Superfluid Properties Research Articles

Topological superfluid in a two-dimensional polarized Fermi gas with spin–orbit coupling and adiabatic rotation

We study the properties of superfluid in a two-dimensional (2D) polarized Fermi gas with spin–orbit coupling and adiabatic rotation which are trapped in a harmonic potential. Due to the competition between polarization, spin–orbit coupling, and adiabatic rotation, the Fermi gas exhibits many intriguing phenomena. By using the Bardeen–Cooper– Schrieffer (BCS) mean-field method with local density approximation, we investigate the dependence of order parameter solution on the spin–orbit coupling strength and the rotation velocity. The energy spectra with different rotation velocities are studied in detail. Besides, the conditions for the zero-energy Majorana fermions in topological superfluid phase to be observed are obtained. By investigating distributions of number density, we find that the rotation has opposite effect on the distribution of number density with different spins, which leads to the enhancement of the polarization of Fermi gas. Here, we focus on the region of BCS pairing and ignore the Fulde–Ferrell–Larkin–Ovchinnikov state.

Equilibrium and Non-equilibrium Properties of Superfluids and Superconductors

We review some rigorous results on the equilibrium and non-equilibrium properties of superfluids and superconductors.

Entrainment in Superfluid Neutron-Star Crusts: Hydrodynamic Description and Microscopic Origin

In spite of the absence of viscous drag, the neutron superfluid permeating the inner crust of a neutron star cannot flow freely, and is entrained by the nuclear lattice similarly to laboratory superfluid atomic gases in optical lattices. The role of entrainment on the neutron superfluid dynamics is reviewed. For this purpose, a minimal hydrodynamical model of superfluidity in neutron-star crusts is presented. This model relies on a fully four-dimensionally covariant action principle. The equivalence of this formulation with the more traditional approach is demonstrated. In addition, the different treatments of entrainment in terms of dynamical effective masses or superfluid density are clarified. The nuclear energy density functional theory employed for the calculations of all the necessary microscopic inputs is also reviewed, focusing on superfluid properties. In particular, the microscopic origin of entrainment and the different methods to estimate its importance are discussed.

Neutrino luminosities and heat capacities of neutron stars in analytic form

We derive analytic approximations for the neutrino luminosities and the heat capacities of neutron stars with isothernal nucleon cores as functions of the mass and radius of stars. The neutrino luminosities are approximated for the three basic neutrino emission mechanisms, and the heat capacities for the five basic combinations of the partial heat capacities. The approximations are valid for for a wide class of equations of state of dense nucleonmatter. The results significantly simplify the theoretical interpretation of observations of cooling neutron stars as well as of quasistationary thermal states of neutron stars in X-ray transients. For illustration, we present an analysis of the neutrino cooling functions of nine isolated neutron stars taking into account the effects of their magnetic fields and of the presence of light elements in their heat blanketing envelopes. These results allow one to investigate the superfluid properties of neutron star cores.

Towards High-Quality Visualization of Superfluid Vortices

Superfluidity is a special state of matter exhibiting macroscopic quantum phenomena and acting like a fluid with zero viscosity. In such a state, superfluid vortices exist as phase singularities of the model equation with unique distributions. This paper presents novel techniques to aid the visual understanding of superfluid vortices based on the state-of-the-art non-linear Klein-Gordon equation, which evolves a complex scalar field, giving rise to special vortex lattice/ring structures with dynamic vortex formation, reconnection, and Kelvin waves, etc. By formulating a numerical model with theoretical physicists in superfluid research, we obtain high-quality superfluid flow data sets without noise-like waves, suitable for vortex visualization. By further exploring superfluid vortex properties, we develop a new vortex identification and visualization method: a novel mechanism with velocity circulation to overcome phase singularity and an orthogonal-plane strategy to avoid ambiguity. Hence, our visualizations can help reveal various superfluid vortex structures and enable domain experts for related visual analysis, such as the steady vortex lattice/ring structures, dynamic vortex string interactions with reconnections and energy radiations, where the famous Kelvin waves and decaying vortex tangle were clearly observed. These visualizations have assisted physicists to verify the superfluid model, and further explore its dynamic behavior more intuitively.

