Role of the Majorana fermion and the edge mode in chiral superfluidity near a p-wave Feshbach resonance

The visualization of chiral p-wave superfluidity in Fermi gases near p-wave Feshbach resonances is theoretically examined. It is proposed that the superfluidity becomes detectable in the entire BCS-BEC regimes through (i) vortex visualization by the density depletion inside the vortex core and (ii) intrinsic angular momentum in vortex-free states. It is revealed that both (i) and (ii) are closely connected with the Majorana zero energy mode of the vortex core and the edge mode, which survive until the strong coupling BCS regime is approached from the weak coupling limit and vanish in the Bose-Einstein condensation regime.     

Three-boson problem near a narrow Feshbach resonance

We consider a three-boson system with resonant binary interactions and show that for sufficiently narrow resonances three-body observables depend only on the resonance width and the scattering length. The effect of narrow resonances is qualitatively different from that of wide resonances revealing novel physics of three-body collisions. We calculate the rate of three-body recombination to a weakly bound level and the atom-dimer scattering length and discuss implications for experiments on Bose-Einstein condensates and atom-molecule mixtures near Feshbach resonances.     

Quantum phase transitions across a p-wave Feshbach resonance

We study a single-species polarized Fermi gas tuned across a narrow p-wave Feshbach resonance. We show that in the course of a Bose-Einstein condensation (BEC)-BCS crossover, the system can undergo a magnetic-field-tuned quantum phase transition from a px-wave to a px+ipy-wave superfluid. The latter state, that spontaneously breaks time-reversal symmetry, furthermore undergoes a topological px+ipy to px+ipy transition at zero chemical potential mu. In two dimensions, for mu > 0 it is characterized by a Pfaffian ground state exhibiting topological order and non-Abelian excitations familiar from fractional quantum Hall systems.     

Photoassociation of a Bose-Einstein condensate near a Feshbach resonance

We measure the effect of a magnetic Feshbach resonance (FR) on the rate and light-induced frequency shift of a photoassociation resonance in ultracold 7Li. The photoassociation-induced loss-rate coefficient K_{p} depends strongly on magnetic field, varying by more than a factor of 10;{4} for fields near the FR. At sufficiently high laser intensities, K_{p} for a thermal gas decreases with increasing intensity, while saturation is observed for the first time in a Bose-Einstein condensate. The frequency shift is also strongly field dependent and exhibits an anomalous blueshift for fields just below the FR.     

Efimov states in a Bose-Einstein condensate near a Feshbach resonance

Recent experiments with Bose-Einstein condensates of 85Rb atoms near a Feshbach resonance have produced evidence for a condensate of diatomic molecules coexisting with the atom condensate. It should also be possible to create condensates of the triatomic molecules predicted by Efimov coexisting with the atom and dimer condensates. The smoking gun for the trimer condensate would be oscillatory dependence of observables on the binding energy of the trimer. It may also be possible to deduce the existence of the trimer condensate from the spectra of the bursts of atoms and dimers created in the disappearance of the trimers.     

Superfluid transitions in bosonic atom-molecule mixtures near a Feshbach resonance

We study bosonic atoms near a Feshbach resonance and predict that, in addition to standard normal and atomic superfluid phases, this system generically exhibits a distinct phase of matter: a molecular superfluid, where molecules are superfluid while atoms are not. We explore zero- and finite-temperature properties of the molecular superfluid (a bosonic, strong-coupling analog of a BCS superconductor), and study quantum and classical phase transitions between the normal, molecular superfluid, and atomic superfluid states.     

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.     

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.     

Pauli blocking effect on Efimov states near a Feshbach resonance

In this Letter we study the effect of Pauli blocking on Efimov states in a quantum Fermi gas and illustrate that the universal Efimov potential is altered at large distances. We obtain the universal spectrum flow of Efimov trimers when the Fermi density is varied and further consider the effect of scattering of trimers by the Fermi sea. We argue that the universal flow is robust against fluctuating particle-hole pairs that result in an infrared catastrophe in impurity problems.     

Atom-dimer and dimer-dimer scattering in fermionic mixtures near a narrow Feshbach resonance

We develop a diagrammatic approach for solving few-body problems in heteronuclear fermionic mixtures near a narrow interspecies Feshbach resonance. We calculate s-, p-, and d-wave phaseshifts for the scattering of an atom by a weakly-bound dimer. The fermionic statistics of atoms and the composite nature of the dimer lead to a strong angular momentum dependence of the atom-dimer interaction, which manifests itself in a peculiar interference of the scattered s- and p-waves. This effect strengthens with the mass ratio and is remarkably pronounced in ⁴⁰K-(⁴⁰K-⁶Li) atom-dimer collisions. We calculate the scattering length for two dimers formed near a narrow interspecies resonance. Finally, we discuss the collisional relaxation of the dimers to deeply bound states and evaluate the corresponding rate constant as a function of the detuning and collision energy.     

