Atomic Fermi Gas Research Articles

Unitary Thermodynamics from Thermodynamic Geometry

Degenerate Fermi gases of atoms near a Feshbach resonance show universal thermodynamic properties, which are here calculated with the geometry of thermodynamics, and the thermodynamic curvature $R$. Unitary thermodynamics is expressed as the solution to a pair of ordinary differential equations, a "superfluid" one valid for small entropy per atom $z\equiv S/N k_B$, and a "normal" one valid for high $z$. These two solutions are joined at a second-order phase transition at $z=z_c$. Define the internal energy per atom in units of the Fermi energy as $Y=Y(z)$. For small $z$, $Y(z)=y_0+y_1 z^{\alpha}+y_2 z^{2 \alpha}+\cdots,$ where $\alpha$ is a constant exponent, $y_0$ and $y_1$ are scaling factors, and the series coefficients $y_i$ ($i\ge 2$) are determined uniquely in terms of $(\alpha, y_0, y_1)$. For large $z$ the solution follows if we also specify $z_c$, with $Y(z)$ diverging as $z^{5/3}$ for high $z$. The four undetermined parameters $(\alpha,y_0,y_1,z_c)$ were determined by fitting the theory to experimental data taken by a Duke University group on $^6$Li in an optical trap with a Gaussian potential. The very best fit of this theory to the data had $\alpha=2.1$, $z_c=4.7$, $y_0=0.277$, and $y_1=0.0735$, with $\chi^2=0.95$. The corresponding Bertsch parameter is $\xi_B=0.462(40)$.

Fulde-Ferrell pairing instability of a Rashba spin-orbit-coupled Fermi gas

We theoretically analyze the pairing instability of a three-dimensional ultracold atomic Fermi gas towards a Fulde-Ferrell superfluid, in the presence of Rashba spin-orbit coupling and in-plane Zeeman field. We use the standard Thouless criterion for the onset of superfluidity, with which the effect of pair fluctuations is partially taken into account by approximately using a mean-field chemical potential at zero temperature. This gives rise to an improved prediction of the superfluid transition temperature beyond mean-field, particularly in the strong-coupling unitary limit. We also investigate the pairing instability with increasing Rashba spin-orbit coupling, along the crossover from a Bardeen-Cooper-Schrieffer superfluid to a Bose-Einstein condensate of Rashbons (i.e., the tightly bound state of two fermions formed by strong Rashba spin-orbit coupling

Three-Dimensional Anderson Localization in Variable Scale Disorder

We report on the impact of variable-scale disorder on 3D Anderson localization of a noninteracting ultracold atomic gas. A spin-polarized gas of fermionic atoms is localized by allowing it to expand in an optical speckle potential. Using a sudden quench of the localized density distribution, we verify that the density profile is representative of the underlying single-particle localized states. The geometric mean of the disordering potential correlation lengths is varied by a factor of 4 via adjusting the aperture of the speckle focusing lens. We observe that the root-mean-square size of the localized gas increases approximately linearly with the speckle correlation length, in qualitative agreement with the scaling predicted by weak scattering theory.

Pairing fluctuation effects in a strongly coupled color superfluid/superconductor

We investigate the effects of pairing fluctuations in fermionic superfluids/superconductors where pairing occurs among three species (colors) of fermions. Such color superfluids/superconductors can be realized in three-component atomic Fermi gases and in dense quark matter. The superfluidity/superconductivity is characterized by a three-component order parameter which denotes the pairing among the three colors of fermions. Due to the SU$(3)$ symmetry of the Hamiltonian, one color does not participate pairing. This branch of fermionic excitation is gapless in the naive BCS mean-field description. In this paper, we adopt a pairing-fluctuation theory to investigate the pairing fluctuation effects on the unpaired color in strongly coupled atomic color superfluids and quark color superconductors. At low temperature, a large pairing gap of the paired colors suppresses the pairing fluctuation effects for the unpaired color, and the spectral density of the unpaired color shows a single Fermi-liquid peak, which indicates the naive mean-field picture remains valid. As the temperature is increased, the spectral density of the unpaired color generally exhibits a three-peak structure: the Fermi-liquid peak remains but get suppressed, and two pseudogap-like peaks appears. At and above the superfluid transition temperature, the Fermi-liquid peak disappears completely and the all three colors exhibits pseudogap-like spectral density. The coexistence of Fermi liquid and pseudogap behavior is generic for both atomic color superfluids and quark color superconductors.

