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arXiv:quant-ph/0701148 · Physical Review A

Mode-exchange collisions in an exactly solvable two-mode Bose-Einstein condensate

Pablo Barberis-Blostein, Ivette Fuentes

Published Jul 31, 2008• 5 citations
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Abstract

Mode-exchange collisions occur in multimode Bose-Einstein condensates, in some cases, producing particle loss in the system. Nevertheless, little is known about mode-exchange collisions in the case when particles do not escape the trap. We show that these processes are relevant in quantum properties of the system such as the evolution of the relative population, the self-trapping effect, and the probability distribution of particles. Surprisingly, including mode-exchange terms in the model of the two-mode condensate allows for an exact analytical solution. Using this solution, we show that collisions favor the generation of entanglement between the modes of the condensate.

DOI
10.1103/physreva.78.013641

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Mode-exchange collisions occur in multimode Bose-Einstein condensates, in some cases, producing particle loss in the system. Nevertheless, little is known about mode-exchange collisions in the case when particles do not escape the trap. We show that these processes are relevant in quantum properties of the system such as the evolution of the relative population, the self-trapping effect, and the probability distribution of particles. Surprisingly, including mode-exchange terms in the model of the two-mode condensate allows for an exact analytical solution. Using this solution, we show that collisions favor the generation of entanglement between the modes of the condensate.
We study the effects of three-body collisions in the physical properties of a two-mode Bose-Einstein condensate. The model introduced here includes two-body and three-body elastic and mode-exchange collisions and can be solved analytically. We will use this fact to show that three-body interactions can produce drastic changes in the probability distribution of the ground state and the dynamics of the relative population. In particular, we find that three-body interactions under certain circumstances may inhibit the collapse of the relative population.
It has recently been discovered that for certain rates of mode-exchange collisions analytic solutions can be found for a Hamiltonian describing the two-mode Bose-Einstein condensate. We proceed to study the behavior of the system using perturbation theory if the coupling constants only approximately match these parameter constraints. We find that the model is robust to such perturbations. We study the effects of degeneracy on the perturbations and find that the induced changes differ greatly from the non-degenerate case. We also model inelastic collisions that result in particle loss or condensate decay as external perturbations and use this formalism to examine the effects of three-body recombination and background collisions.
We investigate the entanglement characteristics of two general bimodal Bose-Einstein condensates---a pair of tunnel-coupled Bose-Einstein condensates and the atom-molecule Bose-Einstein condensate. We argue that the entanglement is only physically meaningful if the system is viewed as a bipartite system, where the subsystems are the two modes. The indistinguishibility of the particles in the condensate means that the atomic constituents are physically inaccessible and, thus, the degree of entanglement between individual particles, unlike the entanglement between the modes, is not experimentally relevant so long as the particles remain in the condensed state. We calculate the entanglement between the two modes for the exact ground state of the two bimodal condensates and consider the dynamics of the entanglement in the tunnel-coupled case.
We discuss the dynamics of Bose-Einstein condensates in a double-well potential subject to decoherence (or particle loss). Starting from the full many-body dynamics described by the master equation, an effective Gross-Pitaevskii-like equation is derived in the mean-field approximation. By numerically solving the GP equation, we find that macroscopic quantum self-trapping disappears for strong decoherence, while generalized self-trapping occurs under weak decoherence. The fixed points have been calculated, and we find that an abrupt change from elliptic to an attractor and a repeller occurs, reflecting the metastable behavior of the system around these points.
We introduce a microscopic computation which shows that the Hamiltonian of a Bose-Einstein Condensate can be analytically solved in the two-mode approximation, in particular, in the case of an asymmetric double-well condensate in the dilute regime. Our model is exactly diagonalisable when the overlap of the quasilocalized modes in each well is small enough with respect to the trap asymmetry. For larger overlaps or highly symmetric traps, our diagonalisable Hamiltonian acquires extra terms that we treat within perturbation theory.