Microscopic description of average level spacing in even-even nuclei

A microscopic theoretical approach to the average level spacing at the neutron binding energy in even-even nuclei is proposed. The approach is derived based on the Bardeen-Cooper-Schrieffer (BCS) theory at finite temperature and projection M of the total angular momentum J, which is often used to describe the superfluid properties of hot rotating nuclei. The exact relation of the J-dependent total level density to the M-dependent state densities, based on which the average level spacing is calculated, was employed. The numerical calculations carried out for several even-even nuclei have shown that in order to reproduce the experimental average level spacing, the M-dependent pairing gaps as well as the exact relation of the J-dependent total level density formula should be simultaneously used.

Fulde-Ferrell-Larkin-Ovchinnikov state to topological superfluidity transition in bilayer spin-orbit-coupled degenerate Fermi gases

Recently a scheme has been proposed for generating the 2D Rashba-type spin-orbit coupling (SOC) for ultracold atomic bosons in a bilayer geometry [S.-W. Su et al, Phys. Rev. A \textbf{93}, 053630 (2016)]. Here we investigate the superfluidity properties of a degenerate Fermi gas affected by the SOC in such a bilayer system. We demonstrate that a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state appears in the regime of small to moderate atom-light coupling. In contrast to the ordinary SOC, the FFLO state emerges in the bilayer system without adding any external fields or spin polarization. As the atom-light coupling increases, the system can transit from the FFLO state to a topological superfluid state. These findings are also confirmed by the BdG simulations with a weak harmonic trap added.

Trapped Yb173 Fermi gas across an orbital Feshbach resonance

Starting with the two-band description of an orbital Feshbach resonance, we study superfluid properties of a trapped $^{173}\mathrm{Yb}$ Fermi gas under the assumptions of a local-density approximation for the trapping potential and a mean-field approximation for the intraband Cooper pairings. In particular, we investigate the competition and interplay between the pair-breaking effect that is caused by the interband detuning energy, and the pair-breaking and thermal-broadening effects that are simultaneously caused by the temperature. We predict several experimental signatures that are directly caused by this interplay including a spatial separation of superfluid and normal phases within the trap, and could play decisive roles in probing two-band superfluidity in these systems.

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

In an article in 2013, Caldas et al. [Phys. Rev. A 88, 023615 (2013)] derived analytical expressions of the induced interaction within the Gorkov--Melik-Barkhudarov correction in quasi-two-dimensional Fermi gases with Rashba spin-orbit coupling (SOC). They claimed that the induced interaction is exactly the same as the one for the case without SOC when the SOC is weak, and in the region of strong SOC, it starts from a reduced value and then recovers the value for the zero SOC in the limit of large SOC. We point out that their calculations contain critical errors and inconsistencies that significantly affect the basis of these claims.

Perturbative Approach to Superfluidity under Nonuniform Potential

A perturbative way to investigate superfluid properties of various systems under nonuniform potential is presented. We derive the perturbation expansion of the superfluid fraction, which indicates how liquid exhibits nonclassical rotational inertia, in terms of the strength of nonuniform potential and find that the coefficient of the leading term reflects the density fluctuation of the system. Our formulation does not assume anything about Bose-Einstein condensation and thus is applicable to wide variety of systems. Superfluid properties of some examples including (non-)interacting Bose systems, especially Bose gas in the mean field limit, (non-)interacting Fermi sytems, Tomonaga-Luttinger liquid and spinless chiral $p$-wave superfluid are investigated.

