Atomic Fermi Gas Research Articles

BCS-BEC crossover in three-dimensional Fermi gases with spherical spin-orbit coupling

We present a systematic theoretical study of the BCS-BEC crossover problem in three-dimensional atomic Fermi gases at zero temperature with a spherical spin-orbit coupling which can be generated by a synthetic non-Abelian gauge field coupled to neutral fermions. Our investigations are based on the path integral formalism which is a powerful theoretical scheme for the study of the properties of the bound state, the superfluid ground state, and the collective excitations in the BCS-BEC crossover. At large spin-orbit coupling, the system enters the BEC state of a novel type of bound state (referred to as rashbon) which possesses a non-trivial effective mass. Analytical results and interesting universal behaviors for various physical quantities at large spin-orbit coupling are obtained. Our theoretical predictions can be tested in future experiments of cold Fermi gases with three-dimensional spherical spin-orbit coupling.

Boltzmann equation simulation for a trapped Fermi gas of atoms

The dynamics of an interacting Fermi gas of atoms at sufficiently high temperatures can be efficiently studied via a numerical simulation of the Boltzmann equation. In this paper, we describe in detail the setup we used recently to study the oscillations of two spin-polarized fermionic clouds in a trap. We focus here on the evaluation of interparticle interactions. We compare different ways of choosing the phase space coordinates of a pair of atoms after a successful collision and demonstrate that the exact microscopic setup has no influence on the macroscopic outcome.

On the role of the uncertainty principle in superconductivity and superfluidity

We discuss the general interplay between the uncertainty principle and the onset of dissipationless transport phenomena such as superconductivity and superfluidity. We argue that these phenomena are possible because of the robustness of many-body quantum states with respect to the external environment, which is directly related to the uncertainty principle as applied to coordinates and momenta of the carriers. In the case of superconductors, this implies relationships between macroscopic quantities such as critical temperature and critical magnetic field, and microscopic quantities such as the amount of spatial squeezing of a Cooper pair and its correlation time. In the case of ultracold atomic Fermi gases, this should be paralleled by a connection between the critical temperature for the onset of superfluidity and the corresponding critical velocity. Tests of this conjecture are finally sketched with particular regard to the understanding of the behaviour of superconductors under external pressures or mesoscopic superconductors, and the possibility to mimic these effects in ultracold atomic Fermi gases using Feshbach resonances and atomic squeezed states.

Polaron-to-Polaron Transitions in the Radio-Frequency Spectrum of a Quasi-Two-Dimensional Fermi Gas

We measure radio-frequency spectra for a two-component mixture of a 6Li atomic Fermi gas in a quasi-two-dimensional regime with the Fermi energy comparable to the energy level spacing in the tightly confining potential. Near the Feshbach resonance, we find that the observed resonances do not correspond to transitions between confinement-induced dimers. The spectral shifts can be fit by assuming transitions between noninteracting polaron states in two dimensions.

Josephson effect in superfluid atomic Fermi gases at finite temperature

By using Green's function method and linear response theory the Josephson effect of neutral fermions at finite temperature is investigated. Four different hyperfine states of the atoms are assumed to be trapped and to form two superfluids via the BCS-type of pairing. The Josephson effect can be realized by coupling the superfluids with two laser fields. The laser interaction is assumed to be a small perturbation and its effect is calculated using linear response theory. Both, single particle tunneling and the Josephson current, at finite temperature are calculated in Matsubara formalism.

Repulsive polarons found

Quasiparticles known as repulsive polarons are predicted to occur when 'impurity' fermionic particles interact repulsively with a fermionic environment. They have now been detected in two widely differing systems. See Letters p.615 & p.619 Metastable states in Fermi gases with strong repulsive interactions are of fundamental interest, but the realization of such systems is challenging because they are intrinsically unstable against decay. Two groups have overcome this obstacle and report the detection of the theoretically predicted repulsive Fermi polarons. Kohstall et al. study a three-dimensional system of ultracold potassium impurities resonantly interacting with a Fermi sea of lithium atoms. The character of the interaction stabilizes the repulsive regime, enabling the authors to detect long-lived, metastable repulsive polarons. Koschorreck et al. study both attractive and repulsive Fermi polarons in a two-dimensional, spin-imbalanced Fermi gas of potassium atoms, and find evidence for a pairing transition. The results from these two studies hold promise for the creation of exotic states with ultracold fermionic atoms, such as ferromagnetic quantum phases.

