BCS-BEC Crossover in Atomic Fermi Gases with a Narrow Resonance

We determine the effects on the BCS-BEC crossover of the energy dependence of the effective two-body interaction, which at low energies is determined by the effective range. To describe interactions with an effective range of either sign, we consider a single-channel model with a two-body interaction having an attractive square well and a repulsive square barrier. We investigate the two-body scattering properties of the model, and then solve the Eagles-Leggett equations for the zero temperature crossover, determining the momentum dependent gap and the chemical potential self-consistently. From this we investigate the dependence of the crossover on the effective range of the interaction.Comment: 12 pages, 14 figure

Collective oscillations of a trapped Fermi gas near a Feshbach resonance

The frequencies of the collective oscillations of a harmonically trapped Fermi gas interacting with large scattering lengths are calculated at zero temperature using hydrodynamic theory. Different regimes are considered, including the molecular Bose-Einstein condensate and the unitarity limit for collisions. We show that the frequency of the radial compressional mode in an elongated trap exhibits a pronounced non monotonous dependence on the scattering length, reflecting the role of the interactions in the equation of state.Comment: 3 pages, including 1 figur

Analytical Results for Cold Asymmetrical Fermion Superfluids at the Mean-Field Level

We present the analytical results at the mean-field level for the asymmetrical fermion system with attractive contact interaction at the zero temperature. The results can be expressed in terms of linear combinations of the elliptic integrals of the first and second kinds. In the limit of small gap parameter, we discuss how the asymmetry in fermion species affects the phases of the ground state. In the limit of large gap parameter, we show that two candidate phases are competing for the system's ground state. The Sarma phase containing a pure Fermi fluid and a mixed condensate is favored at large degree of asymmetry. The separated phase consisting of a pure Fermi fluid and a boson condensate supports the system at smaller degree of asymmetry. The two phases are degenerate in the limit of infinite pairing gap.Comment: 23 pages, no figur

Pair Wave Functions in Atomic Fermi Condensates

Recent experiments have observed condensation behavior in a strongly interacting system of fermionic atoms. We interpret these observations in terms of a mean-field version of resonance superfluidity theory. We find that the objects condensed are not bosonic molecules composed of bound fermion pairs, but are rather spatially correlated Cooper pairs whose coherence length is comparable to the mean spacing between atoms. We propose experiments that will help to further probe these novel pairs

The potential energy of a 40^{40}K Fermi gas in the BCS-BEC crossover

We present a measurement of the potential energy of an ultracold trapped gas of $^{40}$K 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 non-interacting gas, and in the T=0 limit we extract the universal many-body parameter $\beta$. We find $\beta = -0.54^{+0.05}_{-0.12}$; this value is consistent with previous measurements using $^{6}$Li atoms and also with recent theory and Monte Carlo calculations. This result demonstrates the universality of ultracold Fermi gases in the strongly interacting regime

Magnetic field control of elastic scattering in a cold gas of fermionic lithium atoms

We study elastic collisions in an optically trapped spin mixture of fermionic lithium atoms in the presence of magnetic fields up to 1.5kG by measuring evaporative loss. Our experiments confirm the expected magnetic tunability of the scattering length by showing the main features of elastic scattering according to recent calculations. We measure the zero crossing of the scattering length that is associated with a predicted Feshbach resonance at 530(3)G. Beyond the resonance we observe the expected large cross section in the triplet scattering regime

Observation of the Pairing Gap in a Strongly Interacting Fermi Gas

We study fermionic pairing in an ultracold two-component gas of $^6$Li atoms by observing an energy gap in the radio-frequency excitation spectra. With control of the two-body interactions via a Feshbach resonance we demonstrate the dependence of the pairing gap on coupling strength, temperature, and Fermi energy. The appearance of an energy gap with moderate evaporative cooling suggests that our full evaporation brings the strongly interacting system deep into a superfluid state.Comment: 18 pages, 3 figure

General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas

We show that the Lagrangian for interacting nonrelativistic particles can be coupled to an external gauge field and metric tensor in a way that exhibits a nonrelativistic version of general coordinate invariance. We explore the consequences of this invariance on the example of the degenerate Fermi gas at infinite scattering length, where conformal invariance also plays an important role. We find the most general effective Lagrangian consistent with both general coordinate and conformal invariance to leading and next-to-leading orders in the momentum expansion. At the leading order the Lagrangian contains one phenomenological constant and reproduces the results of the Thomas-Fermi theory and superfluid hydrodynamics. At the next-to-leading order there are two additional constants. We express various physical quantities through these constants.Comment: 33 pages, 2 figures; v2: small typos fixed, references adde

Exploring the BEC-BCS Crossover with an Ultracold Gas of 6^6Li Atoms

We present an overview of our recent measurements on the crossover from a Bose-Einstein condensate of molecules to a Bardeen-Cooper-Schrieffer superfluid. The experiments are performed on a two-component spin-mixture of $^6$Li atoms, where a Fesh\-bach resonance serves as the experimental key to tune the s-wave scattering length and thus to explore the various interaction regimes. In the BEC-BCS crossover, we have characterized the interaction energy by measuring the size of the trapped gas, we have studied collective excitation modes, and we have observed the pairing gap. Our observations provide strong evidence for superfluidity in the strongly interacting Fermi gas.Comment: Proceedings of ICAP-2004 (Rio de Janeiro). Review on Innsbruck BEC-BCS crossover experiments with updated Feshbach resonance positio

Precision Measurements of Collective Oscillations in the BEC-BCS Crossover

We report on precision measurements of the frequency of the radial compression mode in a strongly interacting, optically trapped Fermi gas of Li-6 atoms. Our results allow for a test of theoretical predictions for the equation of state in the BEC-BCS crossover. We confirm recent quantum Monte-Carlo results and rule out simple mean-field BCS theory. Our results show the long-sought beyond-mean-field effects in the strongly interacting BEC regime.Comment: improved discussion of small ellipticity and anharmonicity correction