Ultracold Fermi Gases Research Articles

Feasibility of a Fulde-Ferrell-Larkin-Ovchinnikov superfluid Fermi atomic gas

We theoretically explore a promising route to achieve the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state in a spin-imbalanced ultracold Fermi gas. In the current stage of cold atom physics, search for this exotic Fermi superfluid is facing two serious difficulties: One is the desperate destruction of the FFLO long-range order by FFLO pairing fluctuations, which precludes entering the phase through a second-order transition, even in three dimension. The other is the fierce competition with the phase separation into the BCS (Bardeen-Cooper-Schrieffer) state and the spin-polarized normal state. Including strong FFLO pairing fluctuations within the framework of the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink, we show that the anisotropy of Fermi surface introduced by an optical lattice makes the FFLO state stable against the paring fluctuations. This stabilized FFLO state is also found to be able to overcome the competition with the phase separation under a certain condition. Since the realization of unconventional Fermi superfluids is one of the most exciting challenges in cold atom physics, our results would contribute to the further development of this field.

Isothermal compressibility and effects of multibody molecular interactions in a strongly interacting ultracold Fermi gas

We theoretically investigate the isothermal compressibility $\kappa_{T}$ in the normal state of an ultracold Fermi gas. Including pairing fluctuations, as well as preformed-pair formations, within the framework of the self-consistent $T$-matrix approximation (SCTMA), we evaluate the temperature dependence of this thermodynamic quantity over the entire BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover region. While $\kappa_T$ in the weak-coupling BCS regime is dominated by Fermi atoms near the Fermi surface, correlations between tightly bound Cooper-pair molecules are found to play crucial roles in the strong-coupling BEC regime. In the latter region, besides a two-body molecular interaction, a three-body one is shown to sizably affect $\kappa_T$ near the superfluid phase transition temperature. Our results indicate that the strong-coupling BEC regime of an ultracold Fermi gas would provide a unique opportunity to study multi-body correlations between Cooper-pair molecules.

Dark solitons impinging on interfaces in a superfluid Fermi gas

Ultracold quantum gases in the superfluid regime exhibit solitons, localized excitations that require nonlinearity of the underlying field equation in order to preserve their shape as they propagate. Here, we investigate the behavior of solitons at an inhomogeneity: an interface that separates two different interaction regimes of a superfluid Fermi gas. It is known that the soliton properties depend on the interaction regime, but what happens as a soliton impinges on such an interface is not clear. Using an effective field theory to describe the superfluid Fermi gas, we reveal the nontrivial dynamics of such a collision. Whether the original soliton makes it through the interface depends on the amplitude of the soliton. Regardless of whether the original soliton is transmitted or not, there will always be a shock wave with a phonon train created behind the interface and reflected secondary solitons. The details of this dynamics depends strongly on the equation of state corresponding to underlying microscopic theory describing the superfluid Fermi gas, and we argue that these collisions are realistic experimental probes to test microscopic theories of pairing in ultracold Fermi gases.

Scattering hypervolume of fermions in two dimensions

We define the three-body scattering hypervolume ${D}_{F}$ for identical spin-polarized fermions in two dimensions by considering the wave function of three such fermions colliding at zero energy and zero orbital angular momentum. We derive the asymptotic expansions of such a wave function when three fermions are far apart or one pair and the third fermion are far apart, and ${D}_{F}$ appears in the coefficients of such expansions. For weak-interaction potentials, we derive an approximate formula of ${D}_{F}$ by using the Born expansion. We then study the shift of energy of three such fermions in a large periodic area due to ${D}_{F}$. This shift is proportional to ${D}_{F}$ times the square of the area of the triangle formed by the momenta of the fermions. We also calculate the shifts of energy and of pressure of spin-polarized two-dimensional Fermi gases due to a nonzero ${D}_{F}$ and the three-body recombination rate of spin-polarized ultracold atomic Fermi gases in two dimensions.

Ground states of atomic Fermi gases in a two-dimensional optical lattice with and without population imbalance

We study the ground state phase diagram of population balanced and imbalanced ultracold atomic Fermi gases with a short range attractive interaction throughout the crossover from BCS to Bose-Einstein condensation (BEC), in a two-dimensional optical lattice (2DOL) comprised of two lattice and one continuum dimensions. We find that the mixing of lattice and continuum dimensions, together with population imbalance, has an extraordinary effect on pairing and the superfluidity of atomic Fermi gases. In the balanced case, the superfluid ground state prevails the majority of the phase space. However, for relatively small lattice hopping integral $t$ and large lattice constant $d$, a pair density wave (PDW) emerges unexpectedly at intermediate coupling strength, and the nature of the in-plane and overall pairing changes from particle-like to hole-like in the BCS and unitary regimes, associated with an abnormal increase in the Fermi volume with the pairing strength. In the imbalanced case, the stable polarized superfluid phase shrinks to only a small portion of the entire phase space spanned by $t$, $d$, imbalance $p$ and interaction strength $U$, mainly in the bosonic regime of low $p$, moderately strong pairing, and relatively large $t$ and small $d$. Due to the Pauli exclusion between paired and excessive fermions within the confined momentum space, a PDW phase emerges and the overall pairing evolves from particle-like into hole-like, as the pairing strength grows stronger in the BEC regime. In both cases, the ground state property is largely governed by the Fermi surface topology. These findings are very different from the cases of pure 3D continuum, 3D lattice or 1DOL.

