It has recently been shown that the spin-orbit coupling gives rise to topologically-nontrivial and thermodynamically-stable gapless superfluid phases when the pseudo-spin populations of an atomic Fermi gas is 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 pseudo-spin components counterflow near the edge of the cylinder, the strength of which increases with increasing spin-orbit coupling.
Variational wavefunctions that introduce zeros (vortices) to screen repulsive interactions are typically difficult to verify in unbiased microscopic calculations. An approach is constructed to insert vortices into ansatz wavefunctions using a matrix product representation. This approach opens the door to validation of a broad class of Jastrow-based wavefunctions. The formalism is applied to a model motivated by experiments on ultracold atomic gases in the presence of synthetic spin-orbit coupling. Validated wavefunctions show that vortices in atomic Fermi gases with flat Rashba spin-orbit band…
Vortex arrays in type-II superconductors admit the translational symmetry of an infinite system. There are cases, however, like ultra-cold trapped Fermi gases and the crust of neutron stars, where finite-size effects make it quite more complex to account for the geometrical arrangement of vortices. Here, we self-consistently generate these arrays of vortices at zero and finite temperature through a microscopic description of the non-homogeneous superfluid based on a differential equation for the local order parameter, obtained by coarse graining the Bogoliubov-de Gennes (BdG) equations. In thi…
We discuss the effects of quantum fluctuations on the properties of vortex lattices in rapidly rotating ultracold atomic gases. We develop a variational method that goes beyond the Bogoliubov theory by including the effects of interactions between the quasiparticle excitations. These interactions are found to have significant quantitative effects on physical properties even at relatively large filling factors. We use our theory to predict the expected experimental signatures of quantum fluctuations of vortices, and to assess the competition of the triangular vortex lattice phase with other pha…
We present numerical simulations of phase imprinting experiments in ultracold trapped Fermi gases which are in good agreement with recent, independent 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 illustrate their dramatic effects. The former causes vor…
Multiply quantized vortices in the BCS-to-BEC evolution of p-wave resonant Fermi gases are investigated theoretically. The vortex structure and the low-energy quasiparticle states are discussed, based on the self-consistent calculations of the Bogoliubov-de Gennes and gap equations. We reveal the direct relation between the macroscopic structure of vortices, such as particle densities, and the low-lying quasiparticle state. In addition, the net angular momentum for multiply quantized vortices with a vorticity $κ$ is found to be expressed by a simple equation, which reflects the chirality of th…
We perform a theoretical study into how dipole-dipole interactions modify the properties of superfluid vortices within the context of a two-dimensional atomic Bose gas of co-oriented dipoles. The reduced density at a vortex acts like a giant anti-dipole, changing the density profile and generating an effective dipolar potential centred at the vortex core whose most slowly decaying terms go as $1/ρ^2$ and $\ln(ρ)/ρ^3$. These effects modify the vortex-vortex interaction which, in particular, becomes anisotropic for dipoles polarized in the plane. Striking modifications to vortex-vortex dynamics …
We investigate the superfluidity of a two-component Fermi gas with spin-orbital-angular-momentum coupling (SOAMC). Due to the intricate interplay of SOAMC, two-photon detuning and atom-atom interaction, a family of vortex ground states emerge in a broad parameter regime of the phase diagram, in contrast to the usual case where an external rotation or magnetic field is generally required. More strikingly, an unprecedented vortex state, which breaks the continuous rotational symmetry to a discrete one spontaneously, is predicted to occur. The underlying physics are elucidated and verified by num…
We present a pairing fluctuation theory which self-consistently incorporates finite momentum pair excitations in the context of BCS--Bose-Einstein condensation (BEC) crossover, and we apply this theory to high $T_c$ superconductors and ultracold Fermi gases. There are strong similarities between Fermi gases in the unitary regime and high Tc superconductors. Here we address key issues of common interest, especially the pseudogap. In the Fermi gases we summarize recent experiments including various phase diagrams (with and without population imbalance), as well as evidence for a pseudogap in the…
I study vortex ring oscillations in a superfluid, trapped in an elongated trap, under the conditions of the Local Density Approximation. On the basis of the Hamiltonian formalism I develop a hydrodynamic theory, which is valid for an arbitrary superfluid and depends only on the equation of state. The problem is reduced to an ordinary differential equation for the ring radius. The cases of the dilute BEC and the Fermi gas at unitarity are investigated in detail. Simple analytical equations for the periods of small oscillations are obtained and the equations of non-linear dynamics are solved in …
A characteristic property of superfluidity and -conductivity is the presence of quantized vortices in rotating systems. To study the BEC-BCS crossover the two most common methods are the Bogoliubov-De Gennes theory and the usage of an effective field theory. In order to simplify the calculations for one vortex, it is often assumed that the hyperbolic tangent yields a good approximation for the vortex structure. The combination of a variational vortex structure, together with cylindrical symmetry yields analytic (or numerically simple) expressions. The focus of this article is to investigate to…
We review some recent developments in the theory of rotating atomic gases. These studies have thrown light on the process of nucleation of vortices in regimes where mean-field methods are inadequate. In our review we shall describe and compare quantum vortex nucleation of a dilute ultracold bosonic gas trapped in three different configurations: a one-dimensional ring lattice, a one-dimensional ring superlattice and a two-dimensional asymmetric harmonic trap. In all of them there is a critical rotation frequency, at which the particles in the ground state exhibit strong quantum correlations. Ho…
We consider the inertial mass of a vortex in a superfluid. We obtain a vortex mass that is well defined and is determined microscopically and self-consistently by the elementary excitation energy of the kelvon quasiparticle localised within the vortex core. The obtained result for the vortex mass is found to be consistent with experimental observations on superfluid quantum gases and vortex rings in water. We propose a method to measure the inertial rest mass and Berry phase of a vortex in superfluid Bose and Fermi gases.
