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Physical Review A

Towards coherent control of a Bose-Einstein condensate in a double well

Martin Holthaus

Published Jun 6, 2001• 104 citations
Publisher

Abstract

A type of solution to the nonlinear Schr\"odinger equation for periodically driven Bose-Einstein condensates is introduced, which generalizes the familiar single-particle Floquet states. These solutions lead to the prediction that the onset of self-trapping of a condensate in a periodically modulated double well can be systematically controlled. This mean-field prediction is confirmed on the N-particle level, and explained by a pairing mechanism.

DOI
10.1103/physreva.64.011601

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A type of solution to the nonlinear Schr"odinger equation for periodically driven Bose-Einstein condensates is introduced, which generalizes the familiar single-particle Floquet states. These solutions lead to the prediction that the onset of self-trapping of a condensate in a periodically modulated double well can be systematically controlled. This mean-field prediction is confirmed on the N-particle level, and explained by a pairing mechanism.
We investigate the effect of an external periodic driving to the self-trapping transitions of two weakly coupled Bose-Einstein condensates in a double-well potential. It is shown that the self-trapping can be effectively controlled by modulating the double-well with a high frequency driving and thus renormalizing the transition parameters. In particular, an exact solution is constructed under the balance condition between the external field and the nonlinear interaction among particles, which allows one to precisely control theself-trapping states.
We investigate the exact ac control of two periodically driven and weakly coupled Bose–Einstein condensates in a double-well trap. By employing two balance conditions we construct new exact Floquet solutions with the degenerate Floquet energy, and give the balance region on the parameter space. It is revealed that for some different parameters in the balance region the Floquet solutions exactly describe the macroscopic quantum self-trapping, nonlinear coherent construction and destruction of quantum tunneling, respectively. Therefore, we can accurately perform the coherent control by suitably adjusting the system parameters.
A Bose-Einstein condensate in a modulated, one-dimensional, anharmonic potential can exhibit dynamical tunneling between islands of regular motion in phase space. With increasingly repulsive atomic interactions, dynamical tunneling is predicted to cease due to self-trapping [S. Wüster ]. This suppression of tunneling oscillations is related to the same phenomenon that occurs in the two-mode dynamics of a repulsively interacting Bose-Einstein condensate in a double-well potential. Here we present a two-mode model for dynamical tunneling based on nonlinear Floquet states and examine the range of validity of the approximation. We characterize nonlinear dynamical tunneling for different trap strengths, modulation amplitudes, and effective Planck constants. Using the linear Floquet states we derive an expression for the critical nonlinearity beyond which tunneling ceases. Finally we demonstrate the dynamical instability of selected nonlinear Floquet states and show how to initialize some Floquet states in experiments. Our detailed survey will enable experiments to target accessible parameter regimes for the study of nonlinear dynamical tunneling.
Self-trapping of Bose-Einstein condensates (BEC) in double-well trap is investigated. Two kinds of self-trapping are discussed through phase space analysis in the mean-field approximation: 1) The number of atoms oscillates near an equilibrium point in the phase space, while relative phase increases monotonously with time (running-phase); 2) Both the number of particles and the relative phase oscillate near an equilibrium point in the phase space. In particular, we investigate how an external periodic filed influence the self-trapping. It is found that the external periodic field may dramatically modulate the critical points at which the transition to self-trapping occurs. With this, we can observe self-trapping phenomenon in a dilute Bose-Einstein condensate with a very weak interaction as well. Finally, the effect of many-body quantum fluctuation on self-trapping is also studied. We also discuss how to observe the self-trapping phenomenon with present experimental techniques.