We report Bose-Einstein condensation of weakly bound 6 Li2 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.PACS numbers: 03.75. Ss, 05.30.Fk, 32.80.Pj, By applying a magnetic field to a gas of ultra-cold atoms, it is possible to tune the strength and the sign of the effective interaction between particles. This phenomenon, known as Feshbach resonance, offers in the case of fermions the unique possibility to study the crossover between situations governed by Bose-Einstein and FermiDirac statistics. Indeed, when the scattering length a characterizing the 2-body interaction at low temperature is positive, the atoms are known to pair in a bound molecular state. When the temperature is low enough, these bosonic dimers can form a Bose-Einstein condensate (BEC) as observed very recently in 40 K [1] and 6 Li [2,3]. On the side of the resonance where a is negative, one expects the well known Bardeen-Cooper-Schrieffer (BCS) model for superconductivity to be valid. However, this simple picture of a BEC phase on one side of the resonance and a BCS phase on the other is valid only for small atom density n. When n|a| 3 > ∼ 1 the system enters a strongly interacting regime that represents a challenge for many-body theories [4,5,6] and that now begins to be accessible to experiments [7,8,9].In this letter, we report on Bose-Einstein condensation of 6 Li dimers in a crossed optical dipole trap and a study of the BEC-BCS crossover region. Unlike all previous observations of molecular BEC made in single beam dipole traps with very elongated geometries, our condensates are formed in nearly isotropic traps. Analyzing free expansions of pure condensates with up to 4×10 4 molecules, we measure the molecule-molecule scattering length a m = 170 +100 −60 nm at a magnetic field of 770 gauss. This measurement is in good agreement with the value deduced from the resonance position [9] and the relation a m = 0.6 a of ref. [10]. Combined with tight confinement, these large scattering lengths lead to a regime of strong interactions where the chemical potential µ is on the order of k B T C where T C ≃ 1.5 µK is the condensation temperature. As a consequence, we find an important modification of the thermal cloud time of flight expansion induced by the large condensate mean field. Moreover, the gas parameter n m a 3 m is no longer small but on the order of 0.3. In this regime, the validity of mean field theory becomes questionable [11,12,13]. We show, in particular, that the anisotropy and gas energy released during expansion varies monotonically across the Feshbach resonance.Our experimental setup has been described previously [14,15]. A gas of 6 Li atoms is prepared in the absolute ground state |1/2, 1/2 in a Nd-YAG crossed beam optical dipole trap. The horizontal beam (resp. vertical) propagates along x (y)...

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 0.5 TF . 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.The achievement of Bose-Einstein condensation in atomic vapors [1] has given great impetus to efforts to realize superfluidity in dilute fermionic alkali gases. While conditions of quantum degeneracy have been obtained in potassium (, the lowest achievable temperatures to date have been limited to around 0.2T F [3]. Although this limit is essentially technical in nature, it appears likely that it will be necessary to utilize a strong pairing mechanism yielding superfluid transition temperatures close to this value.Even in high-T c superconductors, the typical critical temperatures are of the order of 10 −2 T F . In the context of strong-coupling superconductivity there has been much work on constructing minimal models to study the crossover from the seminal BCS theory [4] for conventional superconductivity to the Bose-Einstein condensation of tightly bound pairs, passing through nonperturbative regimes in T c /T F [5,6]. In this letter, we treat explicitly a short range quasibound resonant state by extending the theory given in Refs. [7] to predict the existence of a Feshbach resonance superfluidity in a gas of fermionic potassium atoms. This system has an ultrahigh critical phase transition temperature in close proximity to the Fermi temperature. This is a novel regime for quantum fluids, as illustrated in Fig. 1 where our system and others which exhibit superfluidity or BEC are compared.The seminal Bardeen-Cooper-Schrieffer (BCS) theory [4] of superconductivity applied to a dilute gas considers binary interactions between particles in two distinguishable quantum states, say | ↑ and | ↓ . For a uniform system, the fermionic field operators may be Fourierexpanded in a box with periodic boundary conditions giving wavevector-k dependent creation and annihilation operators a † kσ and a kσ for states |σ . At low energy, the binary scattering processes are assumed to be completely characterized by the s-wave scattering length a in terms of a contact quasipotential U = 4πh 2 an/m, where n is the number density. The Hamiltonian describing such a system is given bywhere ǫ k =h 2 k 2 /2m is the kinetic energy, m is the mass, and the constraint k 4 = k 1 + k 2 − k 3 gives momentum conservation.

