BCS-BEC crossover in a random external potential

We investigate the ground state properties of a disordered superfluid Fermi gas across the BCS-BEC (Bose-Einstein condensate) crossover. We show that, for weak disorder, both the depletion of the condensate fraction of pairs and the normal fluid density exhibit a nonmonotonic behavior as a function of the interaction parameter 1/k{F}a, reaching their minimum value near unitarity. We find that, moving away from the weak-coupling BCS regime, Anderson's theorem ceases to apply and the superfluid order parameter is more and more affected by the random potential.     

Josephson effect throughout the BCS-BEC crossover

We study the stationary Josephson effect for neutral fermions across the BCS-BEC (Bose-Einstein condensate) crossover, by solving numerically the Bogoliubov-de Gennes equations at zero temperature. The Josephson current is found to be considerably enhanced for all barriers at about unitarity. For vanishing barrier, the Josephson critical current approaches the Landau limiting value which, depending on the coupling, is determined by either pair-breaking or sound-mode excitations. In the coupling range from the BCS limit to unitarity, a procedure is proposed to extract the pairing gap from the Landau limiting current.     

BCS-BEC crossover in a two-dimensional Fermi gas

We investigate the crossover from Bardeen-Cooper-Schrieffer (BCS) superfluidity to Bose-Einstein condensation (BEC) in a two-dimensional Fermi gas at T=0 using the fixed-node diffusion Monte?Carlo method. We calculate the equation of state and the gap parameter as a function of the interaction strength, observing large deviations compared to mean-field predictions. In the BEC regime our results show the important role of dimer-dimer and atom-dimer interaction effects that are completely neglected in the mean-field picture. Results on Tan's contact parameter associated with short-range physics are also reported along the BCS-BEC crossover.     

BCS-BEC crossover on the two-dimensional honeycomb lattice

The attractive Hubbard model on the honeycomb lattice exhibits, at half filling, a quantum critical point between a semimetal with massless Dirac fermions and an s-wave superconductor (SC). We study the BCS-BEC crossover in this model away from half filling at zero temperature and show that the appropriately defined crossover line (in the interaction-density plane) passes through the quantum critical point at half filling. For a range of densities around half filling, the "underlying Fermi surface" of the SC, defined as the momentum space locus of minimum energy quasiparticle excitations, encloses an area which changes nonmonotonically with interaction. We also study fluctuations in the SC and the semimetal, and show the emergence of an undamped Leggett mode deep in the SC. Finally, we consider possible implications for ultracold atoms in optical lattices and the high temperature SCs.     

Dynamics of the BCS-BEC crossover in a degenerate Fermi gas

We study the short-time dynamics of a degenerate Fermi gas positioned near a Feshbach resonance following an abrupt jump in the atomic interaction resulting from a change of magnetic field. We investigate the dynamics of the condensate order parameter and pair wave function for a range of field strengths. When the jump is sufficient to span the BCS to Bose-Einstein condensation crossover, we show that the rigidity of the momentum distribution precludes any atom-molecule oscillations in the entrance channel dominated resonances observed in 40K and 6Li. Focusing on material parameters tailored to the 40K Feshbach resonance at 202.1 G, we comment on the integrity of the fast sweep projection technique as a vehicle to explore the condensed phase in the crossover region.     

Released momentum distribution of a Fermi gas in the BCS-BEC crossover

We develop a time-dependent mean-field theory to investigate the released momentum distribution and the released energy of an ultracold Fermi gas in the BCS-BEC crossover after the scattering length has been set to zero by a fast magnetic-field ramp. For a homogeneous gas we analyze the nonequilibrium dynamics of the system as a function of the interaction strength and of the ramp speed. For a trapped gas the theoretical predictions are compared with experimental results.     

Momentum distribution of a Fermi gas of atoms in the BCS-BEC crossover

We observe dramatic changes in the atomic momentum distribution of a Fermi gas in the crossover region between the BCS theory superconductivity and Bose-Einstein condensation (BEC) of molecules. We study the shape of the momentum distribution and the kinetic energy as a function of interaction strength. The momentum distributions are compared to a mean-field crossover theory, and the kinetic energy is compared to theories for the two weakly interacting limits. This measurement provides a unique probe of pairing in a strongly interacting Fermi gas.     