Fulde–Ferrell superfluidity in ultracold Fermi gases with Rashba spin–orbit coupling

We theoretically investigate the inhomogeneous Fulde–Ferrell (FF) superfluidity in a three-dimensional atomic Fermi gas with Rashba spin–orbit coupling near a broad Feshbach resonance. We show that within mean-field theory the FF superfluid state is always more favorable than the standard Bardeen–Cooper–Schrieffer superfluid state when an in-plane Zeeman field is applied. We present a qualitative finite-temperature phase diagram near resonance and argue that the predicted FF superfluid is observable with experimentally attainable temperatures (i.e. T ∼ 0.2TF, where TF is the characteristic Fermi degenerate temperature).

Topological Fulde-Ferrell superfluid in spin-orbit-coupled atomic Fermi gases

We theoretically predict a new topological matter - topological inhomogeneous Fulde-Ferrell superfluid - in one-dimensional atomic Fermi gases with equal Rashba and Dresselhaus spin-orbit coupling near s-wave Feshbach resonances. The realization of such a spin-orbit coupled Fermi system has already been demonstrated recently by using a two-photon Raman process and the extra one-dimensional confinement is easy to achieve using a tight two-dimensional optical lattice. The topological Fulde-Ferrell superfluid phase is characterized by a nonzero center-of-mass momentum and a non-trivial Berry phase. By tuning the Rabi frequency and the detuning of Raman laser beams, we show that such an exotic topological phase occupies a significant part of parameter space and therefore it could be easily observed experimentally, by using, for example, momentum-resolved and spatially resolved radio-frequency spectroscopy.

Influence of induced interactions on superfluid properties of quasi-two-dimensional dilute Fermi gases with spin-orbit coupling

We study the effects of induced interactions on the pairing gap, transition temperature and chemical potential of a quasi-two dimensional Fermi gas of atoms with spin-orbit coupling. We find that these mean-field parameters are significantly modified when induced interactions are taken into account. We also investigate the implications of induced interactions corrections for the BCS-BEC crossover driven by spin-orbit coupling, that happens even for small (compared to the Fermi energy) values of the binding energy.

Raman-Induced Interactions in a Single-Component Fermi Gas Near ans-Wave Feshbach Resonance

Ultracold gases of interacting spin-orbit-coupled fermions are predicted to display exotic phenomena such as topological superfluidity and its associated Majorana fermions. Here, we experimentally demonstrate a route to strongly interacting single-component atomic Fermi gases by combining an s-wave Feshbach resonance (giving strong interactions) and spin-orbit coupling (creating an effective p-wave channel). We identify the Feshbach resonance by its associated atomic loss feature and show that, in agreement with our single-channel scattering model, this feature is preserved and shifted as a function of the spin-orbit-coupling parameters.

BCS-BEC crossover in a quasi-two-dimensional Fermi gas

We consider a two-component gas of fermionic atoms confined to a quasi-two-dimensional (quasi-2D) geometry by a harmonic trapping potential in the transverse direction. We construct a mean field theory of the BCS-BEC crossover at zero temperature that allows us to extrapolate to an infinite number of transverse harmonic oscillator levels. In the extreme BEC limit, where the confinement length exceeds the dimer size, we recover 3D dimers confined to 2D with weak repulsive interactions. However, even when the interactions are weak and the Fermi energy is less than the confinement frequency, we find that the higher transverse levels can substantially modify fermion pairing. We argue that recent experiments on pairing in quasi-2D Fermi gases [Y. Zhang et al., Phys. Rev. Lett. 108, 235302 (2012)] have already observed the effects of higher transverse levels.

