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

A Bose-Einstein condensate was produced in a vapor of rubidium-87 atoms that was confined by magnetic fields and evaporatively cooled. The condensate fraction first appeared near a temperature of 170 nanokelvin and a number density of 2.5 x 10 12 per cubic centimeter and could be preserved for more than 15 seconds. Three primary signatures of Bose-Einstein condensation were seen. (i) On top of a broad thermal velocity distribution, a narrow peak appeared that was centered at zero velocity. (ii) The fraction of the atoms that were in this low-velocity peak increased abruptly as the sample temperature was lowered. (iii) The peak exhibited a nonthermal, anisotropic velocity distribution expected of the minimum-energy quantum state of the magnetic trap in contrast to the isotropic, thermal velocity distribution observed in the broad uncondensed fraction.

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Observation of Bose-Einstein Condensation in a Dilute Atomic Vapor

The phenomenon of Bose-Einstein condensation of dilute gases in traps is reviewed from a theoretical perspective. Mean-field theory provides a framework to understand the main features of the condensation and the role of interactions between particles. Various properties of these systems are discussed, including the density profiles and the energy of the ground-state configurations, the collective oscillations and the dynamics of the expansion, the condensate fraction and the thermodynamic functions. The thermodynamic limit exhibits a scaling behavior in the relevant length and energy scales. Despite the dilute nature of the gases, interactions profoundly modify the static as well as the dynamic properties of the system; the predictions of mean-field theory are in excellent agreement with available experimental results. Effects of superfluidity including the existence of quantized vortices and the reduction of the moment of inertia are discussed, as well as the consequences of coherence such as the Josephson effect and interference phenomena. The review also assesses the accuracy and limitations of the mean-field approach.

https://arxiv.org/pdf/cond-mat/9806038.pdf

Theory of Bose-Einstein condensation in trapped 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

Recent interest in aspects common to quantum information and condensed matter has prompted a flurry of activity at the border of these disciplines that were far distant until a few years ago. Numerous interesting questions have been addressed so far. Here an important part of this field, the properties of the entanglement in many-body systems, are reviewed. The zero and finite temperature properties of entanglement in interacting spin, fermion, and boson model systems are discussed. Both bipartite and multipartite entanglement will be considered. In equilibrium entanglement is shown tightly connected to the characteristics of the phase diagram. The behavior of entanglement can be related, via certain witnesses, to thermodynamic quantities thus offering interesting possibilities for an experimental test. Out of equilibrium entangled states are generated and manipulated by means of many-body Hamiltonians.

/pdf/entanglement-in-many-body-systems-sqpatuxt14.pdf

Entanglement in many-body systems

In this paper we describe numerical simulations of the response of atoms confined in an optical lattice in the region of a quantum phase transition. We use the increase in the number variance of atoms as the diagnostic of excitations produced by tilting the lattice. We show that this locally determined quantity is a good indicator of the resulting coherence changes as observed in recent experiments. This is found to hold for commensurate and noncommensurate filling of the lattice, implying that our results should hold for a wide range of conditions. In accordance with this view, we find that the qualitative features of our results are in good agreement with recent experiments. We do, however, find extra features in the excitation spectra that may well be of use in future experimental studies. We also show that the variation of the spectra with the duration of the perturbation is a useful diagnostic of the atom dynamics that take place during the tilt.

http://www.dunningham.org/papers/braunmunzinger04.pdf

Excitations of Bose-Einstein condensates in optical lattices

Role of off-resonant excitation in cold collisions in a strong laser field.

We propose a spatiotemporal interferometric scheme based on near-field diffraction of Bose-Einstein condensates confined in a one-dimensional hard wall potential. The scheme is closely related to the phenomenon of intermode traces recently studied for noncondensed wave packets; we show how the scheme may be used in the detection of weak forces.

Spatiotemporal interferometry for trapped atomic Bose-Einstein condensates

Loss from magneto-optical traps in strong laser fields.

We investigate the limitations arising from atomic collisions on the storage and delay times of probe pulses in electromagnetically induced transparency experiments. We find that the atomic collisions can be described by an effective decay rate that limits storage and delay times. We calculate the momentum and temperature dependence of the decay rate and find that it is necessary to excite atoms at a particular momentum depending on temperature and spacing of the energy levels involved in order to minimize the decoherence effects of atomic collisions.

K. Burnett

Papers

Excitations of Bose-Einstein condensates in optical lattices

Role of off-resonant excitation in cold collisions in a strong laser field.

Spatiotemporal interferometry for trapped atomic Bose-Einstein condensates

Loss from magneto-optical traps in strong laser fields.

Limitations of light delay and storage times in electromagnetically induced transparency experiments with condensates