BCS-BEC Crossover Research Articles

Josephson effect with superfluid fermions in the two-dimensional BCS-BEC crossover

We investigate the macroscopic quantum tunneling of fermionic superfluids in the two-dimensional BCS-BEC crossover by using an effective tunneling energy which explicitly depends on the condensate fraction and the chemical potential of the system. We compare the mean-field effective tunneling energy with the beyond-mean-field one, finding that the mean-field tunneling energy is not reliable in the BEC regime of the crossover. Then we solve the Josephson equations of the population imbalance and the relative phase, calculating the frequency of tunneling oscillation both in the linear regime and in the nonlinear one. Our results show that the Josephson frequency is higher in the intermediate regime of the BCS-BEC crossover due to the peculiar behavior of the effective tunneling energy in the crossover.

Linear mapping between magnetic susceptibility and entanglement in conventional and exotic one-dimensional superfluids

We investigate the mapping between magnetic susceptibility and entanglement in the metallic, insulating, conventional and exotic polarized superfluid phases of one-dimensional fermionic lattice systems as described by the Hubbard model. Motivated by recent proposals for determining and quantifying entanglement via magnetic susceptibility measurements, we numerically study the intrinsic relationship between the two quantities at zero temperature. We find signatures of the metal-insulator transition and of the BCS-BEC crossover, but the most relevant result is that for conventional and exotic superfluids the mapping between magnetic susceptibility and entanglement is surprisingly simple: inversely proportional. This linear behavior could be exploited to quantify entanglement in current cold-atoms and condensed-matter experiments.

Quantum Droplets in a Mixture of Bose–Fermi SuperfluidsSupported by the National Natural Science Foundation of China under Grant Nos. 11974331, 11421092 and 11534014, and the National Key Research and Development Program of China under Grant Nos. 2016YFA0301700, 2017YFA0304100, 2018YFA0307600 and 2016YFA0300603.

We study the formation of quantum droplets in the mixture of a single-component Bose–Einstein condensate (BEC), and a two-species Fermi superfluid across a wide Feshbach resonance. With repulsive boson-boson and attractive boson-fermion interactions, we show that quantum droplets can be stabilized by attractive fermion-fermion interactions on the Bardeen–Cooper–Schrieffer (BCS) side of the resonance, and can also exist in the deep BEC regime under weak boson-fermion interactions. We map out the phase diagram for stable droplets with respect to the boson-boson and boson-fermion interactions, and discuss the role of different types of quantum fluctuations in the relevant regions of the BCS-BEC crossover. Our work reveals the impact of fermion pairing on the formation of quantum droplets in Bose–Fermi mixtures, and provides a useful guide for future experiments.

Sound Propagation and Quantum-Limited Damping in a Two-Dimensional Fermi Gas.

Strongly interacting two-dimensional Fermi systems are one of the great remaining challenges in many-body physics due to the interplay of strong local correlations and enhanced long-range fluctuations. Here, we probe the thermodynamic and transport properties of a 2D Fermi gas across the BEC-BCS crossover by studying the propagation and damping of sound modes. We excite particle currents by imprinting a phase step onto homogeneous Fermi gases trapped in a box potential and extract the speed of sound from the frequency of the resulting density oscillations. We measure the speed of sound across the BEC-BCS crossover and compare the resulting dynamic measurement of the equation of state both to a static measurement based on recording density profiles and to quantum MonteCarlo calculations and find reasonable agreement between all three. We also measure the damping of the sound mode, which is determined by the shear and bulk viscosities as well as the thermal conductivity of the gas. We find that the damping is minimal in the strongly interacting regime and the diffusivity approaches the universal quantum bound ℏ/m of a perfect fluid.

Heterobilayers of 2D materials as a platform for excitonic superfluidity

Excitonic condensate has been long-sought within bulk indirect-gap semiconductors, quantum wells, and 2D material layers, all tried as carrying media. Here, we propose intrinsically stable 2D semiconductor heterostructures with doubly-indirect overlapping bands as optimal platforms for excitonic condensation. After screening hundreds of 2D materials, we identify candidates where spontaneous excitonic condensation mediated by purely electronic interaction should occur, and hetero-pairs Sb2Te2Se/BiTeCl, Hf2N2I2/Zr2N2Cl2, and LiAlTe2/BiTeI emerge promising. Unlike monolayers, where excitonic condensation is hampered by Peierls instability, or other bilayers, where doping by applied voltage is required, rendering them essentially non-equilibrium systems, the chemically-specific heterostructures predicted here are lattice-matched, show no detrimental electronic instability, and display broken type-III gap, thus offering optimal carrier density without any gate voltages, in true-equilibrium. Predicted materials can be used to access different parts of electron-hole phase diagram, including BEC-BCS crossover, enabling tantalizing applications in superfluid transport, Josephson-like tunneling, and dissipationless charge counterflow.

