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.

/pdf/many-body-physics-with-ultracold-gases-552s10zfdn.pdf

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.

/pdf/observation-of-bose-einstein-condensation-in-a-dilute-atomic-2wpb5ks2pi.pdf

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

Techniques that use quantum interference effects are being actively investigated to manipulate the optical properties of quantum systems1. One such example is electromagnetically induced transparency, a quantum effect that permits the propagation of light pulses through an otherwise opaque medium2,3,4,5. Here we report an experimental demonstration of electromagnetically induced transparency in an ultracold gas of sodium atoms, in which the optical pulses propagate at twenty million times slower than the speed of light in a vacuum. The gas is cooled to nanokelvin temperatures by laser and evaporative cooling6,7,8,9,10. The quantum interference controlling the optical properties of the medium is set up by a ‘coupling’ laser beam propagating at a right angle to the pulsed ‘probe’ beam. At nanokelvin temperatures, the variation of refractive index with probe frequency can be made very steep. In conjunction with the high atomic density, this results in the exceptionally low light speeds observed. By cooling the cloud below the transition temperature for Bose–Einstein condensation11,12,13 (causing a macroscopic population of alkali atoms in the quantum ground state of the confining potential), we observe even lower pulse propagation velocities (17?m?s−1) owing to the increased atom density. We report an inferred nonlinear refractive index of 0.18?cm2?W−1 and find that the system shows exceptionally large optical nonlinearities, which are of potential fundamental and technological interest for quantum optics.

/pdf/light-speed-reduction-to-17-metres-per-second-in-an-5echiu51el.pdf

Light speed reduction to 17 metres per second in an ultracold atomic gas

We have observed Bose-Einstein condensation of sodium atoms. The atoms were trapped in a novel trap that employed both magnetic and optical forces. Evaporative cooling increased the phase-space density by 6 orders of magnitude within seven seconds. Condensates contained up to 5\ifmmode\times\else\texttimes\fi{}${10}^{5}$ atoms at densities exceeding ${10}^{14}$ ${\mathrm{cm}}^{\ensuremath{-}3}$. The striking signature of Bose condensation was the sudden appearance of a bimodal velocity distribution below the critical temperature of \ensuremath{\sim}2\ensuremath{\mu}K. The distribution consisted of an isotropic thermal distribution and an elliptical core attributed to the expansion of a dense condensate.

Bose-Einstein condensation in a gas of sodium atoms.

We have demonstrated an output coupler for Bose condensed atoms in a magnetic trap. Short pulses of rf radiation were used to create Bose condensates in a superposition of trapped and untrapped hyperfine states. The fraction of out-coupled atoms was adjusted between 0% and 100% by varying the amplitude of the rf radiation. This configuration produces output pulses of coherent atoms and can be regarded as a pulsed ``atom laser.''