Angular topological superfluid and topological vortex in an ultracold Fermi gas

We show that pairing in an ultracold Fermi gas under spin-orbital-angular-momentum coupling (SOAMC) can acquire topological characters encoded in the quantized angular degrees of freedom. The resulting topological superfluid is the angular analog of its counterpart in a one-dimensional Fermi gas with spin-orbit coupling, but characterized by a Zak phase defined in the angular-momentum space. Upon tuning the SOAMC parameters, a topological phase transition occurs, which is accompanied by the closing of the quasiparticle excitation gap. Remarkably, a topological vortex state can also be stabilized by deforming the Fermi surface, which is topologically nontrivial in both the coordinate and angular-momentum space, offering interesting potentials for applications in quantum information and quantum control. We discuss how the topological phase transition and the exotic vortex state can be detected experimentally.

Stochastic dynamics and bound states of heavy impurities in a Fermi bath

We investigate the dynamics of heavy impurities embedded in an ultracold Fermi gas by using a generalized Langevin equation. The latter---derived by means of influence functional theory---describes how the stochastic classical dynamics of the impurities and the quantum nature of the fermionic bath manifests in the emergent interaction between the impurities and in the viscosity tensor. By focusing on the two-impurity case, we predict the existence of bound states, in different conditions of coupling and temperature, whose lifetime can be analytically estimated. Our predictions should be testable using cold-gases platforms within current technology.

Excitation Spectrum and Superfluid Gap of an Ultracold Fermi Gas.

Ultracold atomic gases are a powerful tool to experimentally study strongly correlated quantum many-body systems. In particular, ultracold Fermi gases with tunable interactions have allowed to realize the famous BEC-BCS crossover from a Bose-Einstein condensate (BEC) of molecules to a Bardeen-Cooper-Schrieffer (BCS) superfluid of weakly bound Cooper pairs. However, large parts of the excitation spectrum of fermionic superfluids in the BEC-BCS crossover are still unexplored. In this work, we use Bragg spectroscopy to measure the full momentum-resolved low-energy excitation spectrum of strongly interacting ultracold Fermi gases. This enables us to directly observe the smooth transformation from a bosonic to a fermionic superfluid that takes place in the BEC-BCS crossover. We also use our spectra to determine the evolution of the superfluid gap and find excellent agreement with previous experiments and self-consistent T-matrix calculations both in the BEC and crossover regime. However, toward the BCS regime a calculation that includes the effects of particle-hole correlations shows better agreement with our data.

Topological Lifshitz transitions, orbital currents, and interactions in low-dimensional Fermi gases in synthetic gauge fields

Low-dimensional systems of interacting fermions in a synthetic gauge field have been experimentally realized using two-component ultra-cold Fermi gases in optical lattices. Using a two-leg ladder model that is relevant to these experiments, we have studied the signatures of topological Lifshitz transitions and the effects of the inter-species interaction U on the gauge-invariant orbital current in the regime of large intra-leg hopping Ω. Focusing on non-insulating regimes, we have carried out numerically exact density-matrix renormalization-group (DMRG) calculations to compute the orbital current at fixed particle number as a function of the interaction strength and the synthetic gauge flux per plaquette. Signatures of topological Lifshitz transitions where the number Fermi points changes are found to persist even in the presence of very strong repulsive interactions. This numerical observation suggests that the orbital current can be computed from an appropriately renormalized mean-field band structure, which is also described here. Quantitative agreement between the mean-field and the DMRG results in the intermediate interaction regime where U ≲ Ω is demonstrated. We also have observed that interactions can change the sign of the current susceptibility at zero field and induce Lifshitz transitions between two metallic phases, which is also captured by the mean-field theory. Correlation effects beyond mean-field theory in the oscillations of the local inter-leg current are also reported. We argue that the observed robustness against interactions makes the orbital current a good indicator of the topological Lifshitz transitions.