Potential energy of a 40K Fermi gas in the BCS-BEC crossover

We present a measurement of the potential energy of an ultracold trapped gas of 40K atoms in the BCS-BEC crossover and investigate the temperature dependence of this energy at a wide Feshbach resonance, where the gas is in the unitarity limit. In particular, we study the ratio of the potential energy in the region of the unitarity limit to that of a noninteracting gas, and in the T=0 limit we extract the universal many-body parameter beta. We find beta=-0.54_{-0.12};{+0.05}; this value is consistent with previous measurements using 6Li atoms and also with recent theory and Monte Carlo calculations. This result demonstrates the universality of ultracold Fermi gases in the strongly interacting regime.     

BCS-BEC渡越过程中超流费米气体Efimovian膨胀的研究

基于耦合流体力学方程组,分别研究了各向同性和各向异性轴对称势阱下Bardeen-CooperSchrieffer–Bose-Einstein condensate(BCS-BEC)渡越过程中超流费米气体的Efimovian膨胀.当费米气体处于幺正极限,体系标度不变,气体膨胀尺寸展现出一系列平台结构,气体的演化由对数周期函数描述;当费米气体处于非幺正极限超流区域,体系标度不变性破缺,气体的演化偏离对数周期变化;另外我们还发现对于各向异性的费米气体,即使处于幺正极限,谐振子势的各向异性也会导致体系标度不变性破缺.     

Collective modes and ballistic expansion of a fermi gas in the BCS-BEC crossover

We evaluate the frequencies of collective modes and the anisotropic expansion rate of a harmonically trapped Fermi superfluid at varying coupling strengths across a Feshbach resonance driving a BCS-BEC crossover. The equations of motion for the superfluid are obtained from a microscopic mean-field expression for the compressibility and are solved within a scaling ansatz. Our results confirm nonmonotonic behavior in the crossover region and are in quantitative agreement with current measurements of the transverse breathing mode by Kinast et al. [Phys. Rev. Lett. 92, 150402 (2004)]] and of the axial breathing mode by Bartenstein et al. [Phys. Rev. Lett. 92, 203201 (2004)]].     

Momentum distribution and condensate fraction of a fermion gas in the BCS-BEC crossover

By using the diffusion Monte Carlo method we calculate the one- and two-body density matrix of an interacting Fermi gas at T = 0 in the BCS to Bose-Einstein condensate (BEC) crossover. Results for the momentum distribution of the atoms, as obtained from the Fourier transform of the one-body density matrix, are reported as a function of the interaction strength. Off-diagonal long-range order in the system is investigated through the asymptotic behavior of the two-body density matrix. The condensate fraction of pairs is calculated in the unitary limit and on both sides of the BCS-BEC crossover.     

BCS-BEC crossover in a gas of Fermi atoms with a Feshbach resonance

We discuss the BCS-BEC crossover in a degenerate Fermi gas of two hyperfine states interacting close to a Feshbach resonance. We show that, by including fluctuation contributions to the free energy similar to that considered by Nozières and Schmitt-Rink, the character of the superfluid phase transition continuously changes from the BCS-type to the BEC-type, as the threshold of the quasimolecular band is lowered. In the BEC regime, the superfluid phase transition is interpreted in terms of molecules associated with both the Feshbach resonance and Cooper pairing.     

Probing the excitation spectrum of a fermi gas in the BCS-BEC crossover regime

We measure excitation spectra of an ultracold gas of fermionic (40)K atoms in the BCS-Bose-Einstein-condensation (BEC) crossover regime. The measurements are performed with a novel spectroscopy that employs a small modulation of the B field close to a Feshbach resonance to give rise to a modulation of the interaction strength. With this method we observe both a collective excitation as well as the dissociation of fermionic atom pairs in the strongly interacting regime. The excitation spectra reveal the binding energy or excitation gap for pairs in the crossover region.     