Strong-Coupling Effects on Quantum Transport in an Ultracold Fermi Gas

We theoretically investigate quantum conductance across a point contact between two strongly-interacting ultracold Fermi gases. We evaluate the tunneling current, taking into account pairing fluctuations in the Fermi gases within the framework of a combined strong-coupling T-matrix approximation with the Schwinger-Keldysh non-equilibrium formalism. We show that quasi-particle conductance is gradually suppressed, as one passes through the BCS–BEC crossover region from the weak-coupling side. On the other hand, with increasing the strength of a pairing interaction, the fluctuation-pair conductance is found to remarkably increase in the crossover region, which is followed by the suppression in the strong-coupling regime.

Periodic solutions of Ginzburg–Landau theory for atomic Fermi gases near the BCS–BEC crossover

ABSTRACT In this paper, the existence of the time-periodic solution to the time-dependent Ginzburg–Landau(TDGL) equations in the case of BCS–BEC crossover is established relying on the Leray–Schauder fixed point theorem.

Global Attractors of Non-Newtonian Fluids Near the BCS-BEC Crossover

We consider the existence of global attractor for non-Newtonian fluids near the BCS-BEC crossover in this paper. By Gronwall’s inequality, interpolar inequality and the techniques for proving regularity theory in partial differential equations, etc., we establish suitable prior estimates and obtain the global attractor for non-Newtonian fluids.

Strong pairing in two dimensions: pseudogaps, domes, and other implications

This paper addresses the transition from the normal to the superfluid state in strongly correlated two dimensional fermionic superconductors and Fermi gases. We arrive at the Berezinskii–Kosterlitz–Thouless (BKT) temperature TBKT as a function of attractive pairing strength by associating it with the onset of ‘quasi-condensation’ in the normal phase. Our approach builds on a criterion for determining the BKT transition temperature for atomic gases which is based on a well established quantum Monte Carlo analysis of the phase space density. This latter quantity, when derived from BCS–BEC crossover theory for fermions, leads to non-monotonic behavior for TBKT as a function of the attractive interaction or inverse scattering length. In Fermi gases, this implies a robust superconducting dome followed by a long tail from the flat BEC asymptote, rather similar to what is observed experimentally. For lattice systems we find that TBKT has an absolute maximum of the order of 0.1EF. We discuss how our results compare with those derived from the Nelson–Kosterlitz criterion based on the mean field superfluid density and the approach to the transition from below. While there is agreement in the strict mean-field BCS regime at weak coupling, we find that at moderate pairing strength bosonic excitations cause a substantial increase in TBKT followed by an often dramatic decrease before the system enters the BEC regime.

Dipole oscillations of fermionic quantum gases along the BEC-BCS crossover in disordered potentials

We investigate dipole oscillations of ultracold Fermi gases along the BEC-BCS crossover through disordered potentials. We observe a disorder-induced damping of oscillations as well as a change of the fundamental Kohn-mode frequency. The measurement results are compared to numerical density matrix renormalization group calculations as well as to a three-dimensional simulation of non-interacting fermions. Experimentally, we find a disorder-dependent damping, which grows approximately with the second power of the disorder strength. Moreover, we observe experimentally a change of oscillation frequency which deviates from the expected behavior of a damped harmonic oscillator on a percent level. While this behavior is qualitatively expected from the theoretical models used, quantitatively the experimental observations show a significantly stronger effect than predicted by theory. Furthermore, while the frequency shift seems to scale differently with interaction strength in the BEC versus BCS regime, the damping coefficient apparently decreases with the strength of interaction, but not with the sign, which changes for BEC and BCS type Fermi gases. This is surprising, as the dominant damping mechanisms are expected to be different in the two regimes.

Geometric contribution to the Goldstone mode in spin–orbit coupled Fermi superfluids

The so-called quantum metric tensor is a band-structure invariant whose measure corresponds to the quantum distance between nearby states in the Hilbert space, characterizing the geometry of the underlying quantum states. In the context of spin–orbit coupled Fermi gases, we recently proposed that the quantum metric has a partial control over all those superfluid properties that depend explicitly on the mass of the superfluid carriers, i.e., the effective-mass tensor of the corresponding (two- or many-body) bound state. Here we scrutinize this finding by analyzing the collective phase and amplitude excitations at zero temperature. In particular to the Goldstone mode, we present extensive numerical calculations for the Weyl and Rashba spin–orbit couplings, revealing that, despite being small, the geometric contribution is solely responsible for the nonmonotonic evolution of the sound velocity in the BCS–BEC crossover.

