Ultracold Fermi Gases Research Articles

Pairing superfluidity in spin-orbit coupled ultracold Fermi gases

We review some recent progresses on the study of ultracold Fermi gases with synthetic spin-orbit coupling. In particular, we focus on the pairing superfluidity in these systems at zero temperature. Recent studies have shown that different forms of spin-orbit coupling in various spatial dimensions can lead to a wealth of novel pairing superfluidity. A common theme of these variations is the emergence of new pairing mechanisms which are direct results of spin-orbit-coupling-modified single-particle dispersion spectra. As different configurations can give rise to single-particle dispersion spectra with drastic differences in symmetry, spin dependence and low-energy density of states, spin-orbit coupling is potentially a powerful tool of quantum control, which, when combined with other available control schemes in ultracold atomic gases, will enable us to engineer novel states of matter.

Phase imprinting in equilibrating Fermi gases: the transience of vortex rings and other defects.

We present numerical simulations of phase imprinting experiments in ultracold trapped Fermi gases, which were obtained independently and are in good agreement with recent experimental results. Our focus is on the sequence and evolution of defects using the fermionic time-dependent Ginzburg-Landau equation, which contains dissipation necessary for equilibration. In contrast to other simulations, we introduce small, experimentally unavoidable symmetry breaking, particularly that associated with thermal fluctuations and with the phase-imprinting tilt angle, and we illustrate their dramatic effects. As appears consistent with experiment, the former causes vortex rings in confined geometries to move to the trap surface and rapidly decay into more stable vortex lines. The latter aligns the precessing and relatively long-lived vortex filaments, rendering them difficult to distinguish from solitons.

Wave Packet Dynamics of Superfluid Fermi Gases in an Anharmonic Trap

We investigate the collective excitations of a one-dimensional ultracold Fermi gas in the crossover from a Bardeen–Cooper–Schrieffer superfluid to a Bose-Einstein condensate. The trap we consider is a quadratic plus quartic potential in view of the relevant experimental conditions. Using variational approaches, the coupled equations of motions for the center-of-mass coordinate of the Superfluid Fermi gas and its width are derived. Then, two low-energy excitation modes are obtained analytically. The frequency shift induced by the anharmonic distortion, and the collapse and revival of the collective excitations originating from the nonlinear coupling between the two modes are discussed.

Universal Borromean Binding in Spin-Orbit-Coupled Ultracold Fermi Gases

Borromean rings and Borromean binding, a class of intriguing phenomena as three objects are linked (bound) together while any two of them are unlinked (unbound), widely exist in nature and have been found in systems of biology, chemistry and physics. Previous studies have suggested that the occurrence of such a binding in physical systems typically relies on the microscopic details of pairwise interaction potentials at short-range, and is therefore non-universal. Here, we report a new type of Borromean binding in ultracold Fermi gases with Rashba spin-orbit coupling, which is {\it universal} against short-range interaction details, with its binding energy only dependent on the s-wave scattering length and the spin-orbit coupling strength. We show that the occurrence of this universal Borromean binding is facilitated by the symmetry of the single-particle dispersion under spin-orbit coupling, and is therefore {\it symmetry-selective} rather than interaction-selective. The state is robust over a wide range of mass ratio between composing fermions, which are accessible by Li-Li, K-K and K-Li mixtures in cold atoms experiments. Our results reveal the importance of symmetry factor in few-body physics, and shed light on the emergence of new quantum phases in a many-body system with exotic few-body correlations.

Phase correlations and quasicondensate in a two-dimensional ultracold Fermi gas

The interplay between dimensionality, coherence and interaction in superfluid Fermi gases is analyzed by the phase correlation function of the field of fermionic pairs. We calculate this phase correlation function for a two-dimensional superfluid Fermi gas with $s$-wave interactions within the Gaussian pair fluctuation formalism. The spatial behavior of the correlation function is shown to exhibit a rapid (exponential) decay at short distances and a characteristic algebraic decay at large distances, with an exponent matching that expected from Berezinskii-Kosterlitz-Thouless theory of 2D Bose superfluids. We conclude that the Gaussian pair fluctuation approximation is able to capture the physics of quasi long-range order in two-dimensional Fermi gases.

