Quantum fluctuations in atomic Josephson junctions: the role of dimensionality

We investigate the role of quantum fluctuations in the dynamics of a bosonic Josephson junction in \(D\) spatial dimensions, by using beyond mean-field Gaussian corrections. We derive some key dynamical properties in a systematic way for \(D=3, 2, 1\). In particular, we compute the Josephson frequency in the regime of low population imbalance. We also obtain the critical strength of the macroscopic quantum self-trapping. Our results show that quantum corrections increase the Josephson frequency in spatial dimensions \(D=2\) and \(D=3\), but they decrease it in the \(D=1\) case. The critical strength of macroscopic quantum self-trapping is instead reduced by quantum fluctuations in \(D=2\) and \(D=3\) cases, while it is enhanced in the \(D=1\) configuration. We show that the difference between the cases of D = 2 and D = 3 on one side, and D = 1 on the other, can be related to the qualitatively different dependence of the interