We study, in a fully nonperturbative calculation, a dilute system of spin 1/2 interacting fermions, characterized by an infinite scattering length at finite temperatures. Various thermodynamic properties and the condensate fraction are calculated and we also determine the critical temperature for the superfluid-normal phase transition in this regime. The thermodynamic behavior appears as a rather surprising and unexpected mélange of fermionic and bosonic features. The thermal response of a spin 1/2 fermion at the BCS-BEC crossover should be classified as that of a new type of superfluid.
We study, in a fully nonperturbative calculation, a dilute system of spin 1/2 interacting fermions, characterized by an infinite scattering length at finite temperatures. Various thermodynamic properties and the condensate fraction are calculated and we also determine the critical temperature for the superfluid-normal phase transition in this regime. The thermodynamic behavior appears as a rather surprising and unexpected mélange of fermionic and bosonic features. The thermal response of a spin 1/2 fermion at the BCS-BEC crossover should be classified as that of a new type of superfluid.
We study the system of a dilute gas of fermions in 3-dimensions, with attractive interactions tuned to the unitarity point, using the non-perturbative Restricted Path Integral Monte Carlo (R-PIMC) method. The pairing and superfluid properties of this system are calculated at finite temperature. The total energy at very low temperature from our results agrees closely with that of previous ground-state Quantum Monte Carlo calculations. We identify the temperature T � � 0.70ǫF below which pairing correlations develop, and estimate the critical temperature for the superfluid transition Tc � 0.25ǫF from a finite size scaling analysis of the superfluid density. PACS numbers: The recent experiments, starting with generating a degenerate gas of cold atoms[3], the use of Feshbach resonance to tune the effective interaction between the fermions[4, 5], the measurements of the gap to identify a pairing scale[6] and the measurements of vortices[7] to identify the superfluid state, have all given an impetus to the study of superfluidity in the BCS-BEC crossover regime. The nature of superconductivity or superfluidity in a many-particle system with an increasing pairing attraction was shown [1, 2] to interpolate smoothly between the BCS regime for weak attraction between the fermions, and the Bose-Einstein condensation (BEC) regime for strong coupling. In the weak coupling regime, the Cooper pair size is much larger than the interparticle spacing, and the simultaneous pairing and condensation of fermions is well described by the BCS theory. In the strong coupling regime, fermions form strongly bound bosonic molecules at a pairing temperature scale T ∗ that is considerably higher than the BEC temperature Tc. In a two species system of fermions with an attractive interaction between them, the unitary point is defined by the divergence of the zero energy s-channel scattering length, as, for two particles in free space. The unitary point is interesting since it describes a strongly correlated system with universal properties[8]. In general, there are two length scales that define the system: the interparticle spacing ∝ n −1/3 , and the scattering length as which contains information about the interaction potential. At the unitary point however, since as diverges, all the properties of the system are described by a single length scale k −1
The quantum Monte Carlo method for spin-21 fermions at finite temperature is formulated for dilute systems with an s-wave interaction. The motivation and the formalism are discussed along with descriptions of the algorithm and various numerical issues. We report on results for the energy, entropy, and chemical potential as a function of temperature. We give upper bounds on the critical temperature Tc for the onset of superfluidity, obtained by studying the finite-size scaling of the condensate fraction. All of these quantities were computed for couplings around the unitary regime in the range $\ensuremath{-}0.5\ensuremath{\leqslant}{({k}_{F}a)}^{\ensuremath{-}1}\ensuremath{\leqslant}0.2$, where a is the s-wave scattering length and kF is the Fermi momentum of a noninteracting gas at the same density. In all cases our data are consistent with normal Fermi gas behavior above a characteristic temperature T0>Tc, which depends on the coupling and is obtained by studying the deviation of the caloric curve from that of a free Fermi gas. For Tc<T<T0 we find deviations from normal Fermi gas behavior that can be attributed to pairing effects. Low-temperature results for the energy and the pairing gap are shown and compared with Green-function Monte Carlo results by other groups.
The physics of quantum degenerate atomic Fermi gases in uniform as well as in harmonically trapped configurations is reviewed from a theoretical perspective. Emphasis is given to the effect of interactions that play a crucial role, bringing the gas into a superfluid phase at low temperature. In these dilute systems, interactions are characterized by a single parameter, the s-wave scattering length, whose value can be tuned using an external magnetic field near a broad Feshbach resonance. The BCS limit of ordinary Fermi superfluidity, the Bose-Einstein condensation (BEC) of dimers, and the unitary limit of large scattering length are important regimes exhibited by interacting Fermi gases. In particular, the BEC and the unitary regimes are characterized by a high value of the superfluid critical temperature, on the order of the Fermi temperature. Different physical properties are discussed, including the density profiles and the energy of the ground-state configurations, the momentum distribution, the fraction of condensed pairs, collective oscillations and pair-breaking effects, the expansion of the gas, the main thermodynamic properties, the behavior in the presence of optical lattices, and the signatures of superfluidity, such as the existence of quantized vortices, the quenching of the moment of inertia, and the consequences of spin polarization. Various theoretical approaches are considered, ranging from the mean-field description of the BCS-BEC crossover to nonperturbative methods based on quantum Monte Carlo techniques. A major goal of the review is to compare theoretical predictions with available experimental results.
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 ${\ensuremath{\rho}}_{s}$ 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 $\ensuremath{\Delta}$ and Fermi chemical potential $\ensuremath{\mu}$, using the Nozi\`eres--Schmitt-Rink approximation. This treatment is shown to be necessary for consistent treatment of ${\ensuremath{\rho}}_{s}$ over the entire BCS-BEC crossover. We also calculate the condensate fraction Nc as a function of the temperature, a quantity which is quite different from the superfluid density ${\ensuremath{\rho}}_{s}$. We show that the mean-field expression for the condensate fraction Nc is a good approximation even in the strong-coupling BEC regime. Our numerical results show how ${\ensuremath{\rho}}_{s}$ and Nc depend on temperature, from the weak-coupling BCS region to the BEC region of tightly bound Cooper pair molecules. In a companion paper [Phys. Rev. A 74, 063626 (2006)], we derive an equivalent expression for ${\ensuremath{\rho}}_{s}$ from the thermodynamic potential, which exhibits the role of the pairing fluctuations in a more explicit manner.
We analyze the phase diagram of superfluidity for two-species fermion mixtures from the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensation (BEC) limit as a function of scattering parameter, population imbalance, and mass anisotropy. We identify regions corresponding to normal, or uniform or nonuniform superfluid phases, and discuss topological quantum phase transitions in the BCS, unitarity, and BEC limits. We derive the Ginzburg-Landau equation near the critical temperature, and show that it describes a dilute mixture of paired and unpaired fermions in the BEC limit. We also obtain the zero temperature low frequency and long wavelength collective excitation spectrum, and recover the Bogoliubov relation for weakly interacting dilute bosons in the BEC limit. Lastly, we discuss the effects of harmonic traps and the resulting density profiles in the BEC regime.