We study the crossover of a quasi-two-dimensional Fermi gas trapped in the radial plane from the Bardeen-Cooper-Schrieffer (BCS) regime to the Bose-Einstein condensation (BEC) regime by crossing a wide Feshbach resonance. We consider two effective two-dimensional Hamiltonians within the mean-field level, and calculate the zero-temperature cloud size and number density distribution. For a model 1 Hamiltonian with renormalized atom-atom interaction, we observe a constant cloud size for arbitrary detunings. For a model 2 Hamiltonian with renormalized interactions between atoms and dressed molecules, the cloud size deceases from the BCS to BEC side, which is consistent with the picture of BCS-BEC crossover. This qualitative discrepancy between the two models indicates that the inclusion of dressed molecules is essential for a mean-field description of quasi-two-dimensional Fermi systems, especially on the BEC side of the Feshbach resonance.
We pointed out in this work that in dealing with the BEC-BCS crossover problem, the dynamic effect of <b(t)>is not negligible. Accordingly, an equation of motion approach was devised to calculate the Green$^{\prime}$s functions. Based on our result, we concluded that instead of crossover, BCS states and Bose-Einstein condensation always coexist.
By using a Path Integral formalism, we study the fluctuating fields in the order parameter for a 3D uniform Fermi gas at T<Tc. The BCS-BEC crossover condition is included into the analysis in the framework of the usual s-wave scattering approximation. The general expressions for the temperature dependence of the partition function and the quadratic average in the fluctuations fields are explicitly established in terms of the BCS-Gor'kov correlation propagators.
We have analyzed a single vortex at T=0 in a 3D superfluid atomic Fermi gas across a Feshbach resonance. On the BCS side, the order parameter varies on two scales: $k_{F}^{-1}$ and the coherence length $ξ$, while only variation on the scale of $ξ$ is seen away from the BCS limit. The circulating current has a peak value $j_{max}$ which is a non-monotonic function of $1/k_F a_s$ implying a maximum critical velocity $\sim v_F$ at unitarity. The number of fermionic bound states in the core decreases as we move from the BCS to BEC regime. Remarkably, a bound state branch persists even on the BEC s…
We report quantum Monte Carlo evidence of the existence of large gap superfluidity in electron-hole double layers over wide density ranges. The superfluid parameters evolve from normal state to BEC with decreasing density, with the BCS state restricted to a tiny range of densities due to the strong screening of Coulomb interactions, which causes the gap to rapidly become large near the onset of superfluidity. The superfluid properties exhibit similarities to ultracold fermions and iron-based superconductors, suggesting an underlying universal behavior of BCS-BEC crossovers in pairing systems.
We study the superconducting transition in a two-dimensional electron gas with strong Rashba spin-orbit coupling. We assume low electron density, such that only the majority spin band participates in the transition. We show that the superconducting transition follows either the Bose-Einstein condensation (BEC), or the Bardeen-Cooper-Schrieffer (BCS) scenarios, depending on the position of the chemical potential with respect to the bottom of the majority band, and the strength of the Coulomb repulsion between electrons. Hence, the BEC-BCS crossover in this system can be driven either by the cha…
Theoretical predictions for the BCS-BEC crossover of trapped Fermi atoms are compared with recent experimental results for the density profiles of $^6$Li. The calculations rest on a single theoretical approach that includes pairing fluctuations beyond mean field. Excellent agreement with experimental results is obtained. Theoretical predictions for the zero-temperature chemical potential and gap at the unitarity limit are also found to compare extremely well with Quantum Monte Carlo simulations and with recent experimental results.
The crossover from Bardeen-Cooper-Schrieffer (BCS) superconductivity to Bose-Einstein condensation (BEC) is difficult to realize in quantum materials because, unlike in ultracold atoms, one cannot tune the pairing interaction. We realize the BCS-BEC crossover in a nearly compensated semimetal Fe$_{1+y}$Se$_x$Te$_{1-x}$ by tuning the Fermi energy, $ε_F$, via chemical doping, which permits us to systematically change $Δ/ ε_F$ from 0.16 to 0.5 were $Δ$ is the superconducting (SC) gap. We use angle-resolved photoemission spectroscopy to measure the Fermi energy, the SC gap and characteristic chang…
The strongly-correlated regime of the BCS-BEC crossover can be realized by diluting a system of two-component fermions with a short-range attractive interaction. We investigate this system via a novel continuous-space-time diagrammatic determinant Monte Carlo method and determine the universal curve $T_c/ε_F$ for the transition temperature between the normal and the superfluid states as a function of the scattering length with the maximum on the BEC side. At unitarity, we confirm that $T_c/ε_F = 0.152(7)$.