/pdf/output-coupler-for-bose-einstein-condensed-atoms-5gjq4c1wga.pdf

Output Coupler for Bose-Einstein Condensed Atoms

Collective excitations of a dilute Bose condensate have been observed. These excitations are analogous to phonons in superfluid helium. Bose condensates were created by evaporatively cooling magnetically trapped sodium atoms. Excitations were induced by a modulation of the trapping potential, and detected as shape oscillations in the freely expanding condensates. The frequencies of the lowest modes agreed well with theoretical predictions based on mean-field theory. Before the onset of BoseEinstein condensation, we observed sound waves in a dense ultracold gas. [S0031-9007(96)00900-3] In 1941 Landau introduced the concept of elementary excitations to explain the properties of superfluid helium [1]. This phenomenological approach, based on quantum hydrodynamics, gave a quantitative description of the thermodynamic properties and transport processes in liquid helium. Landau rejected any relation to Bose-Einstein condensation (BEC). A microscopic derivation of the elementary excitation spectrum for a weakly interacting Bose gas was given by Bogoliubov in 1947 [2] and for He II by Feynman in 1955 [3], emphasizing the role of Bose statistics [3] and reconciling Landau’s approach with London’s explanation of superfluidity as being due to BEC [2,4]. The elementary excitations determine the spectrum of density fluctuations in a Bose liquid, and have been directly observed in He II by neutron scattering [5]. The low-frequency excitations are phonons, long-wavelength collective modes of the superfluid. So far, a satisfactory microscopic theory for an interacting bosonic system exists only for the dilute quantum gas. The recent realization of BEC in dilute atomic vapors [6 ‐ 8] has opened the door to test this theory experimentally. In this paper we report on the observation of shape oscillations of a trapped Bose condensate, modes analogous to phonons in homogeneous systems [9]. The experimental setup for creating Bose condensates was the same as in our previous work [10]. Briefly, sodium atoms were optically cooled and trapped, and transferred into a magnetic trap where they were further cooled by rf-induced evaporation [11,12]. Every 30 s, condensates containing 5 3 10 6 sodium atoms in the F › 1, mF › 21 ground state were produced. Evaporative cooling was extended well below the transition temperature to obtain a condensate without a discernible normal component. The condensate was confined in a cloverleaf magnetic trap which had cylindrical symmetry with trapping frequencies of 19 Hz axially and 250 Hz radially (see below). The trapping potential is determined by the axial curvature of the magnetic field B 00 › 125 Gc m 2 2 , the radial gradient B 0 › 150 Gc m 2 1 , and the bias field B0 › 1.2 G. The condensate was excited by a time-dependent modulation of the trapping potential. First, we used a sudden step in the gradient B 0 to identify several collective modes of the condensate and to find their approximate frequencies. B 0 was decreased by 15% for a duration of 5 ms with a transition time of about 1 ms, and then returned to its original value. A variable time delay was introduced between the excitation and the observation of the cloud. In this way, we strobed the free time evolution of the system after the excitation. The cloud was observed by absorption imaging after a sudden switch off of the magnetic trap and 40 ms of ballistic expansion. No trap loss was observed during the interval over which the delay was varied. The images were similar to the series shown in Fig. 1. Four modes were identified from the measured center-of-mass positions and the widths of the condensate. The radial and axial center-of-mass oscillations (dipole modes) were excited because a change in B 0 displaced the center of the trap slightly due to asymmetries in the field-producing coils. A fast shape oscillation predominantly showed up as a sinusoidal modulation of the radial width while a slow sinusoidal shape oscillation was observed in the axial width. When a strong parametric drive (see below) was used to excite the slow shape oscillation, a weak oscillation of the radial width was also detected. Note that the widths were observed after ballistic expansion and reflect a convolution of the initial spatial and velocity

/pdf/collective-excitations-of-a-bose-einstein-condensate-in-a-11jhnftyck.pdf

Collective Excitations of a Bose-Einstein Condensate in a Magnetic Trap.

Bose-Einstein condensation of sodium atoms has been observed in a novel ``cloverleaf'' trap. This trap combines tight confinement with excellent optical access, using only dc electromagnets. Evaporative cooling in this trap produced condensates of $5\ifmmode\times\else\texttimes\fi{}{10}^{6}$ atoms, a tenfold improvement over previous results. We measured the condensate fraction and the repulsive mean-field energy, finding agreement with theoretical predictions.

/pdf/bose-einstein-condensation-in-a-tightly-confining-dc-4v5pdbs7bq.pdf

Bose-Einstein Condensation in a Tightly Confining dc Magnetic Trap.

The spatial observation of a Bose condensate is reported. Dispersive light scattering was used to observe the separation between the condensed and normal components of the Bose gas inside a magnetic trap. This technique is nondestructive, and about a hundred images of the same condensate can be taken. The width of the angular distribution of scattered light increased suddenly at the phase transition.

/pdf/direct-nondestructive-observation-of-a-bose-condensate-53ttlkmg4t.pdf

M.-O. Mewes

Papers

Bose-Einstein condensation in a gas of sodium atoms.

Output Coupler for Bose-Einstein Condensed Atoms

Collective Excitations of a Bose-Einstein Condensate in a Magnetic Trap.

Bose-Einstein Condensation in a Tightly Confining dc Magnetic Trap.

Direct, nondestructive observation of a Bose condensate