“Slow” wave of zero-sound in degenerate Fermi gas

Abstract The dynamic Hartree-Fock theory with point-like interaction is used to calculate the speed of sound and damping factor of a zero-sound wave propagating in a degenerate Fermi gas. This wave propagates slower than Fermi velocity. It is shown, that if the interaction is weak and density is small, then the damping of such a wave can be small. A possibility of discovering such waves in ultracold Fermi gases is discussed.

Current reversals in rapidly rotating ultracold Fermi gases

We study the equilibrium current density profiles of harmonically trapped ultracold Fermi gases in quantum Hall-like states that appear when the quasi-two-dimensional trap is set in fast rotation. The density profile of the gas (in the rotating reference frame) consists of incompressible strips of constant quantized density separated by compressible regions in which the density varies. Remarkably, we find that the atomic currents flow in opposite directions in the compressible and incompressible regions---a prediction that should be amenable to experimental verification.

BCS-BEC crossover and quantum phase transition in an ultracold Fermi gas under spin-orbit coupling

In this work, we study the BCS-BEC crossover and quantum phase transition in a Fermi gas under Rashba spin-orbit coupling close to a Feshbach resonance. By adopting a two-channel model, we take into account the closed-channel molecules, and show that combined with spin-orbit coupling, a finite background scattering in the open channel can lead to two branches of solution for both the two-body and the many-body ground states. The branching of the two-body bound-state solution originates from the avoided crossing between bound states in the open and the closed channels, respectively. For the many-body states, we identify a quantum phase transition in the upper branch regardless of the sign of the background scattering length, which is in clear contrast to the case without spin-orbit coupling. For systems with negative background scattering length in particular, we show that the bound state in the open channel, and hence the quantum phase transition in the upper branch, are induced by spin-orbit coupling. We then characterize the critical detuning of the quantum phase transition for both positive and negative background scattering lengths, and demonstrate the optimal parameters for the critical point to be probed experimentally.

The Kohn-Luttinger effect and anomalous pairing in new superconducting systems and graphene

We present a review of theoretical investigations into the Kohn-Luttinger nonphonon superconductivity mechanism in various 3D and 2D repulsive electron systems described by the Fermi-gas, Hubbard, and Shubin-Vonsovsky models. Phase diagrams of the superconducting state are considered, including regions of anomalous $s$-, $p$-, and $d$-wave pairing. The possibility of a strong increase in the superconducting transition temperature $T_c$ even for a low electron density is demonstrated by analyzing the spin-polarized case or the two-band situation. The Kohn-Luttinger theory explains or predicts superconductivity in various materials such as heterostructures and semimetals, superlattices and dichalcogenides, high-$T_c$ superconductors and heavy-fermion systems, layered organic superconductors, and ultracold Fermi gases in magnetic traps. This theory also describes the anomalous electron transport and peculiar polaron effects in the normal state of these systems. The theory can be useful for explaining the origin of superconductivity and orbital currents (chiral anomaly) in systems with the Dirac spectrum of electrons, including superfluid $^3$He-A, doped graphene, and topological superconductors.

Phases of spin- and mass-imbalanced ultracold Fermi gases in harmonic traps

We analyze the phase structure of mass- and spin-imbalanced unitary Fermi gases in harmonic traps. To this end, we employ density functional theory in the local density approximation. Depending on the values of the control parameters measuring mass and spin imbalance, we observe that three regions exist in the trap, namely, a superfluid region at the center, surrounded by a mixed region of resonantly interacting spin-up and spin-down fermions, and, finally, a fully polarized phase surrounding the previous two regions. We also find regimes in the phase diagram where the existence of a superfluid region at the center of the trap is not energetically favored. We point out the limitations of our approach at the present stage and call for more detailed (ab initio) studies of the equation of state of uniform, mass-imbalanced unitary Fermi gases.

Relaxation Dynamics of an Isolated Large-Spin Fermi Gas Far from Equilibrium

A fundamental question in many-body physics is how closed quantum systems reach equilibrium. We address this question experimentally and theoretically in an ultracold large-spin Fermi gas where we find a complex interplay between internal and motional degrees of freedom. The fermions are initially prepared far from equilibrium with only a few spin states occupied. The subsequent dynamics leading to redistribution among all spin states is observed experimentally and simulated theoretically using a kinetic Boltzmann equation with full spin coherence. The latter is derived microscopically and provides good agreement with experimental data without any free parameters. We identify several collisional processes, which occur on different time scales. By varying density and magnetic field, we control the relaxation dynamics and are able to continuously tune the character of a subset of spin states from an open to a closed system.