The pairing of interacting fermions leading to superfluidity has two limiting regimes: the Bardeen-Cooper-Schrieffer (BCS) scheme for weakly interacting degenerate fermions and the Bose-Einstein condensation (BEC) of bosonic pairs of strongly interacting fermions. While the superconductivity that emerges in most metallic systems is the BCS-like electron pairing, strongly correlated electrons with poor Fermi liquidity can condense into the unconventional BEC-like pairs. Quantum spin liquids harbor extraordinary spin correlation free from order and the superconductivity that possibly emerges by …
We investigate the quench dynamics of strongly coupled superconductors within the time-dependent Gutzwiller approximation from the BCS to the BEC regime and evaluate the out-of-equilibrium transient spectral density and optical conductivity relevant for pump probe experiments. Fourier transformation of the order parameter dynamics reveals a frequency $Ω_J$ which, as in the BCS case, is controlled by the spectral gap. However, we find a crossover from the BCS dynamics to a new strong coupling regime where a characteristic frequency $Ω_U$, associated to double occupancy fluctuations controls the…
The reason behind the discrepancy between the phase diagrams of our earlier work [1] and the comment of Sheehy and Radzihovsky [2] is discussed. We show that, in contrast to what is claimed in [2], the requirement of positive susceptibility is sufficient to rule out states that are local maximum of the free energy (as a function of the order parameter $Δ$
We show that single-component fermionic polar molecules confined to a 2D geometry and dressed by a microwave field, may acquire an attractive $1/r^3$ dipole-dipole interaction leading to superfluid p-wave pairing at sufficiently low temperatures even in the BCS regime. The emerging state is the topological $p_x+ip_y$ phase promising for topologically protected quantum information processing. The main decay channel is via collisional transitions to dressed states with lower energies and is rather slow, setting a lifetime of the order of seconds at 2D densities $\sim 10^8$ cm$^{-2}$.
We study dynamic ground state properties in the crossover from weak (BCS) to strong coupling (BEC) superfluidity. Our approach is based on the attractive Hubbard model which is analyzed by the dynamical mean field theory (DMFT) combined with the numerical renormalization group (NRG). We present an extension of the NRG method for effective impurity models to selfconsistent calculations with superconducting symmetry breaking. In the one particle spectra we show quantitatively how the Bogoliubov quasiparticles at weak coupling become suppressed at intermediate coupling. We also present results fo…
It is shown that a cluster expansion technique, which is usually applied in the high-temperature regime to calcutate virial coefficients, can be applied to evaluate the superfluid transition temperature of the BCS-BEC crossover à la Lee and Yang. The transition temperature is identified with the emergence of the singularity in the sum of a certain infinite series of cluster functions. In the weak-coupling limit, we reproduce the Thouless criterion and the number equation of Nozières and Schmitt-Rink, and hence the transition temperature of the BCS theory. In the strong-coupling limit, we repro…
A crossover between the Bose Einstein condensation (BEC) and BCS superconducting state is described topologically in the chiral symmetric fermion system with attractive interaction. Using a local Z_2 Berry phase, we found a quantum phase transition between the BEC and BCS phases without accompanying the bulk gap closing.
We investigate the properties of a spin-orbit coupled quasi-two-dimensional Fermi gas with tunable s-wave interaction between the two spin species. By analyzing the two-body bound state, we find that the population of the excited states in the tightly-confined axial direction can be significant when the two-body binding energy becomes comparable or exceeds the axial confinement. Since the Rashba spin-orbit coupling that we study here tends to enhance the two-body binding energy, this effect can become prominent at unitarity or even on the BCS side of the Feshbach resonance. To study the impact…
We observe a long-lived solitary wave in a superfluid Fermi gas of $^6$Li atoms after phase-imprinting. Tomographic imaging reveals the excitation to be a solitonic vortex, oriented transverse to the long axis of the cigar-shaped atom cloud. The precessional motion of the vortex is directly observed, and its period is measured as a function of the chemical potential in the BEC-BCS crossover. The long period and the correspondingly large ratio of the inertial to the bare mass of the vortex are in good agreement with estimates based on superfluid hydrodynamics that we derive here using the known…
We investigate the quantum and thermal phase diagram of fermionic polar molecules loaded in a bilayer trapping potential with perpendicular dipole moment. We use both a BCS theory approach that is most realiable at weak-coupling and a strong-coupling approach that considers the two-body bound dimer states with one molecules in each layer as the relevant degree of freedom. The system ground state is a Bose-Einstein condensate (BEC) of dimer bound states in the low density limit and a paired superfluid (BCS) state in the high density limit. At zero temperature, the intralayer repulsion is found …
The authors of a recent paper (PRA \textbf{87}, 013613 (2013)) argued that in fermionic systems with d-wave pairing the speed of sound is nonanalytic across the BCS-BEC crossover at the point where the chemical potential vanishes, regardless of the specific details of the interaction potential. On the contrary, the numerical results reported here suggest that the speed of sound across the BCS-BEC evolution of atomic Fermi gases with s- and d-wave pairings in two-dimensional square lattices is a smooth analytic function at the vanishing chemical potential.