Experimental determination ofp-wave scattering parameters in ultracold6Li atoms

We report the experimental determination of the scattering parameters for a p-wave Feshbach resonance in a single component Fermi gas of 6Li atoms in the lowest spin state. The time scale of the cross-dimensional relaxation reflects the elastic scattering rate of the atoms, and scattering parameters are determined from the scattering rate as a function of magnetic field by taking into account the momentum distribution and inhomogeneous density profile of the atoms in a trap. Precise determination of the scattering parameters for a p-wave Feshbach resonance is an important step toward the realization of a p-wave superfluid in an ultracold atomic gas.

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.

Nesting and lifetime effects in the FFLO state of quasi-one-dimensional imbalanced Fermi gases

Motivated by the recent experimental realization of a candidate to the Fulde–Ferrell (FF) and the Larkin–Ovchinnikov (LO) states in one-dimensional (1D) atomic Fermi gases, we study the quantum phase transitions in these enigmatic, finite-momentum-paired superfluids. We focus on the FF state and investigate the effects of the induced interaction on the stability of the FFLO phase in homogeneous spin-imbalanced quasi-1D Fermi gases at zero temperature. When this is taken into account, we find a direct transition from the fully polarized to the FFLO state in agreement with exact solutions. Also, we consider the effect of a finite lifetime of the quasi-particle states in the normal-superfluid instability. In the limit of long lifetimes, the lifetime effect is irrelevant and the transition is directly from the fully polarized to the FFLO state. We show, however, that for sufficiently short lifetimes, there is a quantum critical point, at a finite value of the mismatch of the Fermi wave-vectors of the different quasi-particles, that we fully characterize. In this case, the transition is from the FFLO phase to a normal partially polarized state with increasing mismatch.

Realizing one-dimensional topological superfluids with ultracold atomic gases

We propose an experimental implementation of a topological superfluid with ultracold fermionic atoms. An optical superlattice is used to juxtapose a 1D gas of fermionic atoms and a 2D conventional superfluid of condensed Feshbach molecules. The latter acts as a Cooper pair reservoir and effectively induces a superfluid gap in the 1D system. Combined with a spin-dependent optical lattice along the 1D tube and laser-induced atom tunnelling, we obtain a topological superfluid phase. In the regime of weak couplings to the molecular field and for a uniform gas, the atomic system is equivalent to Kitaev’s model of a p-wave superfluid. Using a numerical calculation, we show that the topological superfluidity is robust beyond the perturbative limit and in the presence of a harmonic trap. Finally, we describe how to investigate some physical properties of the Majorana fermions located at the topological superfluid boundaries. In particular, we discuss how to prepare and detect a given Majorana edge state.

Phonon contribution to the shear viscosity of a superfluid Fermi gas in the unitarity limit

We present a detailed analysis of the contribution of small-angle Nambu–Goldstone boson (phonon) collisions to the shear viscosity, η, in a superfluid atomic Fermi gas close to the unitarity limit. We show that the experimental values of the shear viscosity coefficient to entropy ratio, η/s, obtained at the lowest reached temperature can be reproduced assuming that phonons give the leading contribution to η. The phonon contribution is evaluated considering 1↔2 processes and taking into account the finite size of the experimental system. In particular, for very low temperatures, T≲0.1TF, we find that phonons are ballistic and the contribution of phonons to the shear viscosity is determined by the processes that take place at the interface between the superfluid and the normal phase. This result is independent of the detailed form of the phonon dispersion law and leads to two testable predictions: the shear viscosity should correlate with the size of the optical trap and it should decrease with decreasing temperature. For higher temperatures the detailed form of the phonon dispersion law becomes relevant and, within our model, we find that the experimental data for η/s can be reproduced assuming that phonons have an anomalous dispersion law.