ARC Centre of Excellence for Quantum-Atom Optics, Centre for Atom Optics and Ultrafast Spectroscopy, Swinburne University of Technology, Melbourne 3122, Australia
We show how Fermi liquid theory can be applied to ultra-cold Fermi gases, thereby expanding their "simulation" capabilities to a class of problems of interest to multiple physics sub-disciplines. We introduce procedures for measuring and calculating position dependent Landau parameters. This lays the ground work for addressing important controversial issues: (i) the suggestion that thermodynamically, the normal state of a unitary gas is indistinguishable from a Fermi liquid (ii) that a fermionic system with strong repulsive contact interactions is associated with either ferromagnetism or local…
Achieving a higher superfluid transition $T_c$ has been a goal for the fields of superconductivity and atomic Fermi gases. Here we propose that, by using mixed dimensionality, one may achieve ultra high temperature superfluids in two component atomic Fermi gases, where one component feels a regular three-dimensional (3D) continuum space, while the other is subject to a 1D optic lattice potential. Via tuning the lattice spacing and trap depth, one can effectively raise the Fermi level dramatically upon pairing so that superfluidity may occur at an ultra high temperature (in units of Fermi energ…
Recent experiments on ultracold Bose gases in two dimensions have provided evidence for the existence of the Berezinskii-Kosterlitz-Thouless (BKT) phase via analysis of the interference between two independent systems. In this work we study the two-dimensional quantum degenerate Bose gas at finite temperature using the projected Gross-Pitaevskii equation classical field method. While this describes the highly occupied modes of the gas below a momentum cutoff, we have developed a method to incorporate the higher momentum states in our model. We concentrate on finite-sized homogeneous systems in…
In order to help detecting superfluidity, we theoretically investigate p-wave pairing superfluids in neutral Fermion atom gases confined by a three dimensimentional (3D) harmonic potential. The Ginzburg-Landau framework, which is generic for p-wave superfluids, is used to describe the order parameter spatial structure, or texture characterized by the l-vector both at rest and under rotation. The l-vector configuration is strongly contrained by the boundary condition due to a trap. It is found that the ground state textures exhibit spontaneous supercurrent at rest both cigar and pancake shape t…
Fundamental properties of superfluids with d-wave pairing symmetry are investigated theoretically. We consider neutral atomic Fermi gases in a harmonic trap, the Cooper pairing being produced by a Feshbach resonance via a d-wave interaction channel. A Ginzburg-Landau (GL) functional is constructed which is symmetry constrained for five component order parameters (OPs). We find stable OP textures and vortices for all the three phases which are known to be the energy minimum of the GL functional; the ferromagnetic, polar and cyclic phases both at rest and under rotation. In particular, we touch …
We present a theoretical study of the finite-temperature Kosterlitz-Thouless (KT) and vortex-antivortex lattice (VAL) melting transitions in two-dimensional Fermi gases with $p$- or $d$-wave pairing. For both pairings, when the interaction is tuned from weak to strong attractions, we observe a quantum phase transition from the Bardeen-Cooper-Schrieffer (BCS) superfluidity to the Bose-Einstein condensation (BEC) of difermions. The KT and VAL transition temperatures increase during this BCS-BEC transition and approach constant values in the deep BEC region. The BCS-BEC transition is characterize…
We study an effect of rotation on the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state of two component Fermi superfluid gases in a toroidal trap. We investigate a stability of the FFLO states in the quasi-one-dimensional regime on the basis of the Bogoliubov-de Gennes equation. We find that two novel FFLO phases, i.e., the half quantum vortex state and the intermediate state of Fulde-Ferrell (FF) state and Larkin-Ovchinnikov (LO) state, are stabilized by the rotation. The phase diagram for the FF state, LO state, intermediate state, and half quantum vortex state is shown in both T-P plane and T-…
It is shown that the jump in the momentum distribution of Fermi gases evolves smoothly for small and intermediate times once an interaction between the fermions is suddenly switched on. The jump does not vanish abruptly. The loci in momentum space where the jumps occur are those of the noninteracting Fermi sea. No relaxation of the Fermi surface geometry takes place.