The J-triplet Cooper pairing with magnetic dipolar interactions

Recently, cold atomic Fermi gases with the large magnetic dipolar interaction have been laser cooled down to quantum degeneracy. Different from electric-dipoles which are classic vectors, atomic magnetic dipoles are quantum-mechanical matrix operators proportional to the hyperfine-spin of atoms, thus provide rich opportunities to investigate exotic many-body physics. Furthermore, unlike anisotropic electric dipolar gases, unpolarized magnetic dipolar systems are isotropic under simultaneous spin-orbit rotation. These features give rise to a robust mechanism for a novel pairing symmetry: orbital p-wave (L = 1) spin triplet (S = 1) pairing with total angular momentum of the Cooper pair J = 1. This pairing is markedly different from both the 3He-B phase in which J = 0 and the 3He-A phase in which J is not conserved. It is also different from the p-wave pairing in the single-component electric dipolar systems in which the spin degree of freedom is frozen.

Short-range correlations in dilute atomic Fermi gases with spin-orbit coupling

We study the short-range correlation strength of three dimensional spin half dilute atomic Fermi gases with spin-orbit coupling. The interatomic interaction is modeled by the contact pseudopotential. In the high temperature limit, we derive the expression for the second order virial expansion of the thermodynamic potential via the ladder diagrams. We further evaluate the second order virial expansion in the limit that the spin-orbit coupling constants are small, and find that the correlation strength between the fermions increases as the forth power of the spin-orbit coupling constants. At zero temperature, we consider the cases in which there are symmetric spin-orbit couplings in two or three directions. In such cases, there is always a two-body bound state of zero net momentum. In the limit that the average interparticle distance is much larger than the dimension of the two-body bound state, the system primarily consists of condensed bosonic molecules that fermions pair to form; we find that the correlation strength also becomes bigger compared to that in the absence of spin-orbit coupling. Our results indicate that generic spin-orbit coupling enhances the short-range correlations of the Fermi gases. Measurement of such enhancement by photoassociation experiment is also discussed.

Ferromagnetic transition of a two-component Fermi gas of hard spheres

We use microscopic many-body theory to analyze the problem of itinerant ferromagnetism in a repulsive atomic Fermi gas of Hard Spheres. Using simple arguments, we show that the available theoretical predictions for the onset of the ferromagnetic transition predict a transition point at a density ($k_F a \sim 1$) that is too large to be compatible with the universal low-density expansion of the energy. We present new variational calculations for the hard-sphere Fermi gas, in the framework of Fermi hypperneted chain theory, that shift the transition to higher densities ($k_F a \sim 1.8$). Backflow correlations, which are mainly active in the unpolarized system, are essential for this shift.

Fermi gas of atoms

A rapidly developing field, experimental physics of ultracold gases of Fermi atoms, is briefly reviewed. The contribution of this field to fundamental physics is shown along with connection to other fields which explore systems of Fermi particles. The basic parameters of atomic Fermi gas are described together with its unique properties and advantages and disadvantages in comparison to other Fermi systems. The prospects of this field and its short history are considered. Research groups working in this field are listed.

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.

Probing Majorana fermions in spin-orbit-coupled atomic Fermi gases

We examine theoretically the visualization of Majorana fermions in a two-dimensional trapped ultracold atomic Fermi gas with spin-orbit coupling. By increasing an external Zeeman field, the trapped gas transits from non-topological to topological superfluid, via a mixed phase in which both types of superfluids coexist. We show that the zero-energy Majorana fermion, supported by the topological superfluid and localized at the vortex core, is clearly visible through (i) the core density and (ii) the local density of states, which are readily measurable in experiment. We present a realistic estimate on experimental parameters for ultracold $^{40}$K atoms.