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Combining the measured binding energies of four of the most weakly bound rovibrational levels of the 87 Rb2 molecule with the results of two other recent high-precision rubidium experiments, we obtain exceptionally strong constraints on the atomic interaction parameters in a highly model independent analysis. The comparison of 85 Rb and 87 Rb data, where the two isotopes are related by a mass scaling procedure, plays a crucial role. Using the consistent picture of the interactions that thus arises we are led to predictions for scattering lengths, clock shifts, Feshbach resonance fields and widths with an unprecedented level of accuracy. To demonstrate this, we predict two Feshbach resonances in mixed-spin scattering channels at easily accessible magnetic field strengths, which we expect to play a role in the damping of coherent spin oscillations. Suggested PACS Numbers: 03.75.Fi, 34.20.Cf, 32.80.Pj After the first realization of Bose-Einstein condensation (BEC) in a dilute ultracold gas of rubidium atoms [1], experiments with the two isotopes 87 Rb and 85 Rb further lead to an amazingly rich variety of BEC phenomena, ranging from the controlled collapse of a condensate with tunable attractive interactions [2] to the realization of an atomic matter wave on a microchip [3]. Because of the large number of groups that have started doing experiments with these atomic species and the growing complexity and subtlety of the planned experiments, there is a clear need for a more precise knowledge of the interactions between ultracold rubidium atoms in the electronic ground state, since these determine most of the properties of the condensate. For instance, despite a widespread interest, until now to our knowledge no experimental group has been able to locate the predicted [4] magnetic-field induced Feshbach resonances that can be used to tune the interactions between ultracold 87 Rb atoms. Being able to switch on or off these interactions at will by a mere change of magnetic field may well be one of the main assets of matter waves compared to light waves in the new matter wave devices. In an atomic interferometry device, in particular, a nonlinear interaction between interfering waves may be introduced or eliminated by changing a field applied at the intersection point.In this Letter, combining the results of three very recent high-precision observations, we come close to a complete and model-independent specification of the interaction properties of ultracold rubidium atoms. The fact that two isotopes 85 Rb and 87 Rb are involved in the measurements makes the constraints exceptionally strong and also increases the predictive power: the interaction properties of any other fermionic or bosonic isotope with mass number 82, 83, 84, or 86 are now known with about the same precision. Using mass scaling to relate the different isotopes we are able for the first time to deduce for each of the isotopes the exact numbers of bound Rb 2 states with total spin S = 0 (singlet) and 1 (triplet). As an illustration of the predictive ...

We report on the observation of Feshbach resonances in an ultracold mixture of two fermionic species, 6 Li and 40 K. The experimental data are interpreted using a simple asymptotic bound state model and full coupled channels calculations. This unambiguously assigns the observed resonances in terms of various s-and p-wave molecular states and fully characterizes the ground-state scattering properties in any combination of spin states.PACS numbers: 34.50. 05.30.Fk Fermion pairing and Fermi superfluidity are key phenomena in superconductors, liquid 3 He, and other fermionic many-body systems. Our understanding of the underlying mechanisms is far from being complete, in particular for technologically relevant high-T c superconductors. The emerging field of ultracold atomic Fermi gases has opened up unprecedented possibilities to realize versatile and well-defined model systems. The control of interactions, offered in a unique way by Feshbach resonances in ultracold gases, is a particularly important feature. Such resonances have been used to achieve the formation of bosonic molecules in Fermi gases and to control pairing in many-body regimes [1,2,3,4,5].So far all experiments on strongly interacting Fermi systems have been based on two-component spin mixtures of the same fermionic species, either 6 Li or 40 K [1, 2]. Control of pairing is achieved via a magnetically tunable s-wave interaction between the two states. After a series of experiments on balanced spin mixtures with equal populations of the two states, recent experiments on 6 Li have introduced spin imbalance as a new degree of freedom and begun to explore novel superfluid phases [6,7]. Mixing two different fermionic species leads to unprecedented versatility and control. Unequal masses and the different responses to external fields lead to a large parameter space for experiments and promise a great variety of new phenomena [8,9,10,11,12]. The combination of the two fermionic alkali species, 6 Li and 40 K, is a prime candidate to realize strongly interacting FermiFermi systems.In this Letter, we realize a mixture of 6 Li and 40 K and identify heteronuclear Feshbach resonances [14,15,16]. This allows us to characterize the basic interaction properties. Figure 1 shows the atomic ground-state energy structure. We label the energy levels Li|i and K|j , counting the states with rising energy. The hyperfine splitting of 6 Li is (3/2)a Li hf /h = 228.2 MHz. For 40 K, the hyperfine structure is inverted and the splitting amounts to (9/2)a K hf /h = −1285.8 MHz [17]. For the low-lying states with i ≤ 3 and j ≤ 10, the projection quantum numbers are given by m Li = −i + 3/2 and m K = j − 11/2. A Li|i K|j mixture can undergo rapid decay via spin relaxation if exoergic two-body processes exist that preserve the total projection quantum number M F = m Li + m K = −i + j − 4. Whenever one of the species is in the absolute ground state and the other one is in a low-lying state (i = 1 and j ≤ 10 or j = 1 and i ≤ 3), spin relaxation is strongly suppressed [18].

We investigate the strongly interacting regime in an optically trapped 6 Li 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.

We create weakly bound Li2 molecules from a degenerate two component Fermi gas by sweeping a magnetic field across a Feshbach resonance. The atom-molecule transfer efficiency can reach 85% and is studied as a function of magnetic field and initial temperature. The bosonic molecules remain trapped for 0.5 s and their temperature is within a factor of 2 from the Bose-Einstein condensation temperature. A thermodynamical model reproduces qualitatively the experimental findings.

We derive a theory of superfluidity for a dilute Fermi gas that is valid when scattering resonances are present. The treatment of a resonance in many-body atomic physics requires a novel mean-field approach starting from an unconventional microscopic Hamiltonian. The mean-field equations incorporate the microscopic scattering physics, and the solutions to these equations reproduce the energy-dependent scattering properties. This theory describes the high-T c behavior of the system, and predicts a value of T c that is a significant fraction of the Fermi temperature. It is shown that this mean-field approach does not break down for typical experimental circumstances, even at detunings close to resonance. As an example of the application of our theory, we investigate the feasibility for achieving superfluidity in an ultracold gas of fermionic 6 Li.