Pairing Phenomena and Superfluidity of Atomic Fermi Gases in a Two‐Dimensional Optical Lattice: Unusual Effects of Lattice‐Continuum Mixing

AbstractThe superfluid behavior of ultracold atomic Fermi gases with a short range attractive interaction in a two‐dimensional optical lattice (2DOL) is studied using a pairing fluctuation theory, within the context of BCS‐BEC crossover. It is found that the mixing of lattice and continuum dimensions leads to exotic phenomena. For relatively large lattice constant d and small hopping integral t, the superfluid transition temperature exhibits a remarkable reentrant behavior as a function of the interaction strength, and leads to a pair density wave ground state, where vanishes, for a range of intermediate coupling strength. In the unitary and BCS regimes, the nature of the in‐plane and overall pairing changes from particle‐like to hole‐like, with an unexpected nonmonotonic dependence of the chemical potential on the pairing strength. The Bose–Einstein condensation asymptotic behaviors exhibit distinct power law dependencies on the interaction strength compared to cases of pure 3D lattice, 3D continuum, and 1DOL. These predictions can be tested in future experiments.

Many-body molecule formation at a domain wall in a one-dimensional strongly interacting ultracold Fermi gas

We analyze how the presence of the bound state on top of strong intercomponent contact repulsion affects the dynamics of a two-component ultracold Fermi gas confined in a one-dimensional harmonic trap. By performing full many-body numerical calculations, we retrieve dynamics of an initially phase-separated state that has been utilized to excite the spin-dipole mode in experimental settings. We observe an appearance of pairing correlations at the domain wall, heralding the onset of a molecular fraction at the interlayer between the components.

Crossover between strongly coupled and weakly coupled exciton superfluids

Following a crossover Superfluidity in fermionic systems occurs through the pairing of fermions into bosons, which can undergo condensation. Depending on the strength of the interactions between fermions, the pairs range from large and overlapping to tightly bound. The crossover between these two limits has been explored in ultracold Fermi gases. Liu et al . observed the crossover in an electronic system consisting of two layers of graphene separated by an insulating barrier and placed in a magnetic field. In this two-dimensional system, the pairs were excitons formed from an electron in one layer and a hole in the other. The researchers used magnetic field and layer separation to tune the interactions and detected the signatures of superfluidity through transport measurements. —JS

Particle scattering by rotating trapped quantum gases at finite temperature

We have analytically explored the quantum phenomena of particle scattering by rotating trapped quantum gases of electrically neutral bosons and fermions for the short-ranged Fermi-Huang interactions between the incident particle and the scatterers. We have predicted differential scattering cross-sections and their temperature and angular velocity dependencies in this regard, in particular, for an ideal Bose gas in a rotating harmonic trap, an ideal Fermi gas in a rotating harmonic trap, and a weakly interacting Bose gas in a slow rotating harmonic trap. We have theoretically probed the lattice-pattern of the vortices in a rapidly rotating strongly interacting Bose–Einstein condensate by the particle scattering method. We also have obtained de Haas-van Alphen-like oscillations in the differential scattering cross-section for an ideal ultracold Fermi gas in a rotating harmonic trap. Our predictions on the differential scattering cross-sections can be tested within the present-day experimental setups.

Scattering hypervolume of spin-polarized fermions

We analyze the collision of three identical spin-polarized fermions at zero collision energy, assuming arbitrary finite-range potentials, and define the corresponding three-body scattering hypervolume ${D}_{F}$. The scattering hypervolume $D$ was first defined for identical bosons in 2008. It is the three-body analog of the two-body scattering length. We solve the three-body Schr\"odinger equation asymptotically when the three fermions are far apart or one pair and the third fermion are far apart, deriving two asymptotic expansions of the wave function. Unlike the case of bosons for which $D$ has the dimension of length to the fourth power, here the ${D}_{F}$ we define has the dimension of length to the eighth power. We then analyze the interaction energy of three such fermions with momenta $\ensuremath{\hbar}{\mathbf{k}}_{1}$, $\ensuremath{\hbar}{\mathbf{k}}_{2}$, and $\ensuremath{\hbar}{\mathbf{k}}_{3}$ in a large periodic cubic box. The energy shift due to ${D}_{F}$ is proportional to ${D}_{F}/{\mathrm{\ensuremath{\Omega}}}^{2}$, where $\mathrm{\ensuremath{\Omega}}$ is the volume of the box. We also calculate the shifts of energy and pressure of spin-polarized Fermi gases due to a nonzero ${D}_{F}$ and the three-body recombination rate of spin-polarized ultracold atomic Fermi gases at finite temperatures.

Finite-range effects in the unitary Fermi polaron

Quantum Monte Carlo techniques are employed to study the properties of polarons in an ultracold Fermi gas, at $T=0$, and in the unitary regime using both a zero-range model and a square-well potential. For a fixed density, the potential range is varied and results are extrapolated and compared against a zero-range model. A discussion regarding the choice of an interacting potential with a finite range is presented. We compute the polaron effective mass, the polaron binding energy, and the effective coupling between them. The latter is obtained using the Landau-Pomeranchuk's weakly interacting quasiparticle model. The contact parameter is estimated by fitting the pair distribution function of atoms in different spin states.

Dynamics of spin-polarized impurity in ultracold Fermi gas

We show that the motion of spin-polarized impurity (ferron) in ultracold atomic gas is characterized by a certain critical velocity which can be traced back to the amount of spin imbalance inside the impurity. We have calculated the effective mass of ferron in two dimensions. We show that the effective mass scales with the surface of the ferron. We discuss the impact of these findings; in particular, we demonstrate that ferrons become unstable in the vicinity of a vortex.

Unitary p -wave Fermi gas in one dimension

We elucidate universal many-body properties of a one-dimensional, two-component ultracold Fermi gas near the $p$-wave Feshbach resonance. The low-energy scattering in this system can be characterized by two parameters, that is, $p$-wave scattering length and effective range. At the unitarity limit where the $p$-wave scattering length diverges and the effective range is reduced to zero without conflicting with the causality bound, the system obeys universal thermodynamics as observed in a unitary Fermi gas with contact $s$-wave interaction in three dimensions. It is in contrast to a Fermi gas with the $p$-wave resonance in three dimensions in which the effective range is inevitably finite. We present the universal equation of state in this unitary $p$-wave Fermi gas within the many-body $T$-matrix approach as well as the virial expansion method. Moreover, we examine the single-particle spectral function in the high-density regime where the virial expansion is no longer valid. On the basis of the Hartree-like self-energy shift at the divergent scattering length, we conjecture that the equivalence of the Bertsch parameter across spatial dimensions holds even for a one-dimensional unitary $p$-wave Fermi gas.

Density-dependent spin-orbit coupling in degenerate quantum gases

In this letter we propose a method to realize a kind of spin-orbit coupling in ultracold Bose and Fermi gases whose format and strength depend on density of atoms. Our method combines two-photon Raman transition and periodical modulation of spin-dependent interaction, which gives rise to the direct Raman process and the interaction assisted Raman process, and the latter depends on density of atoms. These two processes have opposite effects in term of spin-momentum locking and compete with each other. As the interaction modulation increases, the system undergoes a crossover from the direct Raman process dominated regime to the interaction assisted Raman process dominated regime. For this crossover, we show that for bosons, both the condensate momentum and the chirality of condensate wave function change sign, and for fermions, the Fermi surface distortion is inverted. We highlight that there exists an emergent spatial reflection symmetry in the crossover regime, which can manifest itself universally in both Bose and Fermi gases. Our method paves a way to novel phenomena in a non-abelian gauge field with intrinsic dynamics.

Strong boundary and trap potential effects on emergent physics in ultra-cold fermionic gases

The field of quantum simulations in ultra-cold atomic gases has been remarkably successful. In principle it allows for an exact treatment of a variety of highly relevant lattice models and their emergent phases of matter. But so far there is a lack in the theoretical literature concerning the systematic study of the effects of the trap potential as well as the finite size of the systems, as numerical studies of such non periodic, correlated fermionic lattices models are numerically demanding beyond one dimension. We use the recently introduced real-space truncated unity functional renormalization group to study these boundary and trap effects with a focus on their impact on the superconducting phase of the 2D Hubbard model. We find that in the experiments not only lower temperatures need to be reached compared to current capabilities, but also system size and trap potential shape play a crucial role to simulate emergent phases of matter.

Superfluid properties of an ultracold Fermi gas with an orbital Feshbach resonance in the BCS-BEC crossover region

We theoretically investigate superfluid properties of a two-band gas of $^{173}$Yb Fermi atoms with an orbital Feshbach resonance (OFR). To describe the BCS-BEC crossover region, we include superfluid fluctuations caused by inter-band and intra-band pairing interactions associated with OFR, by extending the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink to the two-band case below the superfluid phase transition temperature; however, effects of an experimentally inaccessible deep bound state are removed, to model a real $^{173}$Yb Fermi gas near OFR. We show that the condensate fraction in the upper closed channel gradually becomes smaller than that in the lower open channel, as one moves from the strong- to the weak-coupling regime, because the OFR-pairing mechanism tunes the interaction strengths by adjusting the energy difference between the two bands. However, even when the closed-channel band is much higher in energy than the open-channel band in the weak-coupling regime, the magnitude of the superfluid order parameter in the closed channel is found to be still comparable to that in the open channel. As the reason for this, we point out a pair-tunneling effect by the OFR-induced inter-band interaction. Besides these superfluid quantities, we also examine collective modes, such as the Goldstone mode, Schmid (Higgs) mode, as well as Leggett mode, to clarify how they appear in the spectral weights of pair-correlation functions in each band. Since the realization of a multi-band superfluid Fermi gas is a crucial issue in cold Fermi gas physics, our results would contribute to the basic understanding of this type of Fermi superfluid in the BCS-BEC crossover region.