We determine the temperature $T$ dependence of first and second sound mode frequencies for trapped Fermi gases undergoing BCS to Bose Einstein condensation (BEC) crossover. Our results are based on the two fluid equations in conjunction with a microscopic calculation of thermodynamical variables. As in experiment and at unitarity, we show that the lowest radial breathing mode is $T$ independent. At finite $T$, higher order breathing modes strongly mix with second sound. Their complex $T$ dependence should provide an alternative way of measuring the transition temperature, $T_c$.
Using the field-theoretical methods we studied the evolution from BCS description of a non-Fermi superconductor to that of Bose-Einstein condensation (BEC) in one loop approximation. We showed that the repulsive interaction between composite bosons is determined by the exponent $α$ of the Anderson propagator in a two dimensional model. For $\a\neq 0$ the crossover is also continous and for $\a=0$ we obtain the case of the Fermi liquid.
We present a systematic investigation of the effects of "nonmagnetic" impurities on the $s$-wave BCS-BEC crossover in atomic Fermi gases within a pairing fluctuation theory. Both pairing and impurity scattering $T$-matrices are treated self-consistently at the same time. While the system is less sensitive to impurity scattering in the Born limit, for strong impurity scatterers, both the frequency and the gap function are highly renormalized, leading to significant suppression of the superfluid $T_c$, the order parameter and the superfluid density. We also find the formation of impurity bands a…
Having both elastic and inelastic two-body processes that are characterized by a complex $s$-wave scattering length between $\uparrow$ and $\downarrow$ fermions in mind, here we apply the non-Hermitian extension of the mean-field theory to the BCS-BEC evolution at zero temperature. We construct the phase diagram of the system, where we find a reentrant superfluid (SF) transition that is intervened by a normal and/or a metastable phase as a function of increasing inelasticity. This transition occurs in a large parameter regime away from the unitarity, i.e., both on the BCS and BEC sides of the …
The subject of BCS - Bose Einstein condensation (BEC) crossover is particularly exciting because of its realization in ultracold Fermi gases and its possible relevance to high temperature superconductors. In the paper we review that body of theoretical work on this subject which represents a natural extension of the seminal papers by Leggett and by Nozieres and Schmitt-Rink (NSR). The former addressed only the ground state, now known as the "BCS-Leggett" wave-function and the key contributions of the latter pertain to calculations of the superfluid transition temperature $T_c$. These two paper…
We present a theoretical study of the ground state of the BCS-BEC crossover in dilute two-dimensional Fermi gases. While the mean-field theory provides a simple and analytical equation of state, the pressure is equal to that of a noninteracting Fermi gas in the entire BCS-BEC crossover, which is not consistent with the features of a weakly interacting Bose condensate in the BEC limit and a weakly interacting Fermi liquid in the BCS limit. The inadequacy of the 2D mean-field theory indicates that the quantum fluctuations are much more pronounced than those in 3D. In this work, we show that the …
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 $\nabla θ({\bf r})$ (whe…
We determine the size of the critical region of the superfluid transition in the BCS-BEC crossover of a three-dimensional fermion gas, using a renormalization-group approach to a bosonic theory of pairing fluctuations. For the unitary Fermi gas, we find a sizable critical region $[T_G^-,T_G^+]$, of order $T_c$, around the transition temperature $T_c$ with a pronounced asymmetry: $|T_G^+-T_c|/|T_G^--T_c|\sim8$. The critical region is strongly suppressed on the BCS side of the crossover but remains important on the BEC side.
The aim of this Ph.D. thesis was to investigate superconducting properties in the presence of Zeeman magnetic field in systems with local fermion pairing on the lattice. The study also concerned the evolution from the weak coupling (BCS-like) limit to the strong coupling limit of tightly bound local pairs (BEC) with increasing attraction, both in the ground state and at finite temperatures, within the spin-polarized extended Hubbard model. The analysis was also extended to the case of spin dependent hopping integrals (mass imbalance), with special attention paid to the BCS-BEC crossover physic…
We use the functional renormalization group approach with partial bosonization in the particle-particle channel to study the effect of order parameter fluctuations on the BCS-BEC crossover of superfluid fermions in three dimensions. Our approach is based on a new truncation of the vertex expansion where the renormalization group flow of bosonic two-point functions is closed by means of Dyson-Schwinger equations and the superfluid order parameter is related to the single particle gap via a Ward identity. We explicitly calculate the chemical potential, the single-particle gap, and the superfluid…