BCS-BEC crossover in a gas of Fermi atoms with a p-wave feshbach resonance

We investigate unconventional superfluidity in a gas of Fermi atoms with an anisotropic p-wave Feshbach resonance. Including the p-wave Feshbach resonance as well as the associated three kinds of quasimolecules with finite orbital angular momenta Lz=+/-1,0, we calculate the transition temperature of the superfluid phase. As one passes through the p-wave Feshbach resonance, we find the usual BCS-BEC crossover phenomenon. The p-wave BCS state continuously changes into the BEC of bound molecules with L=1. Our calculation includes the effect of fluctuations associated with Cooper pairs and molecules which are not Bose condensed.     

Comparison of different pairing fluctuation approaches to BCS-BEC crossover

The subject of BCS-Bose-Einstein condensation (BEC) crossover is particularly exciting because of its realization in ultracold atomic Fermi gases and its possible relevance to high temperature superconductors. In this paper we review the body of theoretical work on this subject, which represents a natural extension of the seminal papers by Leggett and by Nozières 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 papers have given rise to two main and, importantly, distinct, theoretical schools in the BCS-BEC crossover literature. The first of these extends the BCS-Leggett ground state to finite temperature and the second extends the NSR scheme away from T_c both in the superfluid and normal phases. It is now rather widely accepted that these extensions of NSR produce a different ground state than that first introduced by Leggett. This observation provides a central motivation for the present paper which seeks to clarify the distinctions in the two approaches. Our analysis shows how the NSR-based approach views the bosonic contributions more completely but treats the fermions as “quasi-free”. By contrast, the BCS-Leggett based approach treats the fermionic contributions more completely but treats the bosons as “quasi-free”. In a related fashion, the NSR-based schemes approach the crossover between BCS and BEC by starting from the BEC limit and the BCS-Leggett based scheme approaches this crossover by starting from the BCS limit. Ultimately, one would like to combine these two schemes. There are, however, many difficult problems to surmount in any attempt to bridge the gap in the two theory classes. In this paper we review the strengths and weaknesses of both approaches. The flexibility of the BCS-Leggett based approach and its ease of handling make it widely used in T=0 applications, although the NSR-based schemes tend to be widely used at . To reach a full understanding, it is important in the future to invest effort in investigating in more detail the T=0 aspects of NSR-based theory and at the same time the T≠0 aspects of BCS-Leggett theory.     

Disorder effects in the BCS-BEC crossover region of the attractive Hubbard model

We study the disorder effects upon superconducting transition temperature T _c and the number of local pairs within the attractive Hubbard model in the combined Nozieres-Schmitt-Rink and DMFT + Σ approximations. We analyze the wide range of attractive interaction U, from the weak coupling region, where instability of the normal phase and superconductivity are well described by the BCS model, to the limit of strong coupling, where superconducting transition is determined by Bose-Einstein condensation of compact Cooper pairs, forming at temperatures much higher than superconducting transition temperature. It is shown that disorder can either suppress T _c in the weak coupling limit, or significantly enhance T _c in the case of strong coupling. However, in all cases we actually prove the validity of generalized Anderson theorem, so that all changes in T _c are related to change in the effective bandwidth due to disorder. Similarly, disorder effects on the number of local pairs are only due to these band-broadening effects.     

Structure of a quantized vortex near the BCS-BEC crossover in an atomic Fermi gas

In order to clarify the structure of a singly quantized vortex in a superfluid fermion gas near the Feshbach resonance, we numerically solve the generalized Bogoliubov-de Gennes equation in the boson-fermion model. The superfluid gap, which contains contributions from both condensed fermion pairs and condensed bosons, is self-consistently determined, and the quasiparticle excitation levels bound in the vortex core are explicitly shown. We find that the boson condensate contributes to enhance the matter density depletion and the discreteness of localized quasiparticle spectrum inside the core. It is predicted that the matter density depletion and the discrete core levels are detectable in the vicinity of the BCS-Bose-Einstein condensation crossover point.     

Quantitative comparison between theoretical predictions and experimental results for the BCS-BEC crossover

Theoretical predictions for the Bardeen-Cooper-Schrieffer-Bose-Einstein condensation crossover of trapped Fermi atoms are compared with recent experimental results for the density profiles of 6Li. 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.