We study the dynamics of vortices in finite temperature atomic Bose-Einstein condensates, focussing on decay rates, precession frequencies and core brightness, motivated by a recent experiment (Freilich et al. Science 329, 1182 (2010)) in which real-time dynamics of a single vortex was observed. Using the ZNG formalism based on a dissipative Gross-Pitaevskii equation for the condensate coupled to a semi-classical Boltzmann equation for the thermal cloud, we find a rapid nonlinear increase of both the decay rate and precession frequency with increasing temperatures. The increase, which is domin…
We study the superfluid state of atomic Fermi gases using a BCS-BEC crossover theory. Our approach emphasizes non-condensed fermion pairs which strongly hybridize with their (Feshbach-induced) molecular boson counterparts. These pairs lead to pseudogap effects above $T_c$ and non-BCS characteristics below. We discuss how these effects influence the experimental signatures of superfluidity.
A mathematical lattice, called the von Neumann lattice, is a subset of coherent states and exists periodically in the phase space. It is unlike solids or Abrikosov lattices that are observable in physical systems. Abrikosov lattices are vortices closely packed into a lattice with a flux quantum through a unit cell. Although Abrikosov lattices appear generally in various physical systems, vortex lattices with multiple-flux quantums through a unit cell are more stable than Abrikosov lattices in some physical regimes of the systems with non-local interactions between particles. No theory is able …
In this letter we show that the vortex lattice structure in the Bose-Fermi superfluid mixture can undergo a sequence of structure transitions when the Fermi superfluid is tuned from the BCS regime to the BEC regime. This is due to different vortex core structure of the Fermi superfluid in the BCS regime and in the BEC regime. In the former the vortex core is nearly filled, while the density at the vortex core gradually decreases until it empties out at the BEC regime. Therefore, with the density-density interaction between the Bose and the Fermi superfluids, the two sets of vortex lattices int…
Polariton formalism is applied for studying the propagation of a probe field of light in a cloud of cold atoms influenced by two control laser beams of larger intensity. The laser beams couple resonantly three hyperfine atomic ground states to a common excited state thus forming a tripod configuration of the atomic energy levels involved. The first control beam can have an optical vortex with the intensity of the beam going to zero at the vortex core. The second control beam without a vortex ensures the loseless (adiabatic) propagation of the probe beam at a vortex core of the first control la…
We present a closed-form expression for the time dynamics of a balanced Fermi superfluid with s-wave pairing and Rashba spin-orbit (SO) coupling. Solving the associated self-consistency conditions for an initial number density given by a Gaussian and an initial gap containing a vortex dipole, we show that Rashba SO coupling results in precession of the vortex dipole. The integrated self-consistent gap decays as a function of time, characterising a "transient Fermi superfluid". Our analytic solution forms a starting point for studies of vortex dynamics -- in particular braiding of Majorana ferm…
We present results on the effect of short-range, attractive interactions on the properties of balanced 2D Fermi gases in the non-superfluid (normal) phase. Our approach combines the renormalization group (RG) with perturbation theory, yielding observables such as the equation of state and compressibility. We find good agreement with recent experiments that measured the equation of state in trapped gases in the balanced regime, showing that these results are consistent with logarithmic corrections in the equation of state.