Superfluid to Normal Fluid Phase Transition in the Bose Gas Trapped in Two-Dimensional Optical Lattices at Finite Temperature

We develop the Hartree-Fock-Bogoliubov theory at finite temperature for Bose gas trapped in the two-dimensional optical lattice with the on-site energy low enough that the gas presents superfluid properties. We obtain the condensate density as function of the temperature neglecting the anomalous density in the thermodynamics equation. The condensate fraction provides two critical temperature. Below the temperature \(T_{C1}\), there is one condensate fraction. Above two condensate fractions merger up to the critical temperature \(T_{C2}\). At temperatures larger than \(T_{C2}\), the condensate fraction is null and, therefore, the gas is normal fluid. We resume by a finite-temperature phase diagram where three domains can be identified: the normal fluid, the superfluid with one stable condensate fraction and the superfluid with two condensate fractions being unstable one of them.

Superfluid density of a spin-orbit-coupled Bose gas

We discuss the superfluid properties of a Bose-Einstein condensed gas with spin-orbit coupling, recently realized in experiments. We find a finite normal fluid density $\rho_n$ at zero temperature which turns out to be a function of the Raman coupling. In particular, the entire fluid becomes normal at the transition point from the zero momentum to the plane wave phase, even though the condensate fraction remains finite. We emphasize the crucial role played by the gapped branch of the elementary excitations and discuss its contributions to various sum rules. Finally, we prove that an independent definition of superfluid density $\rho_s$, using the phase twist method, satisfies the equality $\rho_n+\rho_s=\rho$, the total density, despite the breaking of Galilean invariance.

Electrodynamic duality and vortex unbinding in driven-dissipative condensates

We investigate the superfluid properties of two-dimensional driven Bose liquids, such as polariton condensates, using their long-wavelength description in terms of a compact Kardar-Parisi-Zhang (KPZ) equation for the phase dynamics. We account for topological defects (vortices) in the phase field through a duality mapping between the compact KPZ equation and a theory of non-linear electrodynamics coupled to charges. Using the dual theory we derive renormalization group equations that describe vortex unbinding in these media. When the non-equilibirum drive is turned off, the KPZ non-linearity {\lambda} vanishes and the RG flow gives the usual Kosterlitz-Thouless (KT) transition. On the other hand, with non-linearity {\lambda} > 0 vortices always unbind, even if the same system with {\lambda} = 0 is superfluid. We predict the finite size scaling behavior of the superfluid stiffness in the crossover governed by vortex unbinding showing its clear distinction from the scaling associated with the KT transition.

Verification of an analytic fit for the vortex core profile in superfluid Fermi gases

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 what extent this analytic fit truly reflects the vortex structure throughout the BEC-BCS crossover at finite temperatures. The vortex structure will be determined using the effective field theory presented in [Eur. Phys. Journal B 88, 122 (2015)] and compared to the variational analytic solution. By doing this it is possible to see where these two structures agree, and where they differ. This comparison results in a range of applicability where the hyperbolic tangent will be a good fit for the vortex structure.

Hard-Core Repulsion and Supersolid Cluster Crystals

We study the effect of a short-ranged hard-core repulsion on the stability and superfluid properties of the cluster crystal phase of two-dimensional (2D) soft core bosons. Results of Quantum Monte Carlo simulations on a cogent test case suggest that the main physical properties of the phase remain unaltered if the range d of the inner repulsive core is sufficiently short, even if the strength of the repulsion is several orders of magnitude greater than the outer soft core barrier. Only if d is an appreciable fraction of the size of the clusters (> 5%) does a sufficiently strong hard core repulsion cause the crystal to break down into a homogeneous superfluid; a moderate inner core repulsion enhances the superfluid response of the crystalline phase.