Universal dynamic structure factor of a strongly correlated Fermi gas

Universality of strongly interacting fermions is a topic of great interest in diverse fields. Here we investigate theoretically the universal dynamic density response of resonantly interacting ultracold Fermi atoms in the limit of either high temperature or large frequency. At high temperature, we use quantum virial expansion to derive universal, nonperturbative expansion functions of the dynamic structure factor; at large momentum, we conjecture that the second-order expansion function gives the Wilson coefficient used in the operator product expansion method. The dynamic structure factor is therefore determined by its second-order expansion function with an overall normalization factor given by Tan's [S. Tan, Ann. Phys. (NY) 323, 2952 (2008); S. Tan, Ann. Phys. (NY) 323, 2971 (2008); S. Tan, Ann. Phys. (NY) 323, 2987 (2008)] contact parameter. We show that the spin-parallel and -antiparallel dynamic structure factors have, respectively, a tail of the form $\ensuremath{\sim}\ifmmode\pm\else\textpm\fi{}{\ensuremath{\omega}}^{\ensuremath{-}5/2}$ for $\ensuremath{\omega}\ensuremath{\rightarrow}\ensuremath{\infty}$, decaying slower than the total dynamic structure factor found previously ($\ensuremath{\sim}{\ensuremath{\omega}}^{\ensuremath{-}7/2}$). Our predictions for the dynamic structure factor at high temperature or large frequency are testable using Bragg spectroscopy for ultracold atomic Fermi gases.

Fermion Pairing in Flatland

Superconductivity and superfluidity in two dimensions (2D) has long been a subject of great interest. Materials with the highest known transition temperature Tc, the cuprates, are quasi-2D systems with superconductivity originating in the 2D copper-oxide planes. A deeper understanding of strongly interacting 2D superconductors and their normal states could potentially give insights into the unsolved problem of high-Tc superconductivity. Further, 2D is known to be the lower critical, or marginal, dimension both for pairing of fermions and for superfluidity. Thus 2D represents a borderline dimensionality, above and below which the system behaves qualitatively differently from a classical and a quantum perspective. Classically, thermal fluctuations of the order parameter destroy long-range order in 2D and lead to algebraic order at finite temperatures. In quantum mechanics, 2D is the marginal dimension for bound-state formation, which has important implications for the pairing of fermions that is essential for superfluidity. Finally, the effects of strong interactions in 2D Fermi systems present a formidable theoretical challenge. A paper [1] appearing in Physical Review Letters reports experiments with ultracold Fermi gas of lithium-6 atoms that give new insight into how dimensionality and interactions affect the binding of fermions to form a superfluid. Ariel Sommer and his colleagues at the Massachusetts Institute of Technology, Cambridge, use two independent knobs: a magnetic field to tune interatomic interactions and an optical lattice to tune the dimensionality between 3D and 2D. They then use radio-frequency (rf) spectroscopy to probe pairing in the many-particle system and relate it to bound-state formation in the twobody problem in the 2D limit. Although theorists have predicted how this pairing energy evolves with interaction strength and dimensionality, until now there were no real systems on which to test these ideas. In recent years there has been tremendous progress in controlling the interaction between atoms in ultracold gases with the Feshbach resonance technique, in which a magnetic field is used to tune the attractive s-wave interaction between Fermi atoms in two different hyperfine states [2–4]. This is the analog of tuning the attraction between spin-up and spin-down electrons in a metal, which is, of course, impossible in solid-state materials. An important outcome of this progress has been the ability to explore the crossover from a condensate of Cooper pairs, described by Bardeen-Cooper-Schrieffer (BCS) theory, to a Bose-Einstein condensate (BEC) of tightly bound diatomic molecules in 3D ultracold gases. The most significant new insights have come from studies of the very strongly interacting states at resonance [2, 3], which has scale-invariant properties [4] analogous to problems in nuclear physics and string theory. The experiment of Sommer et al.[1] builds on all of this progress with an optical lattice, which is a periodic potential that arises from interfering laser beams. By tuning the strength of this potential, V0, one can go from an anisotropic 3D system, for weak V0, to an essentially decoupled stack of 2D layers, in the limit of strong V0, which is shown schematically in Fig. 1. The MIT team probes the pairing between atoms with rf spectroscopy [2], in which photons transfer Fermi atoms from one hyperfine state to another. The resulting absorption intensity as a function of photon energy has a characteristic asymmetric line shape with a threshold for bound-to-free transitions that contains information about the spectrum of fermionic excitations. The meanfield theory for a BCS-BEC crossover predicts that the rf threshold is given by [2] hωth = √ μ2 + ∆2 − μ, where μ is the chemical potential and ∆ the BCS gap parameter. It is important to emphasize that the rf threshold is not simply ∆, in contrast to spectroscopic probes of electronic excitations in superconductors like tunneling. The reason is that rf photons excite Fermi atoms in all k states and the threshold is determined by k = 0 fermions. Sommer et al. interpret the rf threshold hωth as the “pair binding energy” in the many-body system. In 2D, the zero temperature mean-field equations for