Unconventional spin-density waves in dipolar Fermi gases

The conventional spin density wave (SDW) phase (Overhauser, 1962), as found in antiferromagnetic metal for example (Fawcett 1988), can be described as a condensate of particle-hole pairs with zero angular momentum, $\ell=0$, analogous to a condensate of particle-particle pairs in conventional superconductors. While many unconventional superconductors with Cooper pairs of finite $\ell$ have been discovered, their counterparts, density waves with non-zero angular momenta, have only been hypothesized in two-dimensional electron systems (Nayak, 2000). Using an unbiased functional renormalization group analysis, we here show that spin-triplet particle-hole condensates with $\ell=1$ emerge generically in dipolar Fermi gases of atoms (Lu, Burdick, and Lev, 2012) or molecules (Ospelkaus et al., 2008; Wu et al.) on optical lattice. The order parameter of these exotic SDWs is a vector quantity in spin space, and, moreover, is defined on lattice bonds rather than on lattice sites. We determine the rich quantum phase diagram of dipolar fermions at half-filling as a function of the dipolar orientation, and discuss how these SDWs arise amidst competition with superfluid and charge density wave phases.

Scaling solutions of the two-fluid hydrodynamic equations in a harmonically trapped gas at unitarity

We prove that the two fluid Landau hydrodynamic equations, when applied to a gas interacting with infinite scattering length (unitary gas) in the presence of harmonic trapping, admit exact scaling solutions of mixed compressional and surface nature. These solutions are characterized by a linear dependence of the velocity field on the spatial coordinates and a temperature independent frequency which is calculated in terms of the parameters of the trap. Our results are derived in the regime of small amplitude oscillations and hold both below and above the superfluid phase transition. They apply to isotropic as well as to deformed configurations, thereby providing a generalization of Castin's theorem (Y. Castin, C. R. Phys. \textbf{5}, 407 (2004)) holding for isotropic trapping. Our predictions agree with the experimental findings in resonantly interacting atomic Fermi gases. The breathing scaling solution, in the presence of isotropic trapping, is also used to prove the vanishing of two bulk viscosity coefficients in the superfluid phase.

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.

Antiferrosmectic ground state of two-component dipolar Fermi gases: An analog of meson condensation in nuclear matter

We show that an antiferrosmectic-$C$ phase has lower energy at high densities than the nonmagnetized Fermi gas and ferronematic phases in an ultracold gas of fermionic atoms, or molecules, with large magnetic dipole moments. This phase, which is analogous to meson condensation in dense nuclear matter, is a one-dimensional periodic structure in which the fermions localize in layers with their pseudospin direction aligned parallel to the layers and staggered layer by layer.

Intrinsic Photoconductivity of Ultracold Fermions in Optical Lattices

We report on the experimental observation of an analog to a persistent alternating photocurrent in an ultracold gas of fermionic atoms in an optical lattice. The dynamics is induced and sustained by an external harmonic confinement. While particles in the excited band exhibit long-lived oscillations with a momentum-dependent frequency, a strikingly different behavior is observed for holes in the lowest band. An initial fast collapse is followed by subsequent periodic revivals. Both observations are fully explained by mapping the system onto a nonlinear pendulum.

Impurity probe of topological superfluids in one-dimensional spin-orbit-coupled atomic Fermi gases

We investigate theoretically non-magnetic impurity scattering in a one-dimensional atomic topological superfluid in harmonic traps, by solving self-consistently the microscopic Bogoliubov-de Gennes equation. In sharp contrast to topologically trivial Bardeen-Cooper-Schrieffer \textit{s}-wave superfluid, topological superfluid can host a mid-gap state that is bound to localized non-magnetic impurity. For strong impurity scattering, the bound state becomes universal, with nearly zero energy and a wave-function that closely follows the symmetry of that of Majorana fermions. We propose that the observation of such a universal bound state could be a useful evidence for characterizing the topolgoical nature of topological superfluids. Our prediction is applicable to an ultracold resonantly-interacting Fermi gas of $^{40}$K atoms with spin-orbit coupling confined in a two-dimensional optical lattice.