This paper reviews recent experimental and theoretical progress concerning many-body phenomena in dilute, ultracold gases. It focuses on effects beyond standard weak-coupling descriptions, such as the Mott-Hubbard transition in optical lattices, strongly interacting gases in one and two dimensions, or lowest-Landau-level physics in quasi-two-dimensional gases in fast rotation. Strong correlations in fermionic gases are discussed in optical lattices or near-Feshbach resonances in the BCS-BEC crossover.

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Many-Body Physics with Ultracold Gases

Bose-Einstein condensation (BEC) has been observed in a dilute gas of sodium atoms. A Bose-Einstein condensate consists of a macroscopic population of the ground state of the system, and is a coherent state of matter. In an ideal gas, this phase transition is purely quantum-statistical. The study of BEC in weakly interacting systems which can be controlled and observed with precision holds the promise of revealing new macroscopic quantum phenomena that can be understood from first principles.

Bose-Einstein condensation in a gas of sodium atoms

Feshbach resonances are the essential tool to control the interaction between atoms in ultracold quantum gases. They have found numerous experimental applications, opening up the way to important breakthroughs. This review broadly covers the phenomenon of Feshbach resonances in ultracold gases and their main applications. This includes the theoretical background and models for the description of Feshbach resonances, the experimental methods to find and characterize the resonances, a discussion of the main properties of resonances in various atomic species and mixed atomic species systems, and an overview of key experiments with atomic Bose-Einstein condensates, degenerate Fermi gases, and ultracold molecules.

Feshbach resonances in ultracold gases

The physics of quantum degenerate atomic Fermi gases in uniform as well as in harmonically trapped configurations is reviewed from a theoretical perspective. Emphasis is given to the effect of interactions that play a crucial role, bringing the gas into a superfluid phase at low temperature. In these dilute systems, interactions are characterized by a single parameter, the $s$-wave scattering length, whose value can be tuned using an external magnetic field near a broad Feshbach resonance. The BCS limit of ordinary Fermi superfluidity, the Bose-Einstein condensation (BEC) of dimers, and the unitary limit of large scattering length are important regimes exhibited by interacting Fermi gases. In particular, the BEC and the unitary regimes are characterized by a high value of the superfluid critical temperature, on the order of the Fermi temperature. Different physical properties are discussed, including the density profiles and the energy of the ground-state configurations, the momentum distribution, the fraction of condensed pairs, collective oscillations and pair-breaking effects, the expansion of the gas, the main thermodynamic properties, the behavior in the presence of optical lattices, and the signatures of superfluidity, such as the existence of quantized vortices, the quenching of the moment of inertia, and the consequences of spin polarization. Various theoretical approaches are considered, ranging from the mean-field description of the BCS-BEC crossover to nonperturbative methods based on quantum Monte Carlo techniques. A major goal of the review is to compare theoretical predictions with available experimental results.

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Theory of ultracold atomic Fermi gases

We review recent developments in the physics of ultracold atomic and molecular gases in optical lattices. Such systems are nearly perfect realisations of various kinds of Hubbard models, and as such may very well serve to mimic condensed matter phenomena. We show how these systems may be employed as quantum simulators to answer some challenging open questions of condensed matter, and even high energy physics. After a short presentation of the models and the methods of treatment of such systems, we discuss in detail, which challenges of condensed matter physics can be addressed with (i) disordered ultracold lattice gases, (ii) frustrated ultracold gases, (iii) spinor lattice gases, (iv) lattice gases in “artificial” magnetic fields, and, last but not least, (v) quantum information processing in lattice gases. For completeness, also some recent progress related to the above topics with trapped cold gases will be discussed. Motto: There are more things in heaven and earth, Horatio, Than are dreamt of in your...

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Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond

Attraction between the atoms of a Bose–Einstein condensate renders it unstable to collapse, although a condensate with a limited number of atoms1 can be stabilized2 by confinement in an atom trap. However, beyond this number the condensate collapses3,4,5. 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 dispersion1. 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.

Formation and propagation of matter-wave soliton trains

We report the attainment of simultaneous quantum degeneracy in a mixed gas of bosons (lithium-7) and fermions (lithium-6). The Fermi gas has been cooled to a temperature of 0.25 times the Fermi temperature by thermal collisions with the evaporatively cooled bosons. At this temperature, the spatial size of the gas is strongly affected by the Fermi pressure resulting from the Pauli exclusion principle and gives clear experimental evidence for quantum degeneracy.

https://science.sciencemag.org/content/sci/291/5513/2570.full.pdf

Observation of Fermi pressure in a gas of trapped atoms.

We have converted an ultracold Fermi gas of $^{6}\mathrm{L}\mathrm{i}$ atoms into an ultracold gas of $^{6}\mathrm{L}\mathrm{i}_{2}$ molecules by adiabatic passage through a Feshbach resonance. Approximately $1.5\ifmmode\times\else\texttimes\fi{}{10}^{5}$ molecules in the least-bound, $v=38$, vibrational level of the ${X}^{1}{\ensuremath{\Sigma}}_{g}^{+}$ 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.

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

We have used optical molecular spectroscopy to probe the many-body state of paired $^{6}\mathrm{L}\mathrm{i}$ 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.

Molecular probe of pairing in the BEC-BCS crossover.

We review recent experimental and theoretical work on the creation of bright matter wave solitons in Bose–Einstein condensates. In two recent experiments, solitons are formed from Bose–Einstein condensates of  7Li by utilizing a Feshbach resonance to switch from repulsive to attractive interactions. The solitons are made to propagate in a one-dimensional potential formed by a focused laser beam. For repulsive interactions, the wavepacket undergoes dispersive wavepacket spreading, while for attractive interactions, localized solitons are formed. In our experiment, a multi-soliton train containing up to ten solitons is observed to propagate without spreading for a duration of 2 s. Adjacent solitons are found to interact repulsively, in agreement with a calculation based on the nonlinear Schrodinger equation assuming that the soliton train is formed with an alternating phase structure. The origin of this phase structure is not entirely clear.

https://iopscience.iop.org/article/10.1088/1367-2630/5/1/373/pdf

K. E. Strecker

Papers

Formation and propagation of matter-wave soliton trains

Observation of Fermi pressure in a gas of trapped atoms.

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

Molecular probe of pairing in the BEC-BCS crossover.

Bright matter wave solitons in Bose–Einstein condensates