study of the superfluidity and the corresponding collective modes in two-component atomic Fermi gases with s-wave attraction and synthetic Rashba spin–orbit coupling. The general effective action for the collective modes is derived from the functional path integral formalism. By tuning the spin–orbit coupling from weak to strong, the system undergoes a crossover from an ordinary BCS/BEC superfluid to a Bose–Einstein condensate of rashbons. We show that the properties of the superfluid density and the Anderson–Bogoliubov mode manifest this crossover. At large spin–orbit coupling, the superfluid density and the sound velocity become independent of the strength of the s-wave attraction. The two-body interaction among the rashbons is also determined. When a Zeeman field is turned on, the system undergoes quantum phase transitions to some exotic superfluid phases which are topologically nontrivial. For the two-dimensional system, the nonanalyticities of the thermodynamic functions and the sound velocity across the phase transition are related to the bulk gapless fermionic excitation which causes infrared singularities. The superfluid density and the sound velocity behave nonmonotonically: they are suppressed by the Zeeman field in the normal superfluid phase, but get enhanced in the topological superfluid phase. The three-dimensional system is also studied.

Location of the vortex phase in the phase diagram of a rotating two-component Fermi gas

We determine the conditions under which superfluidity with and without quantized vortices appears in a weakly interacting two-component atomic Fermi gas that is trapped in a rotating cylindrical symmetric harmonic potential. We compute the phase diagram as a function of rotation frequency, scattering length, temperature, total number of trapped atoms, and population imbalance. Our analysis is based on solving the Bogoliubov--de Gennes equation.

Tuning the Tricritical Point with Spin-Orbit Coupling in Polarized Fermionic Condensates

We investigate a two-component atomic Fermi gas with population imbalance in the presence of Rashba-type spin-orbit coupling (SOC). As a competition between SOC and population imbalance, the finite-temperature phase diagram reveals a large variety of new features, including the expanding of the superfluid state regime and the shrinking of both the phase separation and the normal regimes. For sufficiently strong SOC, the phase separation region disappears, giving way to the superfluid state. We find that the tricritical point moves toward a regime of low temperature, high magnetic field, and high polarization as the SOC increases.

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.

Optical Control of Feshbach Resonances in Fermi Gases Using Molecular Dark States

We propose a general method for optical control of magnetic Feshbach resonances in ultracold atomic gases with more than one molecular state in an energetically closed channel. Using two optical frequencies to couple two states in the closed channel, inelastic loss arising from spontaneous emission is greatly suppressed by destructive quantum interference at the two-photon resonance, i.e., dark-state formation, while the scattering length is widely tunable by varying the frequencies and/or intensities of the optical fields. This technique is of particular interest for a two-component atomic Fermi gas, which is stable near a Feshbach resonance.

Radio-Frequency Spectroscopy of a Strongly Interacting Two-Dimensional Fermi Gas

We realize and study a strongly interacting two-component atomic Fermi gas confined to two dimensions in an optical lattice. Using radio-frequency spectroscopy we measure the interaction energy of the strongly interacting gas. We observe the confinement-induced Feshbach resonance on the attractive side of the 3D Feshbach resonance and find the existence of confinement-induced molecules in very good agreement with theoretical predictions.

Trap- and population-imbalanced two-component Fermi gas in the Bose-Einstein-condensate limit

We study equal mass population imbalanced two-component atomic Fermi gas with unequal trap frequencies $(\omega_{\uparrow} \neq \omega_{\downarrow})$ at zero temperature using the local density approximation (LDA). We consider the strongly attracting Bose-Einstein condensation (BEC) limit where polarized (gapless) superfluid is stable. The system exhibits shell structure: unpolarized SF$\to$polarized SF$\to$normal N. Compared to trap symmetric case, when the majority component is tightly confined the gapless superfluid shell grows in size leading to reduced threshold polarization to form polarized (gapless) superfluid core. In contrast, when the minority component is tightly confined, we find that the superfluid phase is dominated by unpolarized superfluid phase with gapless phase forming a narrow shell. The shell radii for various phases as a function of polarization at different values of trap asymmetry are presented and the features are explained using the phase diagram.

Parametric generation of density and spin modes with formation of stationary condensed states in ultracold two-component quasi-one-dimensional Fermi gases

The temporal evolution of parametrically created collective excitations is studied in an ultracold two-component atomic Fermi gas. We consider quasi-one-dimensional geometry with a permanent modulation of the transverse trap frequency leading to the generation of longitudinal modes for both density and spin branches. After involvement of the interaction between excitations, the evolution comes to the formation of the stationary state with macroscopic filling of a single density or spin mode and zero occupancy for other modes located within the parametric energy interval. In the presence of this state correlation properties of fermions change essentially. Analysis of one-particle density matrix and density-density correlators reveals possibilities for experimental study of density and spin branches.

Polarization plateau in an atomic Fermi gas loaded on a three-leg triangular optical lattice

In order to demonstrate that atomic Fermi gas is a good experimental reality in studying unsolved problems in frustrated interacting-spin systems, we numerically examine the Mott core state emerged by loading two-component atomic Fermi gases on triangular optical lattices. Consequently, we find that plateau like structures are observable in the Mott core polarization as a function of the population imbalance. These plateau states are caused by a flexibility that the surrounding metallic region absorbs the excess imbalance to keep the plateau states inside the Mott core. We also find spin patterns peculiar to the plateau states inside the Mott core.

Spectral Signatures of the Fulde-Ferrell-Larkin-Ovchinnikov Order Parameter in One-Dimensional Optical Lattices

We address an imbalanced two-component atomic Fermi gas restricted by a one-dimensional (1D) optical lattice and an external harmonic potential, within the mean-field Bogoliubov-de Gennes formalism. We show that characteristic features of the Fulde-Ferrell-Larkin-Ovchinnikov state are visible in the rf spectra and in the momentum-resolved photoemission spectra of the gas. Specially, Andreev states or midgap states can be clearly resolved, which gives a direct experimentally observable signature of the oscillating order parameter.

Superfluidity at the BEC-BCS crossover in two-dimensional Fermi gases with population and mass imbalance

We explore the zero-temperature phase behavior of a two-dimensional two-component atomic Fermi gas with population and mass imbalance in the regime of the BEC-BCS crossover. Working in the mean-field approximation, we show that the normal and homogeneous balanced superfluid phases are separated by an inhomogeneous superfluid phase of Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) type. We obtain an analytical expression for the line of continuous transitions separating the normal and inhomogeneous FFLO phases. We further show that the transition from the FFLO phase to the homogeneous balanced superfluid is discontinuous leading to phase separation. If the species have different masses, the superfluid phase is favored when the lighter species is in excess. We explore the implications of these findings for the properties of the two-component Fermi gas in the atomic trap geometry. Finally, we compare and contrast our findings with the predicted phase behavior of the electron-hole bilayer system.

Density Waves and Supersolidity in Rapidly Rotating Atomic Fermi Gases

We study theoretically the low-temperature phases of a two-component atomic Fermi gas with attractive s-wave interactions under conditions of rapid rotation. We find that, in the extreme quantum limit, when all particles occupy the lowest Landau level, the normal state is unstable to the formation of charge density wave (CDW) order. At lower rotation rates, when many Landau levels are occupied, we show that the low-temperature phases can be supersolids, involving both CDW and superconducting order.