Randall G. Hulet

Formation and propagation of matter-wave soliton trains

Attraction between the atoms of a Bose–Einstein condensate renders it unstable to collapse, although a condensate with a limited number of atoms can be stabilized by confinement in an atom trap. However, beyond this number the condensate collapses. Condensates constrained to one-dimensional motion with attractive interactions are predicted to form stable solitons, in which the attractive forces exactly compensate for wave-packet dispersion. Here we report the formation of bright solitons of 7Li atoms in a quasi-one-dimensional optical trap, by magnetically tuning the interactions in a stable Bose–Einstein condensate from repulsive to attractive. The solitons are set in motion by offsetting the optical potential, and are observed to propagate in the potential for many oscillatory cycles without spreading. We observe a soliton train, containing many solitons; repulsive interactions between neighbouring solitons are inferred from their motion.

Pairing and Phase Separation in a Polarized Fermi Gas

We report the observation of pairing in a gas of atomic fermions with unequal numbers of two components. Beyond a critical polarization, the gas separates into a phase that is consistent with a superfluid paired core surrounded by a shell of normal unpaired fermions. The critical polarization diminishes with decreasing attractive interaction. For near-zero polarization, we measured the parameter β = –0.54 ± 0.05, describing the universal energy of a strongly interacting paired Fermi gas, and found good agreement with recent theory. These results are relevant to predictions of exotic new phases of quark matter and of strongly magnetized superconductors.

Conversion of an Atomic Fermi Gas to a Long-Lived Molecular Bose Gas

We have converted an ultracold Fermi gas of 6Li atoms into an ultracold gas of 6Li2 molecules by adiabatic passage through a Feshbach resonance. Approximately 1.5 x 10(5) molecules in the least-bound, v=38, vibrational level of the X1Sigma(+)(g) singlet state are produced with an efficiency of 50%. The molecules remain confined in an optical trap for times of up to 1 s before we dissociate them by a reverse adiabatic sweep.

Spin-imbalance in a one-dimensional Fermi gas

Superconductivity and magnetism generally do not coexist. Changing the relative number of up and down spin electrons disrupts the basic mechanism of superconductivity, where atoms of opposite momentum and spin form Cooper pairs. Nearly forty years ago Fulde and Ferrell and Larkin and Ovchinnikov (FFLO) proposed an exotic pairing mechanism in which magnetism is accommodated by the formation of pairs with finite momentum. Despite intense theoretical and experimental efforts, however, polarized superconductivity remains largely elusive. Unlike the three-dimensional (3D) case, theories predict that in one dimension (1D) a state with FFLO correlations occupies a major part of the phase diagram. Here we report experimental measurements of density profiles of a two-spin mixture of ultracold 6Li atoms trapped in an array of 1D tubes (a system analogous to electrons in 1D wires). At finite spin imbalance, the system phase separates with an inverted phase profile, as compared to the 3D case. In 1D, we find a partially polarized core surrounded by wings which, depending on the degree of polarization, are composed of either a completely paired or a fully polarized Fermi gas. Our work paves the way to direct observation and characterization of FFLO pairing.

Molecular Probe of Pairing in the BEC-BCS Crossover

We have used optical molecular spectroscopy to probe the many-body state of paired 6Li atoms near a broad Feshbach resonance. The optical probe projects pairs of atoms onto a vibrational level of an excited molecule. The rate of excitation enables a precise measurement of the closed-channel contribution to the paired state. This contribution is found to be quite small, supporting the concept of universality for the description of broad Feshbach resonances. The dynamics of the excitation provide clear evidence for pairing across the BEC-BCS crossover and into the weakly interacting BCS regime.

Direct observation of growth and collapse of a Bose–Einstein condensate with attractive interactions

Quantum theory predicts that Bose–Einstein condensation of a spatially homogeneous gas with attractive interactions is precluded by a conventional phase transition into either a liquid or solid. When confined to a trap, however, such a condensate can form, provided that its occupation number does not exceed a limiting value. The stability limit is determined by a balance between the self-attractive forces and a repulsion that arises from position–momentum uncertainty under conditions of spatial confinement. Near the stability limit, self-attraction can overwhelm the repulsion, causing the condensate to collapse. Growth of the condensate is therefore punctuated by intermittent collapses that are triggered by either macroscopic quantum tunnelling or thermal fluctuation. Previous observations of growth and collapse dynamics have been hampered by the stochastic nature of these mechanisms. Here we report direct observations of the growth and subsequent collapse of a 7Li condensate with attractive interactions, using phase-contrast imaging. The success of the measurement lies in our ability to reduce the stochasticity in the dynamics by controlling the initial number of condensate atoms using a two-photon transition to a diatomic molecular state.

