Semiclassical approach to Bose-Einstein condensates in a triple well potential

Abstract

We present a new approach for the analysis of Bose-Einstein condensates in a few mode approximation. This method has already been used to successfully analyze the vibrational modes in various molecular systems and offers a new perspective on the dynamics in many particle bosonic systems. We discuss a system consisting of a Bose-Einstein condensate in a triple well potential. Such systems correspond to classical Hamiltonian systems with three degrees of freedom. The semiclassical approach allows a simple visualization of the eigenstates of the quantum system referring to the underlying classical dynamics. From this classification we can read off the dynamical properties of the eigenstates such as particle exchange between the wells and entanglement without further calculations. In addition, this approach offers new insights into the validity of the mean-field description of the many particle system by the Gross-Pitaevskii equation, since we make use of exactly this correspondence in our semiclassical analysis. We choose a three mode system in order to visualize it easily and, moreover, to have a sufficiently interesting structure, although the method can also be extended to higher dimensional systems.

15 pages, 15 figures

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• Adiabatic Condition for Nonlinear Systems
• Beyond mean-field dynamics of small Bose-Hubbard systems based on the number-conserving phase space approach
• Semiclassical quantization of an N-particle Bose-Hubbard model
• Some remarks on the coherent-state variational approach to nonlinear boson models
• Control of unstable macroscopic oscillations in the dynamics of three coupled Bose condensates
• Tracking quasi-classical chaos in ultracold boson gases
• Ground-state Properties of Small-Size Nonlinear Dynamical Lattices