We investigate the properties of quantized vortices in a dipolar Bose-Einstein condensed gas by means of a generalised Gross-Pitaevskii equation. The size of the vortex core hugely increases by increasing the weight of the dipolar interaction and approaching the transition to the supersolid phase. The critical angular velocity for the existence of an energetically stable vortex decreases in the supersolid, due to the reduced value of the density in the interdroplet region. The angular momentum per particle associated with the vortex line is shown to be smaller than $\hbar$, reflecting the redu…
The rotation of two-component Fermi gases and the subsequent appearance of vortices have been the subject of numerous experimental and theoretical studies. Recent experimental advances in hyperfine state-dependent potentials and highly degenerate heteronuclear Fermi gases suggest that it would be feasible to create component-dependent rotation potentials in future experiments. In this study we use an effective field theory for Fermi gases to consider the effects of rotating only one component of the Fermi gas. We find that the superfluid band gap in bulk exists up to higher rotation frequencie…
The induced interaction among the majority spin species, due to the presence of the minority species, is computed for the case of a population-imbalanced resonantly-interacting Fermi gas. It is shown that this interaction leads to an instability, at low temperatures, of the recently observed polaron Fermi liquid phase of strongly imbalanced Fermi gases to a p-wave superfluid state. We find that the associated transition temperature, while quite small in the weakly interacting BCS regime, is experimentally accessible in the strongly interacting unitary regime.
The two-component Fermi gas in a double-well trap is studied using the density functional theory and the density profile of each component is calculated within the Thomas-Fermi approximation. We show that the two components are spatially separate in the two wells once the repulsive interaction exceeds the Stoner point, signaling the occurrence of the ferromagnetic transition. Therefore, the double-well trap helps to explore itinerant ferromagnetism in atomic Fermi gases, since the spontaneous separation can be examined by measuring component populations in one well.
We study a single quantized vortex in the fermionic component of a mixture of Fermi superfluid and Bose-Einstein condensate. As the density ratio between the boson and the fermion components is tuned, we identify a transition in the vortex-core structure, across which fermions in the vortex core become completely depleted even in the weak-coupling Bardeen-Cooper-Schrieffer regime. This is accompanied by changes in key properties of the vortex state, as well as by the localization of the Bose-Einstein condensate in the vortex core. The transition in the vortex-core structure can be experimental…
Cold gas experiments can be tuned to achieve strongly-interacting regimes such as that of low-density neutron matter found in neutron-stars' crusts. We report $T$=0 diffusion Monte Carlo results (i) for the ground state of both spin-1/2 fermions with short-range interactions and low-density neutron matter in a cylindrical container, and (ii) properties of these systems with a vortex line excitation. We calculate the equation of state for cold atoms and low-density neutron matter in the bulk systems, and we contrast it to our results in the cylindrical container. We compute the vortex line exci…
The zero-temperature and finite-temperature thermodynamics of two-component Fermi gases with finite-range attractive interaction suffer from fermion sign problem, which seems like an insurmountable problem in exact numerical simulations. In a recent work, we find a reliable method to simulate the thermodynamic properties of single-component Fermi gases for both noninteracting and repulsively interacting cases based on the method of parametrized partition function and the $ξ_E$ curve of constant energy. In the present work, this method is generalized to two-component Fermi gases with finite-ran…
The experimental realization of quantum degenerate cold Fermi gases with large hyperfine spins opens up a new opportunity for exotic many-body physics.
The charged Fermi gas with a small Lande-factor $g$ is expected to be diamagnetic, while that with a larger $g$ could be paramagnetic. We calculate the critical value of the $g$-factor which separates the dia- and para-magnetic regions. In the weak-field limit, $g_{c}$ has the same value both at high and low temperatures, $g_{c}=1/\sqrt{12}$. Nevertheless, $g_{c}$ increases with the temperature reducing in finite magnetic fields. We also compare the $g_{c}$ value of Fermi gases with those of Boltzmann and Bose gases, supposing the particle has three Zeeman levels $σ=\pm1, 0$, and find that $g_…
This article reviews developments in the theory of rapidly rotating degenerate atomic gases. The main focus is on the equilibrium properties of a single component atomic Bose gas, which (at least at rest) forms a Bose-Einstein condensate. Rotation leads to the formation of quantized vortices which order into a vortex array, in close analogy with the behaviour of superfluid helium. Under conditions of rapid rotation, when the vortex density becomes large, atomic Bose gases offer the possibility to explore the physics of quantized vortices in novel parameter regimes. First, there is an interesti…
In this paper, we investigate vortex dynamics in a two-dimensional Bose-Hubbard model coupled with a weak artificial magnetic field, a random white noise and a dissipation. Origin of the noise and dissipation is considered as thermal fluctuations of atoms that do not participate the Bose-Einstein condensation (BEC). Solving a stochastic Gross-Pitaevskii equation to this system, we show that the interplay of the magnetic field and the white noise generates vortices in the bulk of the BEC and stable steady states of vortices form after a transition period. We calculate the incompressible part of…
We study a three-component superfluid Fermi gas in a spherically symmetric harmonic trap using the Bogoliubov-deGennes method. We predict a coexistence phase in which two pairing field order parameters are simultaneously nonzero, in stark contrast to studies performed for trapped gases using local density approximation. We also discuss the role of atom number conservation in the context of a homogeneous system.
