Formation dynamics of a fermion pair condensate

The dynamics of pair condensate formation in a strongly interacting Fermi gas close to a Feshbach resonance was studied. We employed a phase-shift method in which the delayed response of the many-body system to a modulation of the interaction strength was recorded. The observable was the fraction of condensed molecules in the cloud after a rapid magnetic field ramp across the Feshbach resonance. The measured response time was slow compared to the rapid ramp, which provides final proof that the molecular condensates reflect the presence of fermion pair condensates before the ramp.     

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.     

Dynamics of the BCS-BEC crossover in a degenerate Fermi gas

We study the short-time dynamics of a degenerate Fermi gas positioned near a Feshbach resonance following an abrupt jump in the atomic interaction resulting from a change of magnetic field. We investigate the dynamics of the condensate order parameter and pair wave function for a range of field strengths. When the jump is sufficient to span the BCS to Bose-Einstein condensation crossover, we show that the rigidity of the momentum distribution precludes any atom-molecule oscillations in the entrance channel dominated resonances observed in 40K and 6Li. Focusing on material parameters tailored to the 40K Feshbach resonance at 202.1 G, we comment on the integrity of the fast sweep projection technique as a vehicle to explore the condensed phase in the crossover region.     

Dressed Feshbach molecules in the BEC-BCS crossover

We present the random phase approximation (RPA) theory of the Bose-Einstein-condensation-Bardeen-Cooper-Schrieffer crossover in an atomic Fermi gas near a Feshbach resonance that includes the relevant two-body atomic physics exactly. This allows us to determine the probability for the dressed molecules in the Bose-Einstein condensate to be in the closed channel of the Feshbach resonance and to compare with the recent experiments of Partridge et al. [95, 020404 (2005)10.1103/PhysRevLett.95.020404] with , who have measured the same quantity.     

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.     

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.     

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.     

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.     

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.     

BEC-BCS crossover in "magnetized" Feshbach-resonantly paired superfluids

We map out the detuning-magnetization phase diagram for a magnetized (unequal number of atoms in two pairing hyperfine states) gas of fermionic atoms interacting via an s-wave Feshbach resonance (FR). The phase diagram is dominated by the coexistence of a magnetized normal gas and a singlet-paired superfluid with the latter exhibiting a BCS-Bose Einstein condensate crossover with reduced FR detuning. On the BCS side of strongly overlapping Cooper pairs, a sliver of finite-momentum paired Fulde-Ferrell-Larkin-Ovchinnikov magnetized phase intervenes between the phase-separated and normal states. In contrast, for large negative detuning a uniform, polarized superfluid, that is, a coherent mixture of singlet Bose-Einstein-condensed molecules and fully magnetized single-species Fermi sea, is a stable ground state.     

超流费米气体相滑移时的密度分布

当前在冷原子和玻色爱因斯坦凝聚(BEC)领域的一个重要问题是在Feshbach共振附近的冷费米气体如何从BEC态演变到BCS(Bardeen Schrieffer Cooper)态.本文进一步研究在Feshbach共振附近超流态的相滑移现象.通过具体的数值计算，给出了费米气体在相滑移时的粒子数密度的分布，并对不同温度下的相滑移的大小进行了分析.结果表明，相滑移现象可以作为实验上判断系统是否处于超流态的一个可行的判据. 关键词： 超流费米气体 相滑移 Feshbach共振     

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.     

Observation of Bose-Einstein condensation of molecules

We have observed Bose-Einstein condensation of molecules. When a spin mixture of fermionic 6Li atoms was evaporatively cooled in an optical dipole trap near a Feshbach resonance, the atomic gas was converted into 6Li2 molecules. Below 600 nK, a Bose-Einstein condensate of up to 900 000 molecules was identified by the sudden onset of a bimodal density distribution. This condensate realizes the limit of tightly bound fermion pairs in the crossover between BCS superfluidity and Bose-Einstein condensation.     

New directions in degenerate dipolar molecules via collective association

We survey results on the creation of heteronuclear Fermi molecules by tuning a degenerate Bose-Fermi mixture into the neighborhood of an association resonance, either photoassociation or Feshbach, as well as the subsequent prospects for Cooper-like pairing between atoms and molecules. In the simplest case of only one molecular state, corresponding to either a Feshbach resonance or one-color photoassociation, the system displays Rabi oscillations and rapid adiabatic passage between a Bose-Fermi mixture of atoms and fermionic molecules. For two-color photoassociation, the system admits stimulated Raman adiabatic passage (STIRAP) from a Bose-Fermi mixture of atoms to stable Fermi molecules, even in the presence of particle-particle interactions. By tailoring the STIRAP sequence it is possible to deliberately convert only a fraction of the initial atoms, leaving a finite fraction of bosons behind to induce atom-molecule Cooper pairing via density fluctuations; unfortunately, this enhancement is insufficient to achieve a superfluid transition with present ultracold technology. We therefore propose the use of an association resonance that converts atoms and diatomic molecules (dimers) into triatomic molecules (trimers), which leads to a crossover from a Bose-Einstein condensate of trimers to atom-dimer Cooper pairs. Because heteronuclear dimers may possess a permanent electric dipole moment, this overall system presents an opportunity to investigate novel microscopic physics.Received: 16 June 2004, Published online: 21 September 2004PACS: 03.75.Ss Degenerate Fermi gases - 05.30.Fk Fermion systems and electron gas - 34.10. + x General theories and models of atomic and molecular collisions and interactions (including statistical theories, transition state, stochastic and trajectory models, etc.) - 74.20.Mn Nonconventional mechanisms (spin fluctuations, polarons and bipolarons, resonating valence bond model, anyon mechanism, marginal Fermi liquid, Luttinger liquid, etc.) - 21.10.-k Properties of nuclei; nuclear energy levels     

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.     

Collective excitations of a degenerate gas at the BEC-BCS crossover

We study collective excitation modes of a fermionic gas of (6)Li atoms in the BEC-BCS crossover regime. While measurements of the axial compression mode in the cigar-shaped trap close to a Feshbach resonance confirm theoretical expectations, the radial compression mode shows surprising features. In the strongly interacting molecular BEC regime, we observe a negative frequency shift with increasing coupling strength. In the regime of a strongly interacting Fermi gas, an abrupt change in the collective excitation frequency occurs, which may be a signature for a transition from a superfluid to a collisionless phase.     

Number statistics of molecules formed from ultracold atoms

We calculate the number statistics of a single-mode molecular field excited by photo-association or via a Feshbach resonance from an atomic Bose-Einstein condensate (BEC), a normal atomic Fermi gas, and a Fermi system with pair correlations (BCS state). We find that the molecule formation from a BEC leads for short times to a coherent molecular state in the quantum optical sense. Atoms in a normal Fermi gas, on the other hand, result for short times in a molecular field analog of a classical chaotic light source. The BCS situation is intermediate between the two and goes from producing an incoherent to a coherent molecular field with an increasing gap parameter. This distinct signature of the initial atomic state in the resulting molecular field makes single molecule counting into a powerful diagnostic tool.     

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.     

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.