Bardeen-Cooper-Schrieffer Regime Research Articles

Temperature-Dependent Decay of Quasi-Two-Dimensional Vortices across the BCS-BEC Crossover.

We systematically study the decay of quasi-two-dimensional vortices in an oblate strongly interacting Fermi gas over a wide interaction range and observe that, as the system temperature is lowered, the vortex lifetime increases in the Bose-Einstein condensate (BEC) regime but decreases at unitarity and in the Bardeen-Cooper-Schrieffer (BCS) regime. The observations can be qualitatively captured by a phenomenological model simply involving diffusion and two-body collisional loss, in which the vortex lifetime is mostly determined by the slower process of the two. In particular, the counterintuitive vortex decay in the BCS regime can be interpreted by considering the competition between the temperature dependence of the vortex annihilation rate and that of unpaired fermions. Our results suggest a competing mechanism for the complex vortex decay dynamics in the BCS-BEC crossover for the fermionic superfluids.

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.

Photoinduced dynamics of a quasicrystalline excitonic insulator

We study the photoinduced dynamics of the excitonic insulator in the two-orbital Hubbard model on the Penrose tiling by means of the time-dependent real-space mean-field approximation. We show that, with a single-cycle electric-field pulse, the bulk (spatially averaged) excitonic order parameter decreases in the Bardeen-Cooper-Schrieffer (BCS) regime, while it increases in the Bose-Einstein condensate (BEC) regime. This behavior is in common with the excitonic insulator in the square lattice reported previously. To explore the dynamics peculiar to the Penrose tiling, we examine the coordination number dependence of observables and analyze the perpendicular space. In the BEC regime, characteristic oscillations of the electron number at each site are induced by the pulse, which are not observed in normal crystals with single coordination number. On the other hand, the dynamics in the BCS regime is characterized by drastic change in the spatial pattern of the excitonic order parameter. Our results imply that potentially interesting nonequilibrium physics is caused by rich local structural patterns involved in quasicrystals.

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.

Reliability of the Ginzburg–Landau Theory in the BCS-BEC Crossover by Including Gaussian Fluctuations for 3D Attractive Fermions

We calculate the parameters of the Ginzburg–Landau (GL) equation of a three-dimensional attractive Fermi gas around the superfluid critical temperature. We compare different levels of approximation throughout the Bardeen–Cooper–Schrieffer (BCS) to the Bose–Einstein Condensate (BEC) regime. We show that the inclusion of Gaussian fluctuations strongly modifies the values of the Ginzburg–Landau parameters approaching the BEC regime of the crossover. We investigate the reliability of the Ginzburg–Landau theory, with fluctuations, studying the behavior of the coherence length and of the critical rotational frequencies throughout the BCS-BEC crossover. The effect of the Gaussian fluctuations gives qualitative correct trends of the considered physical quantities from the BCS regime up to the unitary limit of the BCS-BEC crossover. Approaching the BEC regime, the Ginzburg–Landau equation with the inclusion of Gaussian fluctuations turns out to be unreliable.

Critical Temperature in the BCS-BEC Crossover with Spin-Orbit Coupling

We review the study of the superfluid phase transition in a system of fermions whose interaction can be tuned continuously along the crossover from Bardeen–Cooper–Schrieffer (BCS) superconducting phase to a Bose–Einstein condensate (BEC), also in the presence of a spin–orbit coupling. Below a critical temperature the system is characterized by an order parameter. Generally a mean field approximation cannot reproduce the correct behavior of the critical temperature Tc over the whole crossover. We analyze the crucial role of quantum fluctuations beyond the mean-field approach useful to find Tc along the crossover in the presence of a spin–orbit coupling, within a path integral approach. A formal and detailed derivation for the set of equations useful to derive Tc is performed in the presence of Rashba, Dresselhaus and Zeeman couplings. In particular in the case of only Rashba coupling, for which the spin–orbit effects are more relevant, the two-body bound state exists for any value of the interaction, namely in the full crossover. As a result the effective masses of the emerging bosonic excitations are finite also in the BCS regime.

Impurity-induced Shiba bound state in the BCS–BEC crossover regime of two-dimensional Fermi superfluid**Project supported by the National Key R&D Program of China (Grant No. 2017YFA0206302).