Superfluidity and pairing phenomena in ultracold atomic Fermi gases in one-dimensional optical lattices. I. Balanced case

The superfluidity and pairing phenomena in ultracold atomic Fermi gases have been of great interest in recent years, with multiple tunable parameters. Here we study the BCS-BEC crossover behavior of balanced two-component Fermi gases in a one-dimensional optical lattice, which is distinct from the simple three-dimensional (3D) continuum and a fully 3D lattice often found in a condensed matter system. We use a pairing fluctuation theory which includes self-consistent feedback effects at finite temperatures, and find widespread pseudogap phenomena beyond the BCS regime. As a consequence of the lattice periodicity, the superfluid transition temperature $T_c$ decreases with pairing strength in the BEC regime, where it approaches asymptotically $T_c = \pi an/2m$, with $a$ being the $s$-wave scattering length, and $n$ ($m$) the fermion density (mass). In addition, the quasi-two dimensionality leads to fast growing (absolute value of the) fermionic chemical potential $\mu$ and pairing gap $\Delta$, which depends exponentially on the ratio $d/a$. Importantly, $T_c$ at unitarity increases with the lattice constant $d$ and hopping integral $t$. The effect of the van Hove singularity on $T_c$ is identified. The superfluid density exhibits $T^{3/2}$ power laws at low $T$, away from the extreme BCS limit. These predictions can be tested in future experiments.

Superfluidity and pairing phenomena in ultracold atomic Fermi gases in one-dimensional optical lattices. II. Effects of population imbalance

In this paper, we study the effect of population imbalance and its interplay with pairing strength and lattice effect in atomic Fermi gases in a one-dimensional optical lattice. We compute various phase diagrams as the system undergoes BCS-BEC crossover, using the same pairing fluctuation theory as in Part I of this work [Phys. Rev. A 101, 053617 (2020)]. We find widespread pseudogap phenomena beyond the BCS regime and intermediate temperature superfluid states for relatively low population imbalances. The Fermi surface topology plays an important role in the behavior of ${T}_{\mathrm{c}}$. For large $d$ and/or small $t$, which yield an open Fermi surface, superfluidity can be readily destroyed by a small amount of population imbalance $p$. The superfluid phase, especially in the BEC regime, can exist only for a highly restricted volume of the parameter space. An open Fermi surface often leads to destruction of the superfluid ground state in the BEC regime. Due to the continuum-lattice mixing, population imbalance gives rise to a new mechanism for pair hopping, as assisted by excessive majority fermions, which may lead to significant enhancement of ${T}_{\mathrm{c}}$ on the BEC side of the Feshbach resonance, and also render ${T}_{\mathrm{c}}$ approaching a constant asymptote in the BEC limit, when it exists. Furthermore, we find that not all minority fermions will be paired up in BEC limit, unlike the 3D continuum case. These predictions can be tested in future experiments.

Kovtun–Son–Starinets Conjecture and Effects of Mass Imbalance in the Normal State of an Ultracold Fermi Gas in the BCS–BEC Crossover Region

We theoretically assess the conjecture proposed by Kovtun, Son, and Starinets, stating that the ratio $\eta/s$ of the shear viscosity $\eta$ to the entropy density $s$ has the lower bound as $\eta/s\ge\hbar/(4\pi k_{\mathrm{B}})$. In the normal state of a mass-imbalanced ultracold Fermi gas, consistently including strong-coupling corrections to both $\eta$ and $s$ within the self-consistent $T$-matrix approximation, we evaluate $\eta/s$ over the entire BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover region, in the presence of mass imbalance. We find that $\eta/s$ achieves the minimum value $4.5\times \hbar/(4\pi k_{\mathrm{B}})$, not at the unitarity, but slightly in the BEC regime, $(k_{\mathrm{F}}a_s)^{-1}\simeq 0.4>0$ (where $a_s$ is the $s$-wave scattering length, and $k_{\mathrm{F}}$ is the Fermi momentum). In contract to the previous expectation, we find that this lower bound is almost independent of mass imbalance: Our results predict that all the mass-balanced $^6$Li-$^6$Li and $^{40}$K-$^{40}$K mixtures and the mass-imbalanced $^{40}$K-$^{161}$Dy mixture give almost the same lower bound of $\eta/s$. We also point out that the two quantum phenomena, Pauli blocking and bound-state formation, are crucial keys for the lower bound of $\eta/s$.

