We investigate the energy structures and the dynamics of a Bose-Einstein condensates (BEC) in a triple-well potential coupled a high finesse optical cavity within a mean field approach. Due to the intrinsic atom-cavity field nonlinearity, several int
eresting phenomena arise which are the focuses of this work. For the energy structure, the bistability appears in the energy levels due to this atoms-cavity field nonlinearity, and the same phenomena can be found in the intra-cavity photons number. With an increase of the pump-cavity detunings, the higher and lower energy levels show a loop structure due to this cavity-mediated effects. In the dynamical process, an extensive numerical simulation of localization of the BECs for atoms initially trapped in one-, two-, and three-wells are performed for the symmetric and asymmetric cases in detail. It is shown that the the transition from oscillation to the localization can be modified by the cavity-mediated potential, which will enlarge the regions of oscillation. With the increasing of the atomic interaction, the oscillation is blocked and the localization emerges. The condensates atoms can be trapped either in one-, two-, or in three wells eventually where they are initially uploaded for certain parameters. In particular, we find that the transition from the oscillation to the localization is accompanied with some irregular regime where tunneling dynamics is dominated by chaos for this cavity-mediated system.
The transmission spectrum of two dipole-dipole coupled atoms interacting with a single-mode optical cavity in strong coupling regime is investigated theoretically for the lower and higher excitation cases, respectively. The dressed states containing
the dipole-dipole interaction (DDI) are obtained by transforming the two-atom system into an effective single-atom one. We found that the DDI can enhance the effects resulting from the positive atom-cavity detunings but weaken them for the negative detunings cases for lower excitation, which can promote the spectrum exhibiting two asymmetric peaks and shift the heights and the positions of them. For the higher excitation cases, DDI can augment the atomic saturation and lead to the deforming of the spectrum. Furthermore, the large DDI can make the atom and the cavity decouple, making a singlet of the normal-mode spectrum.