For a two-dimensional ultra-cold Fermi superfluid with an effective static magnetic impurity, we theoretically investigated the variation of the Yu–Shiba–Rusinov (YSR) bound state in the Bardeen–Cooper–Schrieffer (BCS) to Bose–Einstein condensation (BEC) crossover regime. Within the framework of mean-field theory, analytical results of the YSR bound state energy were obtained as a function of the interaction parameters. First, when the background Fermi superfluid system stays in the weakly interacting BCS regime, we found that the YSR bound state energy is linearly dependent on the gap parameter with its coefficient slightly different from previous results. Second, we discovered re-entrance phenomena for the YSR state and an upper bound of the strength of the interaction between the paired atoms. By carefully analyzing the bound state energy as a function of the interaction parameters, we obtained a phase diagram showing the existence of the YSR state. Finally, we concluded that the re-entrance phenomena and the critical point can be easily experimentally detected through measurement of radio-frequency spectroscopy and density of states using current experimental techniques.

Super Efimovian expansions of superfluid Fermi gases in the BCS–BEC crossover

We study the super Efimovian expansions of a superfluid Fermi gas in the crossover from Bardeen–Cooper–Schrieffer (BCS) superfluid to a Bose–Einstein condensate (BEC), by using superfluid hydrodynamic equations with the equation of state fitting from the experimental data and a scaling approach. We find that in an isotropic trap, the super Efimovian expansion of the Fermi superfluid in the unitary limit is characterized by the double-log periodicity, while for an axially symmetric trap, the double-log periodicity only emerges in the longer direction for a large anisotropy of the trapping frequencies. Away from unitarity where the scale invariance is broken, the super Efimovian expansions of the superfluid Fermi gases deviate from the double-log oscillations. The oscillations in the BCS regime deviate upward from the double-log oscillations, whereas the oscillations in the BEC regime deviate downward and the deviation in the BEC limit is the most significant. This difference can be used to discriminate different superfluid regimes.

Dynamical instability of a driven-dissipative electron-hole condensate in the BCS-BEC crossover region

We present a stability analysis on a driven-dissipative electron-hole condensate in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein-condensation)-crossover region. Extending the combined BCS-Leggett theory with the generalized random phase approximation (GRPA) to the non-equilibrium case by employing the Keldysh formalism, we show that the pumping-and-decay of carriers causes a depairing effect on excitons. This phenomenon gives rise to an attractive interaction between excitons in the BEC regime, as well as a supercurrent that anomalously flows anti-parallel to $\nabla \theta({\bf r})$ (where $\theta({\bf r})$ is the phase of the condensate) in the BCS regime, both leading to dynamical instabilities of an exciton-BEC. Our result suggests that substantial region of the exciton-BEC phase in the phase diagram (in terms of the interaction strength and the decay rate) is unstable.

Intermode-coupling modulation in the fermion-boson model: heating effects in the Bardeen–Cooper–Schrieffer regime

Heating induced by an oscillating modulation of the interaction strength in an atomic Fermion pair condensate is analyzed. The coupled fermion-boson model, generalized by incorporating a time-dependent intermode coupling through a magnetic Feshbach resonance, is applied. The dynamics are analytically characterized in a perturbative scheme. The results account for experimental findings which have uncovered a damped and delayed response of the condensate to the modulation. The delay is due to the variation of the quasiparticle energies and the subsequent relaxation of the condensate. The detected damping results from the excitations induced by a nonadiabatic modulation: for driving frequencies larger than twice the pairing gap, quasiparticles are generated and, consequently, heating sets in.

Self-Consistent T-Matrix Approach to an Interacting Ultracold Fermi Gas with Mass Imbalance

We investigate the superfluid phase transition in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover regime of an ultracold Fermi gas with mass imbalance. In the presence of mass imbalance, it is known that the strong-coupling Gaussian fluctuation theory, as well as the ordinary non-self-consistent T-matrix theory, that have been extensively used to clarify various BCS-BEC crossover physics in the mass-balanced case, unphysically give double valued superfluid phase transition temperature T c in the crossover region. In our previous paper (R. Hanai et al., J. Low Temp. Phys. 171:389, 2013), this difficulty was shown to be eliminated by an extended T-matrix approximation (ETMA). However, it was also found that this improved theory still gives vanishing T c in the BCS regime, when the mass imbalance ratio remarkably deviates from unity. In this paper, further extending ETMA to include higher order pairing fluctuations to the fully self-consistent T-matrix level, we clarify whether the vanishing T c obtained in ETMA is an intrinsic phenomenon or an artifact of this approximation. We show that the self-consistent T-matrix theory always gives a finite T c, even in the region where ETMA predicts the absence of superfluid instability. The key to the recovery of T c is found to be a consistent treatment with respect to the Fermi surface sizes of the light mass and heavy mass components, which ETMA lacks in. Since Fermi condensates with mass imbalance have been recently discussed in various systems, such as a 40K–6Li Fermi gas, exciton-polariton condensate, as well as color superconductivity, our results would be useful in constructing a reliable strong-coupling theory to examine physical properties of these novel Fermi superfluids.