Quantum Hall fractions in rotating Bose-Einstein condensates

We study the quantum Hall phases that appear in the dilute limit of rotating Bose-Einstein condensates. By exact diagonalization in a spherical geometry we obtain the ground state and low-lying excited states of a small number of bosons as a function of the filling fraction nu, the ratio of the number of bosons to the number of vortices. We show the occurrence of the Jain principal sequence of incompressible liquids for nu=2/3,3/4,4/3,5/4 in addition to the Laughlin state nu=1/2 as well as the Pfaffian state for nu=1. We give gap estimates by finite-size scaling of both charged and neutral excitations.     

Decay of an ultracold fermionic lithium gas near a Feshbach resonance

We studied the magnetic field dependence of the inelastic decay of an ultracold, optically trapped fermionic 6Li gas of different spin compositions. The spin mixture of the two lowest hyperfine states showed two decay resonances at 550 and 680 G, consistent with the predicted Feshbach resonances for elastic s-wave collisions. The observed lifetimes of several hundred ms are much longer than the expected time for Cooper pair formation and the phase transition to superfluidity in the vicinity of the Feshbach resonance.     

Formation of molecules near a Feshbach resonance in a 1D optical lattice

We study the molecular behavior of two atoms interacting near a Feshbach resonance in the presence of a 1D periodic potential. The critical value of the scattering length needed to produce a molecule and the binding energy at resonance are calculated as a function of the intensity of the periodic potential. Because of the non-separability of the center of mass and relative motion, the binding energy depends on the quasimomentum of the molecule. This has dramatic consequences on the molecular tunneling properties, which become strongly dependent on the scattering length.     

Dynamics of Bose-Einstein condensates near Feshbach resonance in external potential

We review our recent theoretical advances in the dynamics of Bose-Einstein condensates with tunable interactions using Feshbach resonance and external potential. A set of analytic and numerical methods for Gross-Pitaevskii equations are developed to study the nonlinear dynamics of Bose-Einstein condensates. Analytically, we present the integrable conditions for the Gross-Pitaevskii equations with tunable interactions and external potential, and obtain a family of exact analytical solutions for one- and two-component Bose-Einstein condensates in one and two-dimensional cases. Then we apply these models to investigate the dynamics of solitons and collisions between two solitons. Numerically, the stability of the analytic exact solutions are checked and the phenomena, such as the dynamics and modulation of the ring dark soliton and vector-soliton, soliton conversion via Feshbach resonance, quantized soliton and vortex in quasi-two-dimensional are also investigated. Both the exact and numerical solutions show that the dynamics of Bose-Einstein condensates can be effectively controlled by the Feshbach resonance and external potential, which offer a good opportunity for manipulation of atomic matter waves and nonlinear excitations in Bose-Einstein condensates.     

Exact ground states of rotating Bose gases close to a Feshbach resonance

We study the ground states of rotating Bose gases when interactions are affected by a nearby Feshbach resonance. We show that exact ground states at high angular momentum can be found analytically for a general model for the resonant interactions. We identify parameter regimes where the exact ground states are exotic fractional quantum Hall states, the excitations of which obey nonabelian exchange statistics.     

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.     

轨道Feshbach共振附近类碱土金属原子的杂质态问题

近年来,碱土金属原子和类碱土金属原子体系的研究成为冷原子物理的研究热点之一.特别是最近在~(173)Yb原子中发现的轨道Feshbach共振,使得研究有强相互作用的碱土金属和类碱土金属原子系统成为可能,极大扩展了此类原子体系的研究范围.本文介绍了~(173)Yb费米气体在轨道Feshbach共振附近的杂质态问题.在此问题中,位于~3P0态的杂质原子与处于基态的背景费米海相互作用,并在费米海表面产生分子态或极化子态.本文使用试探波函数的研究方法,首先对分子态和吸引极化子态进行介绍,并重点描述了分子态与吸引极化子态间的转变.其次归纳总结了排斥极化子态的相关性质,如有效质量、衰变率等.然后考虑双费米面情况,介绍在闭通道中引入另外一个费米面对系统产生的影响.最后简要介绍二维~(173)Yb费米气体中的杂质态问题.     

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.     

Stability of a fully polarized ultracold Fermi gas near zero-crossing of a p-wave Feshbach resonance

We consider a fully polarized ultracold Fermi gas interacting through a p-wave Feshbach resonance. Using a two-channel model, we find the effective potential at the point where the p-wave scattering length goes to zero. Here the effective interaction provides attraction and one can therefore ask about the stability of the system. We calculate the energy density of the system in the Thomas-Fermi approximation, determine the profile of the gas, and the critical number of particle in the system as function of the relevant interaction parameters. The instability can be inferred from a simple breathing mode argument which explains the scaling found numerically. The critical particle number turns out to be extremely large unless the external confinement is very tight. We therefore conclude that the effect is insignificant for standard trapping potentials and that the magnetic dipole interaction is the important term at zero scattering length. However, for tight confinement as in an optical lattice higher-order corrections can become important.