BCS-BEC Crossover Regime Research Articles

Superfluid density and condensate fraction in the BCS-BEC crossover regime at finite temperatures

The superfluid density is a fundamental quantity describing the response to a rotation as well as in two-fluid collisional hydrodynamics. We present extensive calculations of the superfluid density \rho_s in the BCS-BEC crossover regime of a uniform superfluid Fermi gas at finite temperatures. We include strong-coupling or fluctuation effects on these quantities within a Gaussian approximation. We also incorporate the same fluctuation effects into the BCS single-particle excitations described by the superfluid order parameter \Delta and Fermi chemical potential \mu, using the Nozi\`eres and Schmitt-Rink (NSR) approximation. This treatment is shown to be necessary for consistent treatment of \rho_s over the entire BCS-BEC crossover. We also calculate the condensate fraction N_c as a function of the temperature, a quantity which is quite different from the superfluid density \rho_s. We show that the mean-field expression for the condensate fraction N_c is a good approximation even in the strong-coupling BEC regime. Our numerical results show how \rho_s and N_c depend on temperature, from the weak-coupling BCS region to the BEC region of tightly-bound Cooper pair molecules. In a companion paper by the authors (cond-mat/0609187), we derive an equivalent expression for \rho_s from the thermodynamic potential, which exhibits the role of the pairing fluctuations in a more explicit manner.

Acoustic Attenuation Probe for Fermion Superfluidity in Ultracold-Atom Gases

Dilute gas Bose-Einstein condensates (BEC's), currently used to cool fermionic atoms in atom traps, can also probe the superfluidity of these fermions. The damping rate of BEC-acoustic excitations (phonon modes), measured in the middle of the trap as a function of the phonon momentum, yields an unambiguous signature of BCS-like superfluidity, provides a measurement of the superfluid gap parameter, and gives an estimate of the size of the Cooper pairs in the BEC-BCS crossover regime. We also predict kinks in the momentum dependence of the damping rate which can reveal detailed information about the fermion quasiparticle dispersion relation.

Finite-temperature momentum distribution of a trapped Fermi gas

We present measurements of the temperature-dependent momentum distribution of a trapped Fermi gas consisting of $^{40}$K in the BCS-BEC crossover regime. Accompanying theoretical results based upon a simple mean-field ground state are compared to the experimental data. Non-monotonic effects associated with temperature, $T$, arise from the competition between thermal broadening and a narrowing of the distribution induced by the decrease in the excitation gap $\Delta(T)$ with increasing $T$.

Excitations in the BCS–BEC crossover regime of a superfluid Fermi gas with a Feshbach resonance

We investigate single-particle excitations at T=0 in the BCS–BEC crossover regime of a superfluid Fermi gas. We solve the Bogoliubov–de Gennes equations in a trap, including a tunable pairing interaction associated with a Feshbach resonance. We show that the single-particle energy gap Eg is dominated by the lowest-energy Andreev bound state localized at the surface of the gas, which is much smaller than the superfluid order parameter Δ˜(r=0) at the center of the trap. We also calculate the rf-tunneling current spectrum IF(ω). In a broad Feshbach resonance, the peak energy in IF(ω) is shown to give, not Eg, but Δ˜(r=0). In a narrow resonance, significant spectral weight coming from the low-energy Andreev states hides the appearance of the peak in IF(ω) at ω≃Δ˜(r=0). Our results for a broad resonance is in good agreement with the recent rf-tunneling measurement in a superfluid 6Li.

Critical currents in the BEC-BCS crossover regime in an optical lattice

Both the trapping geometry and the interatomic interaction strength of a dilute ultracold fermionic gas can be well controlled experimentally. Adapting the interaction strength between the fermionic atoms allows tuning the gas from a molecular condensate to a Bardeen-Cooper-Schrieffer superfluid. We adopt a functional integral point of view to investigate how the superfluid properties vary during this crossover. In particular, the critical superfluid velocity for flowing through an optical lattice is derived. The observation of undamped motion in an optical lattice constitutes a hallmark of superfluidity, also in the fermionic systems. We discuss our theoretical results for the critical velocity of a fermionic superfluid in comparison to the experimental results for a bosonic superfluid in an optical lattice.

Simple mean-field model for condensates in the BEC-BCS crossover regime

We present a mean field approach based on pairs of fermionic atoms to describe condensates in the BEC-BCS crossover regime. By introducing an effective potential, the mean field equation allows us to calculate the chemical potential, the equation of states and the atomic correlation function. The results agree surprisingly well with recent quantum Monte Carlo calculations. We show that the smooth crossover from the bosonic mean field repulsion between molecules to the Fermi pressure among atoms is associated with the evolution of the atomic correlation function.

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.

Time-dependent density-functional theory for trapped strongly interacting fermionic atoms

The dynamics of strongly interacting trapped dilute two-component Fermi gases (dilute in the sense that the range of interatomic potential is small compared with interparticle spacing) is investigated in a single-equation approach to the time-dependent density-functional theory. For the ground-state energy per particle of the system in the homogeneous phase, we have constructed an Pad\'e parametrization based on Monte Carlo data and asymptotic behavior. Our numerical results for collective frequencies in the BCS-BEC crossover regime are in good agreement with recent experimental data obtained by the Duke University group. In addition, we show that the calculated corrections to the hydrodynamic approximation may be important, even for systems with a rather large number of atoms.

Collective excitations of a degenerate gas at the BEC-BCS crossover.

We study collective excitation modes of a fermionic gas of (6)Li atoms in the BEC-BCS crossover regime. While measurements of the axial compression mode in the cigar-shaped trap close to a Feshbach resonance confirm theoretical expectations, the radial compression mode shows surprising features. In the strongly interacting molecular BEC regime, we observe a negative frequency shift with increasing coupling strength. In the regime of a strongly interacting Fermi gas, an abrupt change in the collective excitation frequency occurs, which may be a signature for a transition from a superfluid to a collisionless phase.

Observation of Resonance Condensation of Fermionic Atom Pairs

We have observed condensation of fermionic atom pairs in the BCS-BEC crossover regime. A trapped gas of fermionic 40K atoms is evaporatively cooled to quantum degeneracy and then a magnetic-field Feshbach resonance is used to control the atom-atom interactions. The location of this resonance is precisely determined from low-density measurements of molecule dissociation. In order to search for condensation on either side of the resonance, we introduce a technique that pairwise projects fermionic atoms onto molecules; this enables us to measure the momentum distribution of fermionic atom pairs. The transition to condensation of fermionic atom pairs is mapped out as a function of the initial atom gas temperature T compared to the Fermi temperature T(F) for magnetic-field detunings on both the BCS and BEC sides of the resonance.