Tunneling and Self-Trapping of Superfluid Fermi Gases in BCS-BEC Crossover

We investigate tunneling and self-trapping of superfluid Fermi gases under a two-mode ansatz in different regimes of the crossover from Bardeen—Cooper—Schrieffer (BCS) superfluid to Bose—Einstein condensates (BEC). Starting from a generalized equation of state, we derive the coupled equations of relative atom-pair number and relative phase about superfluid Fermi gases in a double-well system and then classify the different oscillation behaviors by the tunneling strength and interactions between atoms. Tunneling and self-trapping behaviors are considered in the whole BCS-BEC crossover in the case of a symmetric double-well potential. We show that the nonlinear interaction between atoms makes the self-trapping more easily realized in BCS regime than in the BEC regime and stability analysis is also given.

Magnetic tuning of the relativistic BCS-BEC crossover

The effect of an applied magnetic field in the crossover from Bose-Einstein condensate (BEC) to Bardeen-Cooper-Schrieffer (BCS) pairing regimes is investigated. We use a model of relativistic fermions and bosons inspired by those previously used in the context of cold fermionic atoms and in the magnetic-color-flavor-locking phase of color superconductivity. It turns out that, as with cold atom systems, an applied magnetic field can also tune the BCS-BEC crossover in the relativistic case. We find that no matter what the initial state is at $B=0$, for large enough magnetic fields the system always settles into a pure BCS regime. In contrast to the atomic case, the magnetic field tuning of the crossover in the relativistic system is not connected to a Feshbach resonance, but to the relative numbers of Landau levels with either BEC or BCS type of dispersion relations that are occupied at each magnetic field strength.

Evolution from Bardeen–Cooper–Schrieffer to Bose–Einstein condensate superfluidity in the presence of disorder

We describe the effects of disorder on the critical temperature of s-wave superfluids from the Bardeen–Cooper–Schrieffer (BCS) to the Bose–Einstein condensate (BEC) regime, with direct application to ultracold fermions. We use the functional integral method and the replica technique to study Gaussian correlated disorder due to impurities, and we discuss how this system can be generated experimentally. In the absence of disorder, the BCS regime is characterized by pair breaking and phase coherence temperature scales that are essentially the same, allowing strong correlations between the amplitude and phase of the order parameter for superfluidity. As non-pair-breaking disorder is introduced, the largely overlapping Cooper pairs seek to maintain phase coherence such that the critical temperature remains essentially unchanged, and Anderson's theorem is satisfied. However, in the BEC regime, the pair breaking and phase coherence temperature scales are very different such that non-pair-breaking disorder can dramatically affect phase coherence, and thus the critical temperature, without the requirement of breaking tightly bound fermion pairs simultaneously. In this case, Anderson's theorem does not apply, and the critical temperature can be more easily reduced in comparison to the BCS limit. Lastly, we find that the superfluid is more robust against disorder in the intermediate region near unitarity between the two regimes.

Effects of periodic potentials on the critical velocity of superfluid Fermi gases in the BCS-BEC crossover

We study the effects of an external periodic potential on the critical velocity of a superfluid Fermi gas in the crossover between the Bardeen-Cooper-Schrieffer (BCS) phase and Bose-Einstein condensation (BEC). We numerically solve the Bogoliubov--de Gennes equations to model a three-dimensional gas of ultracold atoms in the superfluid phase flowing through a one-dimensional optical lattice. We find that when the recoil energy is comparable to the Fermi energy, the presence of the periodic potential reduces the effect of pair-breaking excitations. This behavior is a consequence of the peculiar band structure of the quasiparticle energy spectrum in the lattice. When the lattice height is much larger than the Fermi energy, the periodic potential makes pairs of atoms to be strongly bound, even in the BCS regime, and pair-breaking excitations are further suppressed. We have also found that when the recoil energy is comparable to or larger than the Fermi energy, the critical velocity due to long-wavelength phonon excitations shows a nonmonotonic behavior along the BCS-BEC crossover.