Publisher's Note: Uniform spin susceptibility and spin-gap phenomenon in the BCS-BEC-crossover regime of an ultracold Fermi gas [Phys. Rev. A89, 033617 (2014)

Publisher's Note: Uniform spin susceptibility and spin-gap phenomenon in the BCS-BEC-crossover regime of an ultracold Fermi gas [Phys. Rev. A<b>89</b>, 033617 (2014)

Uniform spin susceptibility and spin-gap phenomenon in the BCS-BEC-crossover regime of an ultracold Fermi gas

We investigate the uniform spin susceptibility $\chi_{\rm s}$ in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover regime of an ultracold Fermi gas. Including pairing fluctuations within the framework of an extended $T$-matrix approximation, we show that $\chi_{\rm s}$ exhibits non-monotonic temperature dependence in the normal state. In particular, $\chi_{\rm s}$ is suppressed near the superfluid phase transition temperature $T_{\rm c}$ due to strong pairing fluctuations. To characterize this anomalous behavior, we introduce the spin-gap temperature $T_{\rm s}$ as the temperature at which $\chi_{\rm s}$ takes a maximum value. Determining $T_{\rm s}$ in the whole BCS-BEC crossover region, we identify the spin-gap regime in the phase diagram of a Fermi gas in terms of the temperature and the strength of a pairing interaction. We also clarify how the spin-gap phenomenon is related to the pseudogap phenomenon appearing in the single-particle density of states. Our results indicate that an ultracold Fermi gas in the BCS-BEC crossover region is a very useful system to examine the pseudogap phenomenon and the spin-gap phenomenon in a unified manner.

Crossover from Bardeen-Cooper-Schrieffer to Bose-Einstein Condensation and the Unitary Fermi Gas

The crossover from weak-coupling Bardeen-Cooper-Schrieffer (BCS) pairing to a Bose-Einstein condensate (BEC) of tightly bound pairs, as a function of the attractive interaction in Fermi systems, has long been of interest to theoretical physicists. The past decade has seen a series of remarkable experimental developments in ultracold Fermi gases that have realized the BCS-BEC crossover in the laboratory, bringing with it fresh new insights into the very strongly interacting unitary regime in the middle of this crossover. In this review, we start with a pedagogical introduction to the crossover and then focus on recent progress in the strongly interacting regime. Although our focus is on new theoretical developments, we also describe three key experiments that probe the thermodynamics, transport, and spectroscopy of the unitary Fermi gas. We discuss connections between the unitary regime and other areas of physics—quark-gluon plasmas, gauge-gravity duality, and high-temperature superconductivity—and conclude with open questions about strongly interacting Fermi gases.

Pseudogap phenomenon and effects of population imbalance in the normal state of a unitary Fermi gas

We investigate strong-coupling corrections to single-particle excitations in the normal state of a spin-polarized unitary Fermi gas. Within the framework of an extended T-matrix approximation, we calculate the single-particle density of states, as well as the single-particle spectral weight, to show that the so-called pseudogap phenomenon gradually disappears with increasing the magnitude of an effective magnetic field. In the highly spin-polarized regime, the calculated spin-polarization rate as a function of the effective magnetic field agrees well with the recent experiment on a 6Li Fermi gas. Although this experiment has been considered to be incompatible with the existence of the pseudogap in an unpolarized Fermi gas, our result clarifies that the observed spin-polarization rate in the highly spin-polarized regime and the pseudogap in the unpolarized limit can be explained in a consistent manner, when one correctly includes effects of population imbalance on single-particle excitations. Since it is a crucial issue to clarify whether the pseudogap exists or not in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover regime of an ultracold Fermi gas, our results would be useful for the understanding of this strongly interacting fermion system.

