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.     

Probing pair-correlated fermionic atoms through correlations in atom shot noise

Pair-correlated fermionic atoms are created through dissociation of weakly bound molecules near a magnetic-field Feshbach resonance. We show that correlations between atoms in different spin states can be detected using the atom shot noise in absorption images. Furthermore, using time-of-flight imaging we have observed atom pair correlations in momentum space.     

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.     

费米原子对的玻色-爱因斯坦凝聚

通过磁场可以用原子散射的Feshbach共振来调节原子间的相互作用，使之成为排斥或吸引，以及改变作用的强度，运用这个方法可以使费米原子形成分子，也可以在多体作用下形成费米原子配对，在温度够低的条件下可以得到分子的BEC以及原子配对的凝聚体，这些现象在实验室中的实现是2004年物理学的重要成就之一，本文对此给予简短的评述。     

Effective Hamiltonian for fermions in an optical lattice across a Feshbach resonance

We derive the Hamiltonian for cold fermionic atoms in an optical lattice across a broad Feshbach resonance, taking into account both multiband occupations and neighboring-site collisions. Under typical configurations, the resulting Hamiltonian can be dramatically simplified to an effective single-band model, which describes a new type of resonance between the local dressed molecules and the valence bond states of fermionic atoms at neighboring sites. On different sides of such a resonance, the effective Hamiltonian is reduced to either a t-J model for the fermionic atoms or an XXZ model for the dressed molecules. The parameters in these models are experimentally tunable in the full range, which allows for observation of various phase transitions.     

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.     

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.     

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.     

Feshbach-resonant interactions in 40K and 6Li degenerate Fermi gases

We theoretically examine a system of Fermi degenerate atoms coupled to bosonic molecules by a Feshbach resonance, focusing on the superfluid transition to a molecular Bose-Einstein condensate dressed by Cooper pairs of atoms. This problem raises interest because it is unclear at present whether bimodal density distributions observed recently in 40K and 6Li are due to a condensate of bosonic molecules or fermionic atom pairs. As opposed to 40K, we find that any measurable fraction of above-threshold bosonic molecules is necessarily absent for the 6Li system in question, which strongly implicates Cooper pairs as the culprit behind its bimodal distributions.     

Molecules of fermionic atoms in an optical lattice

We create molecules from fermionic atoms in a three-dimensional optical lattice using a Feshbach resonance. In the limit of low tunneling, the individual wells can be regarded as independent three-dimensional harmonic oscillators. The measured binding energies for varying scattering length agree excellently with the theoretical prediction for two interacting atoms in a harmonic oscillator. We demonstrate that the formation of molecules can be used to measure the occupancy of the lattice and perform thermometry.     

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     

Observation of resonance condensation of fermionic atom pairs

We have observed condensation of fermionic atom pairs in the BCS-BEC crossover regime. A trapped gas of fermionic 40K atoms is evaporatively cooled to quantum degeneracy and then a magnetic-field Feshbach resonance is used to control the atom-atom interactions. The location of this resonance is precisely determined from low-density measurements of molecule dissociation. In order to search for condensation on either side of the resonance, we introduce a technique that pairwise projects fermionic atoms onto molecules; this enables us to measure the momentum distribution of fermionic atom pairs. The transition to condensation of fermionic atom pairs is mapped out as a function of the initial atom gas temperature T compared to the Fermi temperature T(F) for magnetic-field detunings on both the BCS and BEC sides of the resonance.     

Tuning of heteronuclear interactions in a degenerate Fermi-Bose mixture

We demonstrate tuning of interactions between fermionic 40K and bosonic 87Rb atoms by Feshbach resonances and access the complete phase diagram of the harmonically trapped mixture from phase separation to collapse. On the attractive side of the resonance, we observe a strongly enhanced mean-field energy of the condensate due to the mutual mean-field confinement, predicted by a Thomas-Fermi model. As we increase heteronuclear interactions beyond a threshold, we observe an induced collapse of the mixture. On the repulsive side of the resonance, we observe vertical phase separation of the mixture in the presence of the gravitational force, thus entering a completely unexplored part of the phase diagram of the mixture. In addition, we identify the 515 G resonance as p wave by its characteristic doublet structure.     

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.     

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.     

Magnetic field control of elastic scattering in a cold gas of fermionic lithium atoms

We study elastic collisions in an optically trapped spin mixture of fermionic lithium atoms in the presence of magnetic fields up to 1.5 kG by measuring evaporative loss. Our experiments confirm the expected magnetic tunability of the scattering length by showing the main features of elastic scattering according to recent calculations. We measure the zero crossing of the scattering length at 530(3) G which is associated with a predicted Feshbach resonance at approximately 850 G. Beyond the resonance we observe the expected large cross section in the triplet scattering regime.     

Probing fermionic condensates by fast-sweep projection onto Feshbach molecules

Fast-sweep projection onto Feshbach molecules has been widely used as a probe of fermionic condensates. By determining the exact dynamics of a pair of atoms in time-varying magnetic fields, we calculate the number of condensed and noncondensed molecules created after fast magnetic field sweeps from the BCS to the Bose-Einstein condensate side of the resonances in 40K and 6Li, for different sweep rates and a range of initial and final fields. We discuss the relation between the initial fermionic condensate fraction and the molecular condensate fraction measured after the sweep.     

Observation of heteronuclear Feshbach resonances in a mixture of bosons and fermions

Three magnetic-field induced heteronuclear Feshbach resonances were identified in collisions between bosonic 87Rb and fermionic 40K atoms in their absolute ground states. Strong inelastic loss from an optically trapped mixture was observed at the resonance positions of 492, 512, and 543+/-2 G. The magnetic-field locations of these resonances place a tight constraint on the triplet and singlet cross-species scattering lengths, yielding (-281+/-15)a(0) and (-54+/-12)a(0), respectively. The width of the loss feature at 543 G is 3.7+/-1.5 G wide; this broad Feshbach resonance should enable experimental control of the interspecies interactions.     

Linear instability and adiabaticity of a dark state during conversion of two species of fermionic atoms to stable molecules

In the present paper, we investigate the linear instability and adiabaticity of a dark state during conversion of two species of fermionic atoms to stable molecules through the stimulated Raman adiabatic passage aided by Feshbach resonance. We analytically obtain the regions for the appearance of linear instability. Moreover, taking 40 K and 6 Li atom–molecule conversion systems as examples, we give the unstable regions numerically. We also attempt to obtain the adiabatic criterion for this nonlinear system with classical adiabatic dynamics and study the adibaticity of the dark state with the adiabatic condition.     

Atom-molecule coherence in a one-dimensional system

We study a model of one-dimensional fermionic atoms with a narrow Feshbach resonance that allows them to bind in pairs to form bosonic molecules. We show that at low energy, a coherence develops between the molecule and fermion Luttinger liquids. At the same time, a gap opens in the spin excitation spectrum. The coherence implies that the order parameters for the molecular Bose-Einstein condensation and the atomic BCS pairing become identical. Moreover, both bosonic and fermionic charge density wave correlations decay exponentially, in contrast with a usual Luttinger liquid. We exhibit a Luther-Emery point where the systems can be described in terms of noninteracting pseudofermions. At this point we discuss the threshold behavior of density-density response functions.