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arXiv:quant-ph/0106059 · Communications in Theoretical Physics

Multistability and Critical Fluctuation in a Split Bose-Einstein Condensate

Wu Ying, Sun Changpu

Published Dec 15, 2002• 4 citations
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Abstract

By using a two-mode description, we show that there exist the multistability, phase transition and associated critical fluctuations in the macroscopic tunnelling process between the halves of a double-well trap containing a Bose–Einstein condensate. The phase transition that two of the triple stable states and an unstable state merge into one stable state or a reverse process takes place whenever the ratio of the mean field energy per particle to the tunnelling energy goes across a critical value of order one. The critical fluctuation phenomenon corresponds to squeezed states for the phase difference between the two wells accompanying with large fluctuations of atom numbers.

DOI
10.1088/0253-6102/38/6/675

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By using a two-mode description, we show that there exist the multistability, phase transition and associated critical fluctuations in the macroscopic tunnelling process between the halves of a double-well trap containing a Bose–Einstein condensate. The phase transition that two of the triple stable states and an unstable state merge into one stable state or a reverse process takes place whenever the ratio of the mean field energy per particle to the tunnelling energy goes across a critical value of order one. The critical fluctuation phenomenon corresponds to squeezed states for the phase difference between the two wells accompanying with large fluctuations of atom numbers.
By using a two-mode description, we show that there exist the multistability, phase transition and associatedcritical fluctuations in the macroscopic tunnelling process between the halves of a double-well trap containing a Bose-Einstein condensate. The phase transition that two of the triple stable states and an unstable state merge into one stablestate or a reverse process takes place whenever the ratio of the mean field energy per particle to the tunnelling energygoes across a critical value of order one. The critical fluctuation phenomenon corresponds to squeezed states for thephase difference between the two wells accompanying with large fluctuations of atom numbers.
We theoretically study atom number fluctuations between the halves of a double-well trap containing a Bose-Einstein condensate. The basic tool is the two-mode approximation, which assumes that only two one-particle states are involved. An analytical harmonic-oscillator-like model is developed and verified numerically for both stationary fluctuations in the ground state of the system, and for the fluctuations resulting from splitting of a single trap by dynamically erecting a barrier in the middle. With increasing strength of the atom-atom interactions and/or increasing height of the potential barrier, the fluctuations tend to evolve from Poissonian to sub-Poissonian. Limits of validity of the two-mode model and its relations to the phase-atom-number approach of Leggett and Sols [A. J. Leggett and F. Sols, Found. Phys. 21, 353 (1991)] are discussed in detail.
We consider a Bose-Einstein condensate with an attractive particle interaction in a symmetric double well potential. It is known that in the mean field description a symmetric solution for the condensate wavefunction becomes unstable when the interactions are stronger than some critical value. We analyze the system around the critical point applying the number conserving Bogoliubov theory and exact diagonalization of the two mode hamiltonian. It allows for estimation of the density fluctuations in the system. Fluctuations of the order parameter, which is defined in the mean field description, turn out to be maximal at the critical point.
We study the coherent nonlinear tunneling dynamics of a binary mixture of Bose-Einstein condensates in a double-well potential. We demonstrate the existence of a type of mode associated with the ``swapping'' of the two species in the two wells of the potential. In contrast to the symmetry-breaking macroscopic quantum self-trapping (MQST) solutions, the swapping modes correspond to the tunneling dynamics that preserves the symmetry of the double-well potential. As a consequence of two distinct types of broken-symmetry MQST phases where the two species localize in different potential wells or coexist in the same well, the corresponding symmetry-restoring swapping modes result in dynamics where the two species either avoid or chase each other. In view of the possibility to control the interaction between the species, the binary mixture offers a very robust system to observe these novel effects as well as the phenomena of Josephson oscillations and $\ensuremath{\pi}$ modes.