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Kluwer Academic Publishers eBooks

Atom Optics With Bose-Einstein Condensates

Sven Burger, Kai Bongs, K. Sengstock, Wolfgang A. Ertmer

Published Dec 11, 2005• 0 citations
Publisher

Abstract

Summary form only given. The application of coherent matter waves in phase-sensitive experiments, such as atom interferometers, necessitates the understanding of their evolution when being manipulated by atom optical elements like mirrors and beamsplitters. The dynamics of coherent matter waves during and after the interaction with these elements is much more complex than single-atom optics and can be termed 'nonlinear atom optics'.

DOI
10.1007/0-306-47103-5_7

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Summary form only given. The application of coherent matter waves in phase-sensitive experiments, such as atom interferometers, necessitates the understanding of their evolution when being manipulated by atom optical elements like mirrors and beamsplitters. The dynamics of coherent matter waves during and after the interaction with these elements is much more complex than single-atom optics and can be termed 'nonlinear atom optics'.
The coherent manipulation of Bose-Einstein Condensates by far blue detuned dipole potentials is discussed. “Classical” atom optical elements, like mirrors and waveguides, are realised and the dynamics of coherent matter waves interacting with these elements is investigated. The local manipulation of the phase of the condensate wavefunction by temporally applied dipole potentials represents a powerful tool for the design of matter waves. We use this method in particular for the creation of dark solitons in Bose-Einstein condensates and study their dynamics.
This review discusses progress in the new field of coherent matter waves, in particular with respect to Bose-Einstein condensates. We give a short introduction to Bose-Einstein condensation and the theoretical description of the condensate wavefunction. We concentrate on the coherence properties of this new type of matter wave as a basis for fundamental physics and applications. The main part of this review treats various measurements and concepts in the physics with coherent matter waves. In particular we present phase manipulation methods, atom lasers, nonlinear atom optics, optical elements, interferometry and physics in optical lattices. We give an overview of the state of the art in the respective fields and discuss achievements and challenges for the future.
The advent of the laser as an intense, coherent light source gave birth to nonlinear optics, which now plays an important role in many areas of science and technology. One of the first applications of nonlinear optics was the production of coherent light of a new frequency by multi-wave mixing of several optical fields in a nonlinear medium. Until the experimental realization of Bose-Einstein Condensation (BEC) there had been no intense coherent source of matter-waves analogous to the optical laser. BEC has already been exploited to produce a matter-wave 'laser' atom optics was reported: the observation of coherent four wave mixing in which three sodium matter waves mix to produce a fourth. The experiment utilized light pulses to create two high-momentum wavepackets via Bragg diffraction from a stationary Bose- Einstein condensate. The high-momentum components and the remaining zero momentum condensate component interact to form a new momentum component due to the nonlinear self- interaction of the bosonic atoms. We develop a quantum mechanical description, based on the slowly-varying-envelope approximation to the time-dependent nonlinear Schroedinger equation, to describe four-wave mixing in Bose-Einstein condensates and apply this description to understand the experimental observations and to make new predictions. We examine the role of phase-modulation, momentum and energy conservation, and particle number conservation in four-wave mixing of matter waves.
The advent of the laser as an intense, coherent light source gave birth to nonlinear optics, which now plays an important role in many areas of science and technology. One of the first applications of nonlinear optics was the production of coherent light of a new frequency by multi-wave mixing of several optical fields in a nonlinear medium. Until the experimental realization of Bose-Einstein Condensation (BEC) there had been no intense coherent source of matter-waves analogous to the optical laser. FEC has already been exploited to produce a matter-wave `laser' leading to the threshold of a new field of physics: nonlinear atom optics. Recently the first experiment in nonlinear atom optics was reported: the observation of coherent four wave mixing in which three sodium matter waves mix to produce a fourth. The experiment utilized light pulses to create two high-momentum wavepackets via Bragg diffraction from a stationary Bose- Einstein condensate. The high-momentum components and the remaining zero momentum condensate component interact to form a new momentum component due to the nonlinear self- interaction of the bosonic atoms. We develop a quantum mechanical description, based on the slowly-varying-envelope approximation to the time-dependent nonlinear Schrodinger equation (also called the Gross-Pitaevskii equation), to describe four-wave mixing in Bose-Einstein condensates and apply this description to understand the experimental observations and to make new predictions. We examine the role of phase-modulation, momentum and energy conservation (i.e., phase-matching), and particle number conservation in four-wave mixing of matter waves.
The coherent manipulation of Bose-Einstein condensates by far blue detuned dipole potentials is discussed. ‘Classical’ atom optical elements, such as mirrors and waveguides, are realized and the dynamics of coherent matter waves interacting with these elements is investigated. The local manipulation of the phase of the condensate wavefunction by temporally applied dipole potentials represents a powerful tool for the design of matter waves. We use this method in particular for the creation of dark solitons in Bose-Einstein condensates and study their dynamics.
Our ability to manipulate the coherence properties of light has been at the heart of many of the most important scientific and technological innovations of this century. There can hardly be a home in this country that does not possess a laser in the form of a compact disc player or a CDROM. When we talk on the phone, or send messages on the Internet, there is a high probability that our message will be encoded by a laser into pulses of light to be passed through optical fibres. In the last few years physicists have been discovering that it is possible to control the coherence properties of atoms, and are now developing tools analogous to those which have been developed to take advantage of the coherence properties of light. In the next decade we can look forward to seeing the application of lasers, fibres, mirrors and waveguides for atoms. Already we have been able to construct interferometry experiments using beams of atoms and these have proved to be extremely sensitive measurement devices, allowing us to test physical theories and measure fundamental constants to a level of precision not previously possible. Will these developing technologies ever be as ubiquitous as their optical forebears? In this paper we discuss the anticipated uses of this technology for both fundamental science and industrial applications. Starting from an explanation of the meaning of coherence and a comparison of the properties of photons and atoms, we describe the development of the science of atom optics. The tortuous route towards the great achievement of producing a Bose–Einstein condensate is described, and we explain why this is the most important step towards a laser–like source of atoms. Numerous other optical elements for atoms have been built or are on the drawing board, and we describe how these may be used to manipulate atoms with a precision that has never before been achieved, and look ahead to what we can learn about physics using these tools and at how they can be put to practical use.