Universality in three- and four-body bound states of ultracold atoms.

More Is Different, Few Is Exotic As powerful as theoretical physics can be, when it comes to describing the dynamics of several interacting particles, it stumbles at three. This few-body physics is interesting in many contexts, particularly interactions within the nucleus and between atoms and molecules. Although predicted 40 years ago for the special case of resonant interaction, which occurs at the edge of where two-particle bound states start to form, Efimov trimers were only recently observed in ultracold Bose gases. More work followed, revealing evidence of multiple trimer, and even tetramer, states. Now, Pollack et al. (p. 1683, published online 19 November; see the Perspective by Modugno) observe as many as 11 features near a lithium resonance that can be directly related to different few-body processes. The positions of the features with respect to each other are in excellent agreement with the theoretical prediction, although some deviations, attributed to short-range interactions, present a challenge for a future, more detailed theory. Cold lithium gas reveals a universal lineup of Efimov trimers and associated tetramers. Under certain circumstances, three or more interacting particles may form bound states. Although the general few-body problem is not analytically solvable, the so-called Efimov trimers appear for a system of three particles with resonant two-body interactions. The binding energies of these trimers are predicted to be universally connected to each other, independent of the microscopic details of the interaction. By exploiting a Feshbach resonance to widely tune the interactions between trapped ultracold lithium atoms, we find evidence for two universally connected Efimov trimers and their associated four-body bound states. A total of 11 precisely determined three- and four-body features are found in the inelastic-loss spectrum. Their relative locations on either side of the resonance agree well with universal theory, whereas a systematic deviation from universality is found when comparing features across the resonance.

Superfluidity of Spin-Polarized 6Li

We study the prospects for observing superfluidity in a spin-polarized atomic gas of 6Li atoms, using state-of-the-art interatomic potentials. We determine the spinodal line and show that a BCS transition to the superfluid state can indeed occur in the (meta)stable region of the phase diagram if the densities are sufficiently low. We also discuss the stability of the gas due to exchange and dipolar relaxation and conclude that the prospects for observing superfluidity in a magnetically trapped atomic 6Li gas are particularly promising for magnetic bias fields larger than 10 T.

Observation of antiferromagnetic correlations in the Hubbard model with ultracold atoms

Ultracold atoms in optical lattices have great potential to contribute to a better understanding of some of the most important issues in many-body physics, such as high-temperature superconductivity. The Hubbard model—a simplified representation of fermions moving on a periodic lattice—is thought to describe the essential details of copper oxide superconductivity. This model describes many of the features shared by the copper oxides, including an interaction-driven Mott insulating state and an antiferromagnetic (AFM) state. Optical lattices filled with a two-spin-component Fermi gas of ultracold atoms can faithfully realize the Hubbard model with readily tunable parameters, and thus provide a platform for the systematic exploration of its phase diagram. Realization of strongly correlated phases, however, has been hindered by the need to cool the atoms to temperatures as low as the magnetic exchange energy, and also by the lack of reliable thermometry. Here we demonstrate spin-sensitive Bragg scattering of light to measure AFM spin correlations in a realization of the three-dimensional Hubbard model at temperatures down to 1.4 times that of the AFM phase transition. This temperature regime is beyond the range of validity of a simple high-temperature series expansion, which brings our experiment close to the limit of the capabilities of current numerical techniques, particularly at metallic densities. We reach these low temperatures using a compensated optical lattice technique, in which the confinement of each lattice beam is compensated by a blue-detuned laser beam. The temperature of the atoms in the lattice is deduced by comparing the light scattering to determinant quantum Monte Carlo simulations and numerical linked-cluster expansion calculations. Further refinement of the compensated lattice may produce even lower temperatures which, along with light scattering thermometry, would open avenues for producing and characterizing other novel quantum states of matter, such as the pseudogap regime and correlated metallic states of the two-dimensional Hubbard model.

Extreme Tunability of Interactions in a 7Li Bose-Einstein Condensate

We use a Feshbach resonance to tune the scattering length a of a Bose-Einstein condensate of 7Li in the |F=1,mF=1> state. Using the spatial extent of the trapped condensate, we extract a over a range spanning 7 decades from small attractive interactions to extremely strong repulsive interactions. The shallow zero crossing in the wing of the Feshbach resonance enables the determination of a as small as 0.01 Bohr radii. Evidence of the weak anisotropic magnetic dipole interaction is obtained by comparison with different trap geometries for small a.