We consider the superfluid phase transition that arises when a Feshbach resonance pairing occurs in a dilute Fermi gas. We apply our theory to consider a specific resonance in potassium ( 40 K), and find that for achievable experimental conditions, the transition to a superfluid phase is possible at the high critical temperature of about 0.5 TF . Observation of superfluidity in this regime would provide the opportunity to experimentally study the crossover from the superfluid phase of weakly-coupled fermions to the Bose-Einstein condensation of strongly-bound composite bosons.The achievement of Bose-Einstein condensation in atomic vapors [1] has given great impetus to efforts to realize superfluidity in dilute fermionic alkali gases. While conditions of quantum degeneracy have been obtained in potassium (, the lowest achievable temperatures to date have been limited to around 0.2T F [3]. Although this limit is essentially technical in nature, it appears likely that it will be necessary to utilize a strong pairing mechanism yielding superfluid transition temperatures close to this value.Even in high-T c superconductors, the typical critical temperatures are of the order of 10 −2 T F . In the context of strong-coupling superconductivity there has been much work on constructing minimal models to study the crossover from the seminal BCS theory [4] for conventional superconductivity to the Bose-Einstein condensation of tightly bound pairs, passing through nonperturbative regimes in T c /T F [5,6]. In this letter, we treat explicitly a short range quasibound resonant state by extending the theory given in Refs. [7] to predict the existence of a Feshbach resonance superfluidity in a gas of fermionic potassium atoms. This system has an ultrahigh critical phase transition temperature in close proximity to the Fermi temperature. This is a novel regime for quantum fluids, as illustrated in Fig. 1 where our system and others which exhibit superfluidity or BEC are compared.The seminal Bardeen-Cooper-Schrieffer (BCS) theory [4] of superconductivity applied to a dilute gas considers binary interactions between particles in two distinguishable quantum states, say | ↑ and | ↓ . For a uniform system, the fermionic field operators may be Fourierexpanded in a box with periodic boundary conditions giving wavevector-k dependent creation and annihilation operators a † kσ and a kσ for states |σ . At low energy, the binary scattering processes are assumed to be completely characterized by the s-wave scattering length a in terms of a contact quasipotential U = 4πh 2 an/m, where n is the number density. The Hamiltonian describing such a system is given bywhere ǫ k =h 2 k 2 /2m is the kinetic energy, m is the mass, and the constraint k 4 = k 1 + k 2 − k 3 gives momentum conservation.

We create Bose-Einstein condensates of 87 Rb in a static magnetic trap with a superimposed blue-detuned 1D optical lattice. By displacing the magnetic trap center we are able to control the condensate evolution. We observe a change in the frequency of the center-of-mass oscillation in the harmonic trapping potential, in analogy with an increase in effective mass. For fluid velocities greater than a local speed of sound, we observe the onset of dissipative processes up to full removal of the superfluid component. A parallel simulation study visualizes the dynamics of the BEC and accounts for the main features of the observed behavior. 03.75.Fi, 32.80.Pj, 67.57.De Bose-Einstein condensates (BEC) in dilute atomic gases are macroscopic quantum systems which can be manipulated by a variety of experimental techniques [1]. The current development of such techniques is opening up a wealth of possibilities to explore new physics, e.g., in non-linear atom optics [2], and to study various aspects of superfluid behavior in the precisely controllable context of atomic physics [3].Atoms confined in a periodic potential share some properties with systems of electrons in crystals. Effects known from solid state physics, like Bloch oscillations and Wannier-Stark ladders, have been observed by exposing cold atoms to the dipole potential of far detuned optical lattices [4]. Macroscopic quantum interference has been observed in an experiment on a BEC confined to the antinodes of a far detuned optical lattice [5]. Bragg diffraction from a condensate has been induced in moving optical lattices [6]. This has been used, e.g., as an atom-laser outcoupler [7] and as a tool for spectroscopy of the momentum in BEC's [8]. Applications of BEC's in periodic potentials range from matter-wave transport [9] to interferometry [5] and quantum computing [10]. The question of the stability of the BEC during the evolution in optical potentials is crucial for these applications and has been addressed in theoretical works [11].In this Letter we report on some novel aspects of superfluidity in BEC's by studying their center-of-mass oscillations inside the harmonic potential of a magnetic trap in presence of a one-dimensional (1D) optical lattice. We identify different dynamical regimes by varying the initial displacement of the BEC from the bottom of the trap. For small displacements the BEC performs undamped oscillations in the harmonic potential and feels the periodic potential only through a shift in the oscillation frequency. At larger displacements we observe the onset of dissipative processes appearing through a damping in the oscillations. We can describe the experimental results in terms of an inhomogeneous superfluid having a density-dependent critical velocity. In parallel we report numerical studies of the Gross-Pitaevskii equation (GPE), which capture the main features of the observed dynamics.In our experimental setup [12] we now produce BEC's of 87 Rb atoms in the (F=1,m F = −1) state. The fundamental frequencies of our Ioffe-type magne...

We derive a theory of superfluidity for a dilute Fermi gas that is valid when scattering resonances are present. The treatment of a resonance in many-body atomic physics requires a novel mean-field approach starting from an unconventional microscopic Hamiltonian. The mean-field equations incorporate the microscopic scattering physics, and the solutions to these equations reproduce the energy-dependent scattering properties. This theory describes the high-T c behavior of the system, and predicts a value of T c that is a significant fraction of the Fermi temperature. It is shown that this mean-field approach does not break down for typical experimental circumstances, even at detunings close to resonance. As an example of the application of our theory, we investigate the feasibility for achieving superfluidity in an ultracold gas of fermionic 6 Li.

We study the superfluid state of atomic Fermi gases using a BCS-Bose-Einstein-condensation crossover theory. Our approach emphasizes noncondensed fermion pairs which strongly hybridize with their (Feshbach-induced) molecular boson counterparts. These pairs lead to pseudogap effects above T-c and non-BCS characteristics below. We discuss how these effects influence the experimental signatures of superfluidity

We present the application of a fast, explicit time-marching scheme for the solution of the Gross-Pitaevskii equation in cylindrical geometry. The scheme is validated on simple analytical tests and demonstrated for two situations of physical interest in experiments on the Bose-Einstein condensation ͑BEC͒ of trapped alkali-metal vapors. It is tested by reproducing known results on the free expansion of a BEC after removing a cylindrical trap, and it is then used to address the formation of matter-wave pulses that result from gravity-induced transport of a condensate in an optical potential.