Coherent magneto-elastic oscillations in superfluid magnetars

We study the effect of superfluidity on torsional oscillations of highly magnetised neutron stars (magnetars) with a microphysical equation of state by means of two-dimensional, magnetohydrodynamical- elastic simulations. The superfluid properties of the neutrons in the neutron star core are treated in a parametric way in which we effectively decouple part of the core matter from the oscillations. Our simulations confirm the existence of two groups of oscillations, namely continuum oscillations that are confined to the neutron star core and are of Alfv\'enic character, and global oscillations with constant phase and that are of mixed magneto-elastic type. The latter might explain the quasi-periodic oscillations observed in magnetar giant flares, since they do not suffer from the additional damping mechanism due to phase mixing, contrary to what happens for continuum oscillations. However, we cannot prove rigorously that the coherent oscillations with constant phase are normal modes. Moreover, we find no crustal shear modes for the magnetic field strengths typical for magnetars.We provide fits to our numerical simulations that give the oscillation frequencies as functions of magnetic field strength and proton fraction in the core.

Kohn-Sham approach to Fermi gas superfluidity: The bilayer of fermionic polar molecules

By using a well-established ``ab initio'' theoretical approach developed in the past to quantitatively study the superconductivity of condensed matter systems, based on the Kohn-Sham density functional theory, I study the superfluid properties and the BCS-BEC crossover of two parallel bi-dimensional layers of fermionic dipolar molecules, where the pairing mechanism leading to superfluidity is provided by the interlayer coupling between dipoles. The finite temperature superfluid properties of both the homogeneous system and one where the fermions in each layer are confined by a square optical lattice are studied at half filling conditions, and for different values of the strength of the confining optical potential. The T = 0 results for the homogeneous system are found to be in excellent agreement with diffusion Monte Carlo results. The superfluid transition temperature in the BCS region is found to increase, for a given interlayer coupling, with the strength of the confining optical potential. A transition occurs at sufficiently small interlayer distances, where the fermions becomes localized within the optical lattice sites in a square geometry with an increased effective lattice constant, forming a system of localized composite bosons. This transition should be signaled by a sudden drop in the superfluid fraction of the system.

Large gap electron-hole superfluidity and shape resonances in coupled graphene nanoribbons.

We predict enhanced electron-hole superfluidity in two coupled electron-hole armchair-edge terminated graphene nanoribbons separated by a thin insulating barrier. In contrast to graphene monolayers, the multiple subbands of the nanoribbons are parabolic at low energy with a gap between the conduction and valence bands, and with lifted valley degeneracy. These properties make screening of the electron-hole interaction much weaker than for coupled electron-hole monolayers, thus boosting the pairing strength and enhancing the superfluid properties. The pairing strength is further boosted by the quasi one-dimensional quantum confinement of the carriers, as well as by the large density of states near the bottom of each subband. The latter magnifies superfluid shape resonances caused by the quantum confinement. Several superfluid partial condensates are present for finite-width nanoribbons with multiple subbands. We find that superfluidity is predominately in the strongly-coupled BEC and BCS-BEC crossover regimes, with large superfluid gaps up to 100 meV and beyond. When the gaps exceed the subband spacing, there is significant mixing of the subbands, a rounding of the shape resonances, and a resulting reduction in the one-dimensional nature of the system.

Emergence of classical rotation in superfluid Bose-Einstein condensates

Phase transitions can modify quantum behaviour on mesoscopic scales and give access to new and unusual quantum dynamics. Here we investigate the superfluid properties of a rotating two-component Bose--Einstein condensate as a function of changes in the interaction energy and in particular through the phase transition from miscibility to immiscibility. We show that the breaking of one of the hallmarks of superfluid flow, namely the quantisation condition on circulation, is continuous throughout an azimuthal phase separation process and displays intriguing density dynamics. We find that the resulting currents are stable for long times and possess a phase boundary that exhibits classical solid body rotation, despite the quantum nature of superfluid flow. To support this co-existence of classical and quantum behaviour the system develops a unique velocity flow profile, which includes unusual radial flow in regions near the phase boundary.

Superuidity and BEC in a Model of Interacting Bosons in a Random Potential

We report on a mathematically rigorous analysis of the superfluid properties of a Bose- Einstein condensate in the many-body ground state of a one-dimensional model of interacting bosons in a random potential.