The ground-state energy of an attractive Fermi gas along the Bardeen–Cooper–Schrieffer-unitarity crossover

The ratio f(x) of the ground-state energy of an attractive Fermi gas to that of the noninteracting Fermi gas is a smooth and continuous function of x = kFa in the Bardeen–Cooper–Schrieffer (BCS)-unitarity crossover regime −∞ < x ⩽ 0. Here kFℏ is the Fermi momentum, ℏ is the Planck constant and a is the s-wave scattering length. The respective coefficients of the perturbation expansions of f(x) in the BCS regime and in the unitary regime are expected to be related to each other. Unitary Fermi gases are expected to exhibit universal behaviors. So f(−∞) is universal and is only a function of the universal coefficients of the perturbation expansion of f(x) in the BCS regime. Using these facts, we extend the perturbation expansion of f(x) in the BCS regime to the BCS-unitarity crossover regime. f(−∞) is predicted to be 0.400 98(0.422 94) for the Bose (Fermi) function, which are in good agreement with the quantum Monte Carlo results and the experimental results.

Dynamics of dark solitons in superfluid Fermi gases in the BCS-BEC crossover

We study, both analytically and numerically, the formation and propagation of dark solitons in a superfluid Fermi gas in the crossover from Bardeen-Cooper-Schrieffer (BCS) superfluid to a Bose-Einstein condensate (BEC). Starting from a superfluid order-parameter equation, we derive a Korteweg--de Vries equation for weak nonlinear excitations under quasi-one-dimensional and long-wavelength approximations. We present dark soliton solutions valid for both BCS and BEC limits and also for the crossover, and show that dark solitons in different superfluid regimes possess different features. Particularly, a dark soliton in the BCS (BEC) regime has larger (smaller) propagating velocity and smaller (larger) spatial width. Upon moving to the boundary of the condensate, it generally decelerates and generates small radiations, which display different behavior in different superfluid regimes. We study also a head-on collision between two dark solitons and demonstrate that the phase shift due to the collision changes nonmonotonically along the BCS-BEC crossover. All analytical results are checked by numerical simulations, and good agreement between them is found.

Strongly interacting Fermi systems in1/Nexpansion: From cold atoms to color superconductivity

We investigate the $1/N$ expansion proposed recently as a strategy to include quantum fluctuation effects in the nonrelativistic, attractive Fermi gas at and near unitarity. We extend the previous results by calculating the next-to-leading order corrections to the critical temperature along the whole crossover from Bardeen-Cooper-Schrieffer (BCS) superconductivity to Bose-Einstein condensation. We demonstrate explicitly that the extrapolation from the mean-field approximation, based on the $1/N$ expansion, provides a useful approximation scheme only on the BCS side of the crossover. We then apply the technique to the study of strongly interacting relativistic many-fermion systems. Having in mind the application to color superconductivity in cold dense quark matter, we develop, within a simple model, a formalism suitable to compare the effects of order parameter fluctuations in phases with different pairing patterns. Our main conclusion is that the relative correction to the critical temperature is to a good accuracy proportional to the mean-field ratio of the critical temperature and the chemical potential. As a consequence, it is significant even rather deep in the BCS regime, where phenomenologically interesting values of the quark--quark coupling are expected. Possible impact on the phase diagram of color-superconducting quark matter is discussed.

BCS–BEC crossover in one-dimensional integrable model

Abstract The crossover from Bardeen–Cooper–Schrieffer (BCS) superfluid with singlet pairs to Bose–Einstein condensation (BEC) of molecules is studied in one dimension. By use of the nested Bethe ansatz method, the ground state properties of spin-1/2 fermions interacting through attractive δ-function are analyzed explicitly for strong and weak couplings. Based on those results, we confirm a crossover picture, that is, in the BEC regime (strong couplings) the system is described by molecules with weak repulsion while in the BCS regime (weak couplings) it behaves as the weakly attractive fermions.

The validity of Anderson’s theorem for binary alloy s-wave superconductors in theBardeen–Cooper–Schrieffer regime

For a binary alloy s-wave superconductor in the Bardeen–Cooper–Schrieffer regime(weakly attractive electron interaction), the superconducting critical temperature,Tc, iscalculated within the coherent potential approximation as a function of the impurity concentrationc and the randompotentials εi for different band fillings. In contradiction to Anderson’s theorem (AT), we find thatTc is dramaticallysensitive to c and εi. Our results show that for low impurity concentrations and weak on-site energiesεi, AT is valid, while in the strong scattering limit even for low impurity concentration,Tc is very small for the clean system and on increasingc it is completely suppressed; hence AT is violated in this regime.