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Computer Physics Communications

A numerical study of the ground state and dynamics of atomic–molecular Bose–Einstein condensates

Wei Jiang, Hanquan Wang, Xiang‐Gui Li

Published Jun 10, 2013• 4 citations
Publisher
DOI
10.1016/j.cpc.2013.05.024

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We study the exact solution for a two-mode model describing coherent coupling between atomic and molecular Bose–Einstein condensates (BEC), in the context of the Bethe ansatz. By combining an asymptotic and numerical analysis, we identify the scaling behaviour of the model and determine the zero temperature expectation value for the coherence and average atomic occupation. The threshold coupling for production of the molecular BEC is identified as the point at which the energy gap is minimum. Our numerical results indicate a parity effect for the energy gap between ground and first excited state depending on whether the total atomic number is odd or even. The numerical calculations for the quantum dynamics reveals a smooth transition from the atomic to the molecular BEC.
We study the effect of atom-molecule internal tunneling on the ground state of atom-molecule Bose-Einstein condensates in a double-well potential. In the absence of internal tunneling between atomic and molecular states, the ground state is symmetric, which has equal-particle populations in two wells. From the linear stability analysis, we show that the symmetric stationary state becomes dynamically unstable at a certain value of the atom-molecule internal tunneling strength. Above the critical value of the internal tunneling strength, the ground state bifurcates to the particle-localized ground states. The origin of this transition can be attributed to the effective attractive interatomic interaction induced by the atom-molecule internal tunneling. This effective interaction is similar to that familiar in the context of BCS-BEC crossover in a Fermi gas with Feshbach resonance. Furthermore, we point out the possibility of reentrant transition in the case of the large detuning between the atomic and molecular states.