Many strongly coupled fluids are known to share similar hydrodynamic transport properties. In this work we argue that this similarity could extend beyond hydrodynamics to transient dynamics through the presence of non-hydrodynamic modes. We review non-hydrodynamic modes in kinetic theory and gauge/gravity duality and discuss their signatures in trapped Fermi gases close to unitarity. Reanalyzing previously published experimental data, we find hints of non-hydrodynamic modes in cold Fermi gases in two and three dimensions.
The Hartree energy shift is calculated for a unitary Fermi gas. By including the momentum dependence of the scattering amplitude explicitly, the Hartree energy shift remains finite even at unitarity. Extending the theory also for spin-imbalanced systems allows calculation of polaron properties. The results are in good agreement with more involved theories and experiments.
Spin-orbit coupling plays an important role in understanding exotic quantum phases. In this work, we present a scheme to combine spin-orbital-angular-momentum (SOAM) coupling and strong correlations in ultracold atomic gases. Essential ingredients of this setting is the interplay of SOAM coupling and Raman-induced spin-flip hopping, engineered by lasers that couples different hyperfine spin states. In the presence of SOAM coupling only, we find rich quantum phases in the Mott-insulating regime, which support different types of spin defects such as spin vortex and composite vortex with antiferr…
A significant feature of the one-dimensional super Tonks-Girardeau gas is its metastable gas-like state with a stronger Fermi-like pressure than for free fermions which prevents a collapse of atoms. This naturally suggests a way to search for such strongly correlated behaviour in systems of interacting fermions in one dimension. We thus show that the strongly attractive Fermi gas without polarization can be effectively described by a super Tonks-Girardeau gas composed of bosonic Fermi pairs with attractive pair-pair interaction. A natural description of such super Tonks-Girardeau gases is prov…
We investigate the Berezinskii-Kosterlitz-Thouless (BKT) transition in a two-dimensional (2D) Fermi gas with spin-orbit coupling (SOC), as a function of the two-body binding energy and a perpendicular Zeeman field. By including a generic form of the SOC, as a function of Rashba and Dresselhaus terms, we study the evolution between the experimentally relevant equal Rashba-Dresselhaus (ERD) case and the Rashba-only (RO) case. We show that in the ERD case, at fixed non-zero Zeeman field, the BKT transition temperature $T_{BKT}$ is increased by the effect of SOC for all values of the binding energ…
Universal relations are important for understanding strongly interacting Fermi gases, the study of which have been mostly limited to cases with a single scattering channel. Here we discover a series universal relations for strongly interacting Fermi gases with multiple scattering channels. Unlike its counterpart across a single channel wide magnetic Feshbach resonance, a new kind of contact which we call the cross-channel contact naturally appears in this system, this contact is related to varies thermodynamic quantities as well as short range correlation functions.
We study the propagation of dispersive waves in superfluid Fermi gases in the BEC-BCS crossover. Unlike in other superfluid systems, where dispersive waves have already been studied and observed, Fermi gases can exhibit a subsonic dispersion relation for which the dispersive wave pattern appears at the tail of the wave front. We show that this property can be used to distinguish between a subsonic and a supersonic dispersion relation at unitarity.
We treat small trapped unequal-mass two-component Fermi gases at unitarity within a non-perturbative microscopic framework and investigate the system properties as functions of the mass ratio $κ$, and the numbers $N_{1}$ and $N_2$ of heavy and light fermions. While equal-mass Fermi gases with infinitely large interspecies s-wave scattering length $a_s$ are universal, we find that unequal mass Fermi gases are, for sufficiently large $κ$ and in the regime where Efimov physics is absent, not universal. In particular, the $(N_1,N_2)=(2,1)$ and $(3,1)$ systems exhibit three-body (3b) and four-body …
We derive the phonon damping rate due to the four-phonon Landau-Khalatnikov process in low temperature strongly interacting Fermi gases using quantum hydrodynamics, correcting and extending the original calculation of Landau and Khalatnikov [ZhETF, 19 (1949) 637]. Our predictions can be tested in state-of-the-art experiments with cold atomic gases in the collisionless regime.
We present a summary of some recent theoretical results for matter-wave patterns in Fermi and Bose-Fermi degenerate gases, obtained in the framework of the quasi-mean-field approximation. We perform a dimensional reduction from the three-dimensional (3D) equations of motion to 2D and 1D effective equations. In both cases, comparison of the low-dimensional reductions to the full model is performed, showing very good agreement for ground-state solutions. Some complex dynamical regimes are reported too for the corresponding 1D systems.
