Controlling chaos in a Bose-Einstein condensate loaded into a moving optical lattice potential
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TOMS, MOLECULES, OPTICS
Controlling Chaos in a Bose–Einstein Condensate Loaded into a Moving Optical Lattice Potential¶ Zhixia Wanga, b, Xihe Zhangb, and Ke Shen†b a
b
Aviation University of the Air Force, Changchun, 130022 China Department of Physics, Changchun University of Science and Technology, Changchun, 130022 China e-mail: [email protected] Received April 8, 2008
Abstract—The spatial structure of a Bose–Einstein condensate loaded into an optical lattice potential is investigated, and spatially chaotic distributions of the condensates are revealed. By means of changing of the s-wave scattering length with a Feshbach resonance, the chaotic behavior can be well controlled to enter into periodicity. Numerical simulation shows that there are different periodic orbits according to different s-wave scattering lengths only if the maximal Lyapunov exponent of the system is negative. PACS numbers: 42.65.Sf, 37.10.Jk, 42.50.Md DOI: 10.1134/S1063776108110022 ¶
1. INTRODUCTION
Eighty years after its prediction, the Bose–Einstein condensate (BEC) has been observed in trapped gases of rubidium, sodium, and lithium [1]. The mean field theory (the Gross–Pitaevskii, or GP equation) has been quite successful in quantitatively reproducing many experimental observations [2]. The achievement of BEC in dilute alkali vapors has opened the field of a weakly interacting degenerate Bose gas. Subsequent experimental and theoretical progress has been made in studying the properties of this new state of matter. Several remarkable phenomena, which strongly resemble well-known effects in nonlinear optics, have been observed in the BEC, such as four-wave mixing, vortices, dark and bright solitons, and chaos [3–12]. In a realistic experimental setting, an external electromagnetic field is used to produce, trap, and manipulate the BEC. In early experiments, only the harmonic potential was used, but a wide variety of potentials can now be constructed experimentally. Among the most frequently studied both experimentally and theoretically are periodic optical lattice potentials. The optical lattice is created as a standing-wave interference pattern of mutually coherent laser beams. With each lattice site occupied by one mass of alkali atoms in its ground state, the BEC in optical lattices shows a number of potential applications, such as an atomic interferometer, detectors for quantum computers, an atom laser, quantum information processing on the nanometer scale, and others. Optical lattices are therefore of particular interest from the perspective of ¶
The text was submitted by the authors in English.
† Deceased.
both fundamental quantum physics and in applications [8]. Numerous experimental studies have confirmed the general validity of the time-dependent nonlinear Schrödinger equation, also called the GP equation, used to calculate the ground state and excitations of various BECs of trapped alkali atoms. The dynamics of the system are described by a Schrödinger equation with a nonlinear term that represents many-body interactions in
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