Three-Body System with Two-Channel Zero-Range Interaction Model of Feshbach Resonance

We perform three-body calculations of trimers and atom-dimer scattering near a Feshbach resonance using two interaction models. The first model is a one-channel zero-range model, where the scattering length follows the phenomenological dependence on the external magnetic field. The second is a two-channel model capable to describe the Feshbach resonance. The scattering length dependence on magnetic detuning is recovered. We compare the predictions of these two models, and show that near a Feshbach resonance important differences are expected.     

Two-Channel Skyrme–Hartree–Fock Model for Bose–Einstein Condensate Near Feshbach Resonance

We apply a two-channel Skyrme–Hartree–Fock model to describe an atomic Bose–Einstein condensate near a Feshbach resonance. In this model the single-atom wave-function has two components corresponding to the two intrinsic states of the atom related to the Feshbach resonance. From the variational principle we derive the corresponding system of two coupled equations for the single-atom wave-function—a generalization of the Gross–Pitaevskii equation. We carry out an exploratory gaussian variational calculation and show that the two-component model can successfully describe the collapse of the condensate near a Feshbach resonance.     

LOFF and breached pairing with cold atoms

We investigate here the Cooper pairing of fermionic atoms with mismatched Fermi surfaces using a variational construct for the ground state. We determine the state for different values of the mismatch of chemical potential for weak as well as strong coupling regimes including the BCS BEC cross over region. We consider Cooper pairing with both zero and finite net momentum. Within the variational approximation for the ground state and comparing the thermodynamic potentials, we show that (i) the LOFF phase is stable in the weak coupling regime; (ii) the LOFF window is maximum on the BEC side near the Feshbach resonance; and (iii) the existence of stable gapless states with a single Fermi surface for negative average chemical potential on the BEC side of the Feshbach resonance.     

Electric-field-modified Feshbach resonances in ultracold atom–molecule collision

We present a detailed analysis of near zero-energy Feshbach resonances in ultracold collisions of atom and molecule,taking the He–PH system as an example, subject to superimposed electric and magnetic static fields. We find that the electric field can induce Feshbach resonance which cannot occur when only a magnetic field is applied, through couplings of the adjacent rotational states of different parities. We show that the electric field can shift the position of the magnetic Feshbach resonance, and change the amplitude of resonance significantly. Finally, we demonstrate that, for narrow magnetic Feshbach resonance as in most cases of ultracold atom–molecule collision, the electric field may be used to modulate the resonance, because the width of resonance in electric field scale is relatively larger than that in magnetic field scale.     

Measurement of the interaction energy near a Feshbach resonance in a 6Li Fermi gas

We investigate the strongly interacting regime in an optically trapped 6Li Fermi mixture near a Feshbach resonance. The resonance is found at 800(40) G in good agreement with theory. Anisotropic expansion of the gas is interpreted by collisional hydrodynamics. We observe an unexpected and large shift (80 G) between the resonance peak and both the maximum of atom loss and the change of sign of the interaction energy.     

Pure gas of optically trapped molecules created from fermionic atoms

We report on the production of a pure sample of up to 3 x 10(5) optically trapped molecules from a Fermi gas of 6Li atoms. The dimers are formed by three-body recombination near a Feshbach resonance. For purification, a Stern-Gerlach selection technique is used that efficiently removes all trapped atoms from the atom-molecule mixture. The behavior of the purified molecular sample shows a striking dependence on the applied magnetic field. For very weakly bound molecules near the Feshbach resonance, the gas exhibits a remarkable stability with respect to collisional decay.     

Quantum phase transition in an atomic bose gas with a feshbach resonance

We show that in an atomic Bose gas near a Feshbach resonance a quantum phase transition occurs between a phase with only a molecular Bose-Einstein condensate and a phase with both an atomic and a molecular Bose-Einstein condensate. We show that the transition is characterized by an Ising order parameter. We also determine the phase diagram of the gas as a function of magnetic field and temperature: the quantum critical point extends into a line of finite temperature Ising transitions.     

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.     

Lifetime of molecule-atom mixtures near a Feshbach resonance in 40K

We report a dramatic magnetic-field dependence in the lifetime of trapped, ultracold diatomic molecules created through an s-wave Feshbach resonance between fermionic atoms. The molecule lifetime increases from less than 1 ms away from the Feshbach resonance to greater than 100 ms near resonance. We also have measured the trapped atom lifetime as a function of magnetic field near the Feshbach resonance; we find that the atom loss is more pronounced on the side of the resonance containing the molecular bound state.     

Critical temperature and condensate fraction of a fermion pair condensate

We report on measurements of the critical temperature and the temperature dependence of the condensate fraction for a fermion pair condensate of 6Li atoms. Bragg spectroscopy is employed to determine the critical temperature and the condensate fraction after a fast magnetic field ramp to the molecular side of the Feshbach resonance. Our measurements reveal evidence of level off of the critical temperature and limiting behavior of condensate fraction near the unitarity limit.     

