Dynamics of an atomic Bose-Einstein condensation interacting with a laser field in a double-well potential

For the case of an atomic Bose-Einstein condensate formed in a symmetrical double-well potential with well-separated minima, the dynamics of Bose-condensed atoms interacting with a single-mode quantized traveling-wave laser field are investigated in detail. By considering the system consisting of the Bose-condensed atoms and laser field with and without dissipation the eigenstates and eigenvalues of the corresponding Hamiltonian for both cases are obtained. The time development of the Bose-condensed state plays a major role in the discussion. It is shown that the probability of finding all atoms in the Bose-condensed state displays an undamped oscillatory behavior in the absence of dissipation and a damped oscillatory behavior in the presence of dissipation. Moreover, it is found that the tunneling effect can increase the oscillatory frequency among the dressed bosonic states and affect the dynamics of the system. As an application of these results, a characteristic time that may be used to evaluate the number of condensed atoms is introduced.