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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Nonlinear matter wave dynamics in periodic and double well potentials

M. Albiez, Th. Anker, Rudolf Gati, Jonas Fölling, S. Hunsmann, Markus K Oberthaler

Published Jan 25, 2006• 0 citations
Publisher

Abstract

Bose-Einstein condensates in designed potentials represent a model system for the investigation of nonlinear matter wave dynamics, since both the nonlinearity and the potentials can be very well controlled experimentally. The nonlinearity arising from the atom-atom interaction can be adjusted through the atom number. The potentials can be readily realized by employing the atom-light interaction leading to potentials which are proportional to light intensity. Since the techniques for manipulation of light are very well developed almost arbitrary potentials can be realized. In our experiments we employ the most simple light intensity configurations such as focused laser beam and standing light waves

DOI
10.1109/cleoe.2005.1568476

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Bose-Einstein condensates in designed potentials represent a model system for the investigation of nonlinear matter wave dynamics, since both the nonlinearity and the potentials can be very well controlled experimentally. The nonlinearity arising from the atom-atom interaction can be adjusted through the atom number. The potentials can be readily realized by employing the atom-light interaction leading to potentials which are proportional to light intensity. Since the techniques for manipulation of light are very well developed almost arbitrary potentials can be realized. In our experiments we employ the most simple light intensity configurations such as focused laser beam and standing light waves
Bose-Einstein condensates indesigned potentials represent amodelsystem fortheinvestigation ofnonlinear matter wavedynamics, since boththenonlinearity andthepotentials canbeverywellcontrolled experimentally. The nonlinearity arising fromtheatom-atom interaction canbeadjusted through theatomnumber. Thepotentials canbe readily realized byemploying theatom-light interaction leading topotentials which areproportional tolight intensity. Since thetechniques formanipulation oflight areverywelldeveloped almost arbitrary potentials canberealized. Inour experiments weemploy themostsimple light intensity configurations suchasfocused laser beamandstanding light waves.
Recent experimental and theoretical progress in the studies of Bose-Einstein condensation (BEC) has precipitated an intense effort to understand and control interactions of nonlinear matter-waves. Key ingredients in manipulations of matter-waves in BECs are a) external localized impurities (generated by focused laser beams) and b) periodic potentials (generated by interference patterns from multiple laser beams illuminating the condensate). In this work we demonstrate the ability of time-dependent external optical potentials to drag, capture and pin a wide range of localized BEC states, such as dark and bright solitons. The stability and existence of pinned states is analyzed using perturbation techniques, which predict results that are well corroborated by direct numerical simulations. The control of these macroscopic quantum states has important applications in the realm of quantum storage and processing of information, with potential implications for the design of quantum computers.
Matter waves inside periodic potentials are well known from solid-state physics, where electrons interacting with a crystal lattice are considered. Atomic Bose-Einstein condensates inside light-induced periodic potentials (optical lattices) share many features with electrons in solids, but also with light waves in nonlinear materials and other nonlinear systems. Generally, atom-atom interactions in Bose-Einstein condensates lead to rich and interesting nonlinear effects. Furthermore, the experimental control over the parameters of the periodic potential and the condensate make it possible to enter regimes inaccessible in other systems. In this review, an introduction to the physics of ultracold bosonic atoms in optical lattices is given and an overview of the theoretical and experimental advances to date.
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 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.
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.