Temperature dependence of the universal contact parameter in a unitary Fermi gas

The contact I, introduced by Tan, has emerged as a key parameter characterizing universal properties of strongly interacting Fermi gases. For ultracold Fermi gases near a Feshbach resonance, the contact depends upon two quantities: the interaction parameter 1/(k(F)a), where k(F) is the Fermi wave vector and a is the s-wave scattering length, and the temperature T/T(F), where T(F) is the Fermi temperature. We present the first measurements of the temperature dependence of the contact in a unitary Fermi gas using Bragg spectroscopy. The contact is seen to follow the predicted decay with temperature and shows how pair-correlations at high momentum persist well above the superfluid transition temperature.     

Competition between pairing and ferromagnetic instabilities in ultracold Fermi gases near Feshbach resonances

We study the quench dynamics of a two-component ultracold Fermi gas from the weak into the strong interaction regime, where the short time dynamics are governed by the exponential growth rate of unstable collective modes. We obtain an effective interaction that takes into account both Pauli blocking and the energy dependence of the scattering amplitude near a Feshbach resonance. Using this interaction we analyze the competing instabilities towards Stoner ferromagnetism and pairing.     

Experimental study of the BEC-BCS crossover region in lithium 6

We report Bose-Einstein condensation of weakly bound 6Li2 molecules in a crossed optical trap near a Feshbach resonance. We measure a molecule-molecule scattering length of 170(+100)(-60) nm at 770 G, in good agreement with theory. We study the 2D expansion of the cloud and show deviation from hydrodynamic behavior in the BEC-BCS crossover region.     

Molecular Kondo resonance in atomic Fermi gases

The usual Kondo effect is associated with the formation of a many-body ground state that contains a quantum-mechanical entanglement between a (localized) fermion and the free fermions. We show, however, that also a bosonic form of the Kondo effect can occur in degenerate atomic Fermi gases near a Feshbach resonance, if the energy of the diatomic molecular level associated with the Feshbach resonance approaches twice the Fermi energy of the atoms.     

Measurement of positive and negative scattering lengths in a Fermi gas of atoms

We report on progress toward realizing a predicted superfluid phase in a Fermi gas of atoms. We present measurements of both large positive and large negative scattering lengths in a quantum degenerate Fermi gas of atoms near a magnetic-field Feshbach resonance. We employ an rf spectroscopy technique to directly measure the mean-field interaction energy, which is proportional to the s-wave scattering length. Near the peak of the resonance we observe a saturation of the interaction energy; it is in this strongly interacting regime that superfluidity is predicted to occur. We have also observed anisotropic expansion of the gas, which has recently been suggested as a signature of superfluidity. However, we find that this can be attributed to a purely collisional effect.     

Three-Body Recombination Rates Near a Feshbach Resonance within a Two-Channel Contact Interaction Model

We calculate the three-body recombination rate into a shallow dimer in a gas of cold bosonic atoms near a Feshbach resonance using a two-channel contact interaction model. The two-channel model naturally describes the variation of the scattering length through the Feshbach resonance and has a finite effective range. We confront the theory with the available experimental data and show that the two-channel model is able to quantitatively describe the existing data. The finite effective range leads to a reduction of the scaling factor between the recombination minima from the universal value of 22.7. The reduction is larger for larger effective ranges or, correspondingly, for narrower Feshbach resonances.     

Atom-molecule Rabi oscillations in a Mott insulator

We observe large-amplitude Rabi oscillations between an atomic and a molecular state near a Feshbach resonance. The experiment uses 87Rb in an optical lattice and a Feshbach resonance near 414 G. The frequency and amplitude of the oscillations depend on the magnetic field in a way that is well described by a two-level model. The observed density dependence of the oscillation frequency agrees with theoretical expectations. We confirmed that the state produced after a half-cycle contains exactly one molecule at each lattice site. In addition, we show that, for energies in a gap of the lattice band structure, the molecules cannot dissociate.     

Resonance superfluidity in a quantum degenerate Fermi gas

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 0.5T(F). 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.     

Crossover temperature of Bose-Einstein condensation in an atomic Fermi gas

We show that in an atomic Fermi gas near a Feshbach resonance the crossover between a Bose-Einstein condensate of diatomic molecules and a Bose-Einstein condensate of Cooper pairs occurs at positive detuning, i.e., when the molecular energy level lies in the two-atom continuum. We determine the crossover temperature as a function of the applied magnetic field and find excellent agreement with the experiment of C. A. Regal et al. [Phys. Rev. Lett. 92, 040403 (2004)]] who has recently observed this crossover temperature.