Experimental conditions for the observation of electron-hole superfluidity in GaAs heterostructures

The experimental parameter ranges needed to generate superfluidity in optical and drag experiments in GaAs double quantum wells are determined, using a formalism that includes self-consistent screening of the Coulomb pairing interaction in the presence of the superfluid. The very different electron and hole masses in GaAs make this a particularly interesting system for superfluidity, with exotic superfluid phases predicted in the BCS-BEC crossover regime. We find that the density and temperature ranges for superfluidity cover the range for which optical experiments have observed indications of superfluidity, but that existing drag experiments lie outside the superfluid range. However we also show that for samples with low mobility with no macroscopically connected superfluidity, if the superfluidity survived in randomly distributed localized pockets, standard quantum capacitance measurements could detect these pockets.

EVOLUTION OF OVER-CONDUCTIVITY OF YВа2Сu3О7-δ SINGLE CRYSTALS UNDER THE EXPOSURE OF IRRADIATION BY HIGH-ENERGY ELECTRONS

The evolution of the excess conductivity of YВа2Сu3О7-δ single crystals upon electron irradiation is investigated. It was shown that electron irradiation leads to a significant expansion of the temperature range for the existence of excess conductivity, thereby narrowing the region of the linear dependence of ρ(Т) in the ab plane. It was found that the excess conductivity ∆σ(Т) of YВа2Сu3О7-δ single crystals in a wide temperature range Tf<Т<T* (Тf – the transition temperature from the PG to the FP mode) is subject to exponential temperature dependence. Moreover, the description of excess conductivity using the relation ∆σ ~ (1-Т/Т*)exp( ∆*ab/T) (Δ*ab – the pseudogap in ab-plane) can be interpreted in terms of the mean-field theory, where T* is presented as the mean-field temperature of the transition to the PG state, and the temperature dependence of the pseudogap is satisfactorily described in the framework of the BCS-BEC crossover theory. In this case, the value of the transverse coherence length ξс(0) increases 1.4 times and the 2D-3D crossover point shifts in temperature.

Spatial structure of the pair wave function and the density correlation functions throughout the BEC-BCS crossover

By an exact numerical calculation of the BCS pair wavefunction and the density correlation functions both between atoms in the same and in different spin states, we extract the spatial large distance behavior of the respective functions. After different initial transients, those distributions show an algebraic dependence accompanied with their own exponential decay and a well defined periodic oscillatory behavior. While in general, in the BCS side there are long-range correlations and in the BEC region the behavior is dominated by tight pairs formation, each distribution shows its own overall behavior. We derive analytic expressions for the mean pair size and the correlation lengths of the same and different density correlation functions. The whole analysis yields a quite complete description of the spatial structure of the superfluid along the crossover.

Electron irradiation and annealing effects on the pseudogap in optimally doped YBCO single crystals

The effect of room-temperature annealing on the basal-plane conductivity of YBCO single crystals is investigated after their irradiation with fast electrons. It is revealed that the excess conductivity [Formula: see text] of the samples obeys an exponential temperature dependence in a broad temperature range [Formula: see text]. Here, [Formula: see text] is the crossover temperature from the pseudogap to the fluctuation conductivity regime. The description of the excess conductivity with the expression [Formula: see text] can be interpreted in terms of the mean-field theory where [Formula: see text] corresponds to the mean-field transition temperature to the pseudogap state and the dependence [Formula: see text] is described within the framework of the BCS-BEC crossover theory.

Beyond Mean-Field Corrections to the Quasiparticle Spectrum of Superfluid Fermi Gases.

We investigate the fermionic quasiparticle branch of superfluid Fermi gases in the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensation (BEC) crossover and calculate the quasiparticle lifetime and energy shift due to its coupling with the collective mode. The only close-to-resonance process that low-energy quasiparticles can undergo at zero temperature is the emission of a bosonic excitation from the phononic branch. Close to the minimum of the branch we find that the quasiparticles remain undamped, allowing us to compute corrections to experimentally relevant quantities such as the energy gap, location of the minimum, effective mass, and Landau critical velocity.

Pairing and molecule formation along the BCS-BEC crossover for finite range potentials

We address the thermodynamics of the zero temperature BCS-BEC crossover of a balanced two component mixture of a finite range interacting fermions within a mean field approach. For the analysis we consider two wide types of finite range potentials describing the interaction between different Fermi species: purely attractive, as the square well, the exponential and the Yukawa potentials, and others having both a repulsive wall at the origin as well as a finite attractive tail, as Van der Waals and dipolar potentials. We study the energy gap, the chemical potential and the pressure as functions of the scattering length for all the interacting potentials considered. The system spatial structure is further analyzed via the the pair functions associated to each potential. We find that for those with pure attractive contributions the crossover can be recognized either, when the chemical potential changes its sign or when the scattering length diverges. In contrast, the pair functions linked to potentials with both repulsive and attractive terms, show wide crossover regions without sharp distinctions at the sign change of the chemical potential nor at unitarity.