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

The power of feedback.

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

2. GRAVITY 7. MICROSCOPIC PHYSICS 13. TOPOLOGY OF DEFECTS 18. ANOMALOUS NON-CONSERVATION OF FERMIONIC CHARGE 22. EDGE STATES AND FERMION ZERO MODES ON SOLITON 26. LANDAU CRITICAL VELOCITY 29. CASIMIR EFFECT AND VACUUM ENERGY

The Universe in a Helium Droplet

Summary form only given. We report on an experiment performed with a gaseous Bose-Einstein condensate, which is analogous to the rotating bucket experiment performed with liquid He. The atoms are confined in a static, cylindrically symmetric Ioffe-Pritchard magnetic trap upon which we superimpose a nonaxisymmetric, attractive dipole potential created by a stirring laser beam. The combined potential leads to a cigar-shaped harmonic trap with a slightly anisotropic transverse profile. The transverse anisotropy is rotated as the gas is evaporatively cooled to Bose-Einstein condensation, and it plays the role of the bucket wall roughness. Pictures taken at various rotation frequencies, after a ballistic expansion of the condensate, clearly show that for fast enough rotation frequencies, we can generate one or several "holes" in the transverse density distribution corresponding to vortices. We discuss our determination of the critical frequency for the single and multiple vortex formation, and we report measurements of the nucleation time and the lifetime of the vortex state.

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Vortex formation in a stirred Bose-Einstein condensate

We report observation of Wannier-Stark ladders with ultracold sodium atoms in an accelerating one-dimensional standing wave of light. Atoms are trapped in a far-detuned standing wave that is accelerated for a controlled duration. A small oscillatory component is added to the acceleration, and the fraction of trapped atoms is measured as a function of the oscillation frequency. Resonances are observed where the number of trapped atoms drops dramatically. The separation between resonant peaks is found to be proportional to the acceleration. We show that this resonant structure can also be understood as a temporal quantum interference effect. [S0031-9007(96)00369-9]

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Observation of atomic wannier-stark ladders in an accelerating optical potential

Using a focused laser beam we stir a ${}^{87}\mathrm{Rb}$ Bose-Einstein condensate confined in a magnetic trap. We observe that the steady states of the condensate correspond to an elliptic cloud, stationary in the rotating frame. These steady states depend nonlinearly on the stirring parameters (amplitude and frequency), and various solutions can be reached experimentally depending on the path followed in this parameter space. These states can be dynamically unstable and we observe that such instabilities lead to vortex nucleation in the condensate.

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Stationary States of a Rotating Bose-Einstein Condensate: Routes to Vortex Nucleation

An exponential decay law is the universal hallmark of unstable systems and is observed in all fields of science. This law is not, however, fully consistent with quantum mechanics and deviations from exponential decay have been predicted for short as well as long times1,2,3,4,5,6,7,8. Such deviations have not hitherto been observed experimentally. Here we present experimental evidence for short-time deviation from exponential decay in a quantum tunnelling experiment. Our system consists of ultra-cold sodium atoms that are trapped in an accelerating periodic optical potential created by a standing wave of light. Atoms can escape the wells by quantum tunnelling, and the number that remain can be measured as a function of interaction time for a fixed value of the well depth and acceleration. We observe that for short times the survival probability is initially constant before developing the characteristics of exponential decay. The conceptual simplicity of the experiment enables a detailed comparison with theoretical predictions.

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Experimental evidence for non-exponential decay in quantum tunnelling

We study the quadrupole oscillation of a Bose-Einstein condensate of ${}^{87}\mathrm{Rb}$ atoms confined in an axisymmetric magnetic trap, after it has been stirred by an auxiliary laser beam The stirring may lead to the nucleation of one or more vortices, whose presence is revealed unambiguously by the precession of the axes of the quadrupolar mode For a stirring frequency $\ensuremath{\Omega}$ below the single vortex nucleation threshold ${\ensuremath{\Omega}}_{c}$, no measurable precession occurs Just above ${\ensuremath{\Omega}}_{c}$, the angular momentum deduced from the precession is $\ensuremath{\sim}\ensuremath{\Elzxh}$ For stirring frequencies above ${\ensuremath{\Omega}}_{c}$ the angular momentum is a smooth and increasing function of $\ensuremath{\Omega}$, until an angular frequency is reached at which the vortex lattice disappears

Kirk W. Madison

Papers

Vortex formation in a stirred Bose-Einstein condensate

Observation of atomic wannier-stark ladders in an accelerating optical potential

Stationary States of a Rotating Bose-Einstein Condensate: Routes to Vortex Nucleation

Experimental evidence for non-exponential decay in quantum tunnelling

Measurement of the angular momentum of a rotating bose-einstein condensate