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arXiv:cond-mat/0602500 · Annals of Physics

Electron self-trapping at quantum and classical critical points

Mark Auslender, Mikhail I. Katsnelson

Published Apr 20, 2006• 4 citations
arXivHTMLPDF
DOI
10.1016/j.aop.2006.02.012

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In this paper we study self-trapping of Bose-Einstein condensates in a symmetric double-well potential with uniform noise or Gaussian noise existing respectively. We find that both uniform noise and Gaussian noise destroy the critical behavior of self-trapping with the interaction increasing and create a transition zone between Josephson oscillation and self-trapping, between which exists a critical point originally. Furthermore, the stronger the noise becomes, the wider the transition zone is. Meanwhile, we find that the phase space falls into complete confusion when we increase noise intensity to a certain extent with interaction fixed, and the trajectories reappear after we increase the interaction without increasing the noise intensity. In the full-quantum situation, when noise exists there is a transition zone instead of a critical value, and stronger noise creates wider transition zone, which is the same as in mean field treatment. What is different is that in full-quantum situation noise creates self-trapping, and the stronger the noise, the more obvious the self-trapping becomes.

Acta Physica Sinica•Jan 1, 2007•6 citations
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.
In this paper, we exploit two-mode model to investigate the influence of quantum fluctuation on the self-trapping of the Bose-Einstein Condensate(BEC). We found that, even for the finite number of particles, the transition to self-trapping is still observed.In particular, because of the quantum fluctuation due to the finite number of particles, the critical phenomenon becomes fuzzily: the smaller the number of particles is, the more obviously fuzzily the critical phenomenon becomes. Quantum entanglement entropy is then introduced to depict the critical behavior near the transition point.
In this paper we study self-trapping of Bose-Einstein condensates in a symmetric double-well potential with uniform noise or Gaussian noise existing respectively. We find that both uniform noise and Gaussian noise destroy the critical behavior of self-trapping with the interaction increasing and create a transition zone between Josephson oscillation and self-trapping, between which exists a critical point originally. Furthermore, the stronger the noise becomes, the wider the transition zone is. Meanwhile, we find that the phase space falls into complete confusion when we increase noise intensity to a certain extent with interaction fixed, and the trajectories reappear after we increase the interaction without increasing the noise intensity. In the full-quantum situation, when noise exists there is a transition zone instead of a critical value, and stronger noise creates wider transition zone, which is the same as in mean field treatment. What is different is that in full-quantum situation noise creates self-trapping, and the stronger the noise, the more obvious the self-trapping becomes.