Phase separation in low-density neutron matter

Low-density neutron matter has been studied extensively for many decades, with a view to better understanding the properties of neutron-star crusts and neutron-rich nuclei. Neutron matter is beyond experimental control, but in the past decade it has become possible to create systems of fermionic ultracold atomic gases in a regime close to low-density neutron matter. In both these contexts pairing is significant, making simple perturbative approaches impossible to apply and necessitating ab initio microscopic simulations. Atomic experiments have also probed polarized matter. In this work, we study population-imbalanced neutron matter (possibly relevant to magnetars and to density functionals of nuclei) arriving at the lowest-energy configuration to date. For small-to-intermediate relative fractions, the system turns out to be fully normal, while beyond a critical polarization we find phase coexistence between a partially polarized normal neutron gas and a balanced superfluid gas. As in cold atoms, a homogeneous polarized superfluid is close to stability but not stable with respect to phase separation. We also study the dependence of the critical polarization on the density.

Vortex line in spin-orbit coupled atomic Fermi gases

It has recently been shown that the spin-orbit coupling gives rise to topologically nontrivial and thermodynamically stable gapless superfluid phases when the pseudospin populations of an atomic Fermi gas are imbalanced, with the possibility of featuring Majorana zero-energy quasiparticles. In this paper, we consider a Rashba-type spin-orbit coupling, and use the Bogoliubov-de Gennes formalism to analyze a single vortex line along a finite cylinder with a periodic boundary condition. We show that the signatures for the appearance of core- and edge-bound states can be directly found in the density of single-particle states and particle-current density. In particular, we find that the pseudospin components counterflow near the edge of the cylinder, the strength of which increases with increasing 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.

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.

Observation of a pairing pseudogap in a two-dimensional Fermi gas

Pairing of fermions is ubiquitous in nature, underlying many phenomena. Examples include superconductivity, superfluidity of (3)He, the anomalous rotation of neutron stars, and the crossover between Bose-Einstein condensation of dimers and the BCS (Bardeen, Cooper and Schrieffer) regime in strongly interacting Fermi gases. When confined to two dimensions, interacting many-body systems show even more subtle effects, many of which are not understood at a fundamental level. Most striking is the (as yet unexplained) phenomenon of high-temperature superconductivity in copper oxides, which is intimately related to the two-dimensional geometry of the crystal structure. In particular, it is not understood how the many-body pairing is established at high temperature, and whether it precedes superconductivity. Here we report the observation of a many-body pairing gap above the superfluid transition temperature in a harmonically trapped, two-dimensional atomic Fermi gas in the regime of strong coupling. Our measurements of the spectral function of the gas are performed using momentum-resolved photoemission spectroscopy, analogous to angle-resolved photoemission spectroscopy in the solid state. Our observations mark a significant step in the emulation of layered two-dimensional strongly correlated superconductors using ultracold atomic gases.

Many-body theories of density response for a strongly correlated Fermi gas

Recent breakthroughs in the creation of ultra-cold atomic gases in the laboratory have ushered in major changes in physical science. Many novel experiments are now possible, with an unprecedented control of interaction, geometry and purity. Quantum many-body theory is facing severe challenges in quantitatively understanding new experimental results. Here, we review some recently developed theoretical techniques that provide successful predictions for density response of a strongly correlated atomic Fermi gas. These include the strong-coupling random-phase approximation theory, high-temperature quantum virial expansion, and asymptotically exact Tan relations applicable at large momentum.