Effect of phase fluctuations on the Fulde-Ferrell-Larkin-Ovchinnikov state in a three-dimensional Fermi gas

In ultracold Fermi gases, the effect of spin-imbalance on superfluidity has been the subject of intense study. One of the reasons for this is that spin-imbalance frustrates the Bardeen-Cooper-Schrieffer (BCS) superfluid pairing mechanism, in which fermions in different spin states combine into Cooper pairs with zero momentum. In 1964, it was proposed that an exotic superfluid state called the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, in which the Cooper pairs have nonzero momentum, could exist in a spin-imbalanced Fermi gas. At the saddle-point (mean field) level, it has been shown that the FFLO state only occupies a very small sliver in the ground state phase diagram of a 3D Fermi gas. However, a question that remains to be investigated is: what is the influence of phase fluctuations around the saddle point on the FFLO state? In this work we show that phase fluctuations only lead to relatively small quantitative corrections to the presence of the FFLO state in the saddle-point phase diagram of a 3D spin-imbalanced Fermi gas. Starting from the partition function of the system, we calculate the effective action within the path-integral adiabatic approximation. The action is then expanded up to second order in the fluctuation field around the saddle point, leading to the fluctuation free energy. Using this free energy, we calculate corrections due to phase fluctuations to the BCS-FFLO transition in the saddle-point phase diagram. At temperatures at which the FFLO state exists, we find only small corrections to the size of the FFLO area. Our results suggest that fluctuations of the phase of the FFLO order parameter, which can be interpreted as an oscillation of its momentum vector, do not cause an instability of the FFLO state with respect to the BCS state.

Universal Trimers Induced by Spin-Orbit Coupling in Ultracold Fermi Gases

In this Letter we address the issue of how synthetic spin-orbit (SO) coupling can strongly affect three-body physics in ultracold atomic gases. We consider a system which consists of three fermionic atoms, including two spinless heavy atoms and one spin-1/2 light atom subjected to an isotropic SO coupling. We find that SO coupling can induce universal three-body bound states with a negative s-wave scattering length at a smaller mass ratio, where no trimer bound state can exist if in the absence of SO coupling. The energies of these trimers are independent of the high-energy cutoff, and therefore they are universal ones. Moreover, the resulting atom-dimer resonance can be effectively controlled by SO coupling strength. Our results can be applied to systems like a 6Li and 40K mixture.

Effects of the spin-orbit coupling on the phase transition of ultra cold repulsive Fermi gases

Effects of the spin-orbit coupling on the phase transition of ultra cold repulsive Fermi gases

Quantum Breathing Mode of Trapped Particles: From Nanoplasmas to Ultracold Gases

AbstractParticles spatially confined in trapping potentials have attracted increasing interest over the recent decade. Of particular importance are systems of charged particles, such as non‐neutral plasmas, nanoplasmas, electrons in metal clusters, electrons in quantum‐confined semiconductor structures (“artificial atoms”), electrons on the surface of liquid helium, ions in traps or highly charged particles (grains) in dusty plasmas. A second example of recent interest are systems with other kinds of pair interactions, including dipole interaction, which is important for excitons in quantum wells or ultracold Fermi and Bose gases in traps and optical lattices.Trapped systems are fundamentally different from macroscopic systems since they are dominated by strong spatial inhomogeneity and finite size effects (the properties depend on the exact particle number). Furthermore, by changing the strength of the confinement potential, the many‐particle state of the system can be externally controlled—from weak coupling (gas‐like) to strong coupling (crystal‐like). While trapped classical particles are meanwhile well understood and accessible to first‐principle computer simulations, their quantum counterparts still pose big challenges, both for experiment and theory. Therefore, collective properties that can be easily measured or computed and allow to diagnose the many‐particle state of the system are of prime importance. It has been found that the quantum breathing mode (monopole oscillation) is one of the most important such properties. In recent years a number of theoretical studies has demonstrated that the quantum breathing mode is ideally suited to measure the coupling strength (the degree of nonideality) of a trapped system, its kinetic and interaction energy and other key observables. This give rise to a novel kind of “spectroscopy” of trapped systems.In this review these developments are summarized. The quantum breathing mode is studied for trapped fermions and bosons with Coulomb and dipole interaction, respectively. A systematic description of collective oscillations and especially the breathing mode is provided. Making use of time‐dependent perturbation theory, it is shown how the corresponding breathing frequencies are connected to the properties of the initial equilibrium system. This gives rise to the application of the quantum mechanical sum rules. It is demonstrated how an improved version of the conventional sum rule formulas is suitable for an accurate description of the breathing mode in small systems. Finally, the dependence of the breathing mode on the particle number N is analyzed and the limit of large N is studied for one‐dimensional and two‐dimensional systems. (© 2014 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Phases of spin- and mass-imbalanced ultracold Fermi gases in harmonic traps

Phases of spin- and mass-imbalanced ultracold Fermi gases in harmonic traps