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Uspekhi Fizicheskih Nauk

Bose – Einstein condensates in a laser radiation field

Лев П. Питаевский

Published Jan 1, 2006• 51 citations
Publisher

Abstract

The properties of Bose–Einstein condensates in an external potential produced by a laser light field are discussed. Considered are the condensates embedded in periodic lattices produced by standing laser waves and the condensates confined within 'optical traps' near the focus of a traveling wave. Observations of the Mott transition in a periodic lattice are described, as are experiments on atoms near the Feshbach resonance and experiments on the condensates in a double potential well, which permit investigating the tunnel dynamics of condensate phases.

DOI
10.3367/ufnr.0176.200604a.0345

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The properties of Bose–Einstein condensates in an external potential produced by a laser light field are discussed. Considered are the condensates embedded in periodic lattices produced by standing laser waves and the condensates confined within 'optical traps' near the focus of a traveling wave. Observations of the Mott transition in a periodic lattice are described, as are experiments on atoms near the Feshbach resonance and experiments on the condensates in a double potential well, which permit investigating the tunnel dynamics of condensate phases.
Summary form only given. Since the experimental realization of Bose-Einstein condensation in the magnetically trapped quantum atomic gases, there have now been an enormous quantity of theory devoted to the properties of the trapped Bose-Einstein condensates (BEC). Motivated by the existing experiments, the bulk of the theoretical work has assumed a harmonic trap. Although recently a few papers have considered the consequences of exposing a BEC to a periodic optical potential, BEC confined in an optical lattice is still a new topic in this area. In the work, we develop theory to study the stationary and propagating properties of a Bose-Einstein condensate in an optical lattice. Instead of using an infinite optical lattice, we study the realistic case where the BEC is formed in a finite trapping potential and then is exposed to an infinite periodic potential created by off-resonance multiple laser beams.
An optical lattice is a periodic potential for atoms, created using a standing wave pattern of light. Due to the interaction between the light and the atoms, the atoms are attracted to either the nodes or the anti-nodes of the standing wave, depending on the exact wave lenght of the light. This means that if such a lattice is loaded with a sufficiently high number of ultracold atoms, a periodic array of atoms is obtained, we an interatomic distance of a few tenths of a micrometer. In order to obtain such a high number of cold atoms, one first has to create a so-called Bose-Einstein condensate. When an optical lattice is loaded from a Bose-Einstein condensate, it is possible to create a system in which every atom is in the lowest band of the lattice and there is on average one atom in each lattice site. Because the lattice potential is created with laser light, the depth of the lattice can easily be tuned by changing the intensity of the laser. When the intensity of the laser light is low, the atoms can tunnel from one site to the next. Due to this tunneling, the gas of atoms in the lattice will remain superfluid. However, if the intensity of the laser light is increased to above a certain critical value, a quantum phase transition occurs to a so-called Mott insulator. In this state, the atoms can no longer tunnel due to the fact that the on-site interaction between atoms becomes more important then the tunneling probability. In this PhD thesis, a description is given of the experimental setup that is being constructed in our group to create these systems in our lab. Also, a theoretical description is given of these systems and several important quantities our derived, such as the gap of the Mott-insulating state. Furthermore, an experiment is proposed that can be used to accurately measure this gap.
Bose-Einstein condensation in trapped dilute gases1,1,3 was observed only recently. Nevertheless, the experimental developments in this field have advanced rapidly, and the properties of condensates in different circumstances have become a matter of practical interest. In this work we study the influence of a spatially periodic external potential on the properties of a Bose-Einstein condensate, as reported elsewhere in more detail4. Such a periodic potential may be induced by a far-off resonant laser field, and with present trapped condensates it is possible to have a condensate extending over many periods of such a field. The proposed periodic potential could be realized by a simple rearrangement of the laser field in the experiments with an optically trapped condensate5.
The criteria for validity of adiabaticity for nonlinear wave equations are considered within the context of atomic matter waves tunneling from macroscopically populated optical standing-wave traps loaded from a Bose-Einstein condensate. We show that, even when the optical standing wave is slowly turned on and the condensate behaves adiabatically during this turn-on, once the tunneling time between wells in the optical lattice becomes longer than the nonlinear time scale, adiabaticity breaks down and a significant spatially varying phase develops across the condensate wave function from well to well. This phase drastically affects the contrast of the fringe pattern in Josephson-effect interference experiments, and the condensate coherence properties in general.
Bose-Einstein condensates of rubidium atoms are stored in a two-dimensional periodic dipole force potential, formed by a pair of standing wave laser fields. The resulting potential consists of a lattice of tightly confining tubes, each filled with a 1D quantum gas. Tunnel coupling between neighboring tubes is controlled by the intensity of the laser fields. By observing the interference pattern of atoms released from more than 3000 individual lattice tubes, the phase coherence of the coupled quantum gases is studied. The lifetime of the condensate in the lattice and the dependence of the interference pattern on the lattice configuration are investigated.