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.     

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.     

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.     

Radio-frequency association of molecules: an assisted Feshbach resonance

We develop a theoretical model to describe the radio-frequency (rf) induced coupling of a pair of colliding atoms to a Feshbach molecule when a magnetic field arbitrarily far from the Feshbach resonance is modulated in time. We use the dressed atom picture, and show that the coupling strength in presence of rf is equal to the Feshbach coupling strength multiplied by the square of a Bessel function. The argument of this function is equal to the ratio of the atomic rf Rabi frequency to the rf frequency. We experimentally demonstrate this law by measuring the rate of rf-association of molecules using a Feshbach resonance in d wave collisions between ultra-cold chromium atoms.     

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.     

Radio-frequency spectroscopy of weakly bound molecules in ultracold Fermi gas

We create weakly bound Feshbach molecules in ultracold Fermi gas40K by sweeping a magnetic field across a broad Feshbach resonance point 202.2 G with a rate of 20 ms/G and perform the dissociation process using radio-frequency(RF) technology. From RF spectroscopy, we obtain the binding energy of the weakly bound molecules in the vicinity of Feshbach resonance. Our measurement also shows that the number of atoms generated from the dissociation process is different at various magnetic fields with the same RF amplitude, which gives us a deeper understanding of weakly bound Feshbach molecules.     

Cross-molecular coupling in combined photoassociation and Feshbach resonances

We model combined photoassociation and Feshbach resonances in a Bose-Einstein condensate. When the magnetic field is far-off resonance, cross coupling between the two target molecules--enabled by the shared dissociation continuum--leads to an anomalous dispersive shift in the position of laser resonance, as well as unprecedented elimination and enhancement of resonant photoassociation via quantum interference. For off-resonant lasers, a dispersive shift and quantum interference appear similarly in resonant three-body Feshbach losses, except that the Feshbach node is tunable with intensity.     

Radio-frequency spectroscopy of a strongly interacting two-dimensional Fermi gas

We realize and study a strongly interacting two-component atomic Fermi gas confined to two dimensions in an optical lattice. Using radio-frequency spectroscopy we measure the interaction energy of the strongly interacting gas. We observe the confinement-induced Feshbach resonance on the attractive side of the 3D Feshbach resonance and find the existence of confinement-induced molecules in very good agreement with theoretical predictions.     

BCS-BEC crossover in a gas of Fermi atoms with a p-wave feshbach resonance

We investigate unconventional superfluidity in a gas of Fermi atoms with an anisotropic p-wave Feshbach resonance. Including the p-wave Feshbach resonance as well as the associated three kinds of quasimolecules with finite orbital angular momenta Lz=+/-1,0, we calculate the transition temperature of the superfluid phase. As one passes through the p-wave Feshbach resonance, we find the usual BCS-BEC crossover phenomenon. The p-wave BCS state continuously changes into the BEC of bound molecules with L=1. Our calculation includes the effect of fluctuations associated with Cooper pairs and molecules which are not Bose condensed.     

High temperature expansion applied to fermions near Feshbach resonance

We show that, apart from a difference in scale, all of the surprising recently observed properties of a degenerate Fermi gas near a Feshbach resonance persist in the high temperature Boltzmann regime. In this regime, the Feshbach resonance is unshifted. By sweeping across the resonance, a thermal distribution of bound states (molecules) can be reversibly generated. Throughout this process, the interaction energy is negative and continuous. We also show that this behavior must persist at lower temperatures unless there is a phase transition as the temperature is lowered. We rigorously demonstrate universal behavior near the resonance.     

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.     

Nonequilibrium dynamics and thermodynamics of a degenerate fermi gas across a feshbach resonance

We consider a two-species degenerate Fermi gas coupled by a diatomic Feshbach resonance. We show that the resulting superfluid can exhibit a form of coherent BEC-to-BCS oscillations in response to a nonadiabatic change in the system's parameters, such as, for example, a sudden shift in the position of the Feshbach resonance. In the narrow resonance limit, the resulting solitonlike collisionless dynamics can be calculated analytically. In equilibrium, the thermodynamics can be accurately computed across the full range of BCS-BEC crossover, with corrections controlled by the ratio of the resonance width to the Fermi energy.     

Observation of the BEC-BCS crossover in a degenerate Fermi gas of lithium atoms

We observe characteristic atomic behaviors in the Bose-Einstein-condensation-Bardeen-Cooper-Schrieffer(BEC-BCS)crossover,by accurately tuning the magnetic field across the Feshbach resonance of lithium atoms.The magnetic field is calibrated by measuring the Zeeman shift of the optical transition.A non-monotonic anisotropic expansion is observed across the Feshbach resonance.The density distribution is explored in different interacting regimes,where a condensate of diatomic molecules forms in the BEC limit with the indication of a bimodal distribution.We also measure the three-body recombination atom loss in the BEC-BCS crossover,and find that the magnetic field of the maximum atom loss is in the BEC limit and gets closer to the Feshbach resonance when decreasing the atom temperature,which agrees with previous experiments and theoretical prediction.This work builds up a controllable platform for the study on the strongly interacting Fermi gas.     

Ultracold heteronuclear molecules in a 3D optical lattice

We report on the creation of ultracold heteronuclear molecules assembled from fermionic 40K and bosonic 87Rb atoms in a 3D optical lattice. Molecules are produced at a heteronuclear Feshbach resonance on both the attractive and the repulsive sides of the resonance. We precisely determine the binding energy of the heteronuclear molecules from rf spectroscopy across the Feshbach resonance. We characterize the lifetime of the molecular sample as a function of magnetic field and measure lifetimes between 20 and 120 ms. The efficiency of molecule creation via rf association is measured and is found to decrease as expected for more deeply bound molecules.     

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.     

Molecule production via Feshbach resonance in bosonic systems

In this article, we review our recent theoretical works on producing ultracold molecules from ultracold bosonic atoms via magnetically tunable Feshbach resonances. Our analysis relies on a two-channel quantum microscopic model that accounts for many-body effects in the association process. We show that the picture of two-body molecular production depicted by the Landau-Zener model is significantly altered due to many-body effects. We derive an analytic expression for molecular conversion efficiency for the nonadiabatic linearly swept Feshbach resonance, that explains the discrepancy between the prediction of the Landau-Zener formula and the experimental data. With including the thermal dephasing effects in the oscillating magnetic field modulation Feshbach resoance, we reproduce the Lorentzian resonance lineshape and explain the maximum conversion efficiency observed in experiment.     

p-Wave interactions in low-dimensional fermionic gases

We study a spin-polarized degenerate Fermi gas interacting via a p-wave Feshbach resonance in an optical lattice. The strong confinement available in this system allows us to realize one- and two-dimensional gases and, therefore, to restrict the asymptotic scattering states of atomic collisions. When aligning the atomic spins along (or perpendicular to) the axis of motion in a one-dimensional gas, scattering into channels with the projection of the angular momentum of /m/ = 1 (or m = 0) can be inhibited. In two and three dimensions, we observe the doublet structure of the p-wave Feshbach resonance. For both the one-dimensional and the two-dimensional gases, we find a shift of the position of the resonance with increasing confinement due to the change in collisional energy. In a three-dimensional optical lattice, the losses on the Feshbach resonance are completely suppressed.     

Simple mean-field theory for a zero-temperature fermionic gas at a Feshbach resonance

We present a simple two-channel mean-field theory for a zero-temperature two-component Fermi gas in the neighborhood of a Feshbach resonance. Our results agree with recent experiments on the bare-molecule fraction as a function of magnetic field [Partridge, Phys. Rev. Lett. 95, 020404 (2005)]. Even in this strongly coupled gas of 6Li, the experimental results depend on the structure of the molecules formed in the Feshbach resonance and, therefore, are not universal.     

Condensation of pairs of fermionic atoms near a Feshbach resonance

We have observed Bose-Einstein condensation of pairs of fermionic atoms in an ultracold 6Li gas at magnetic fields above a Feshbach resonance, where no stable 6Li2 molecules would exist in vacuum. We accurately determined the position of the resonance to be 822+/-3 G. Molecular Bose-Einstein condensates were detected after a fast magnetic field ramp, which transferred pairs of atoms at close distances into bound molecules. Condensate fractions as high as 80% were obtained. The large condensate fractions are interpreted in terms of preexisting molecules which are quasistable even above the two-body Feshbach resonance due to the presence of the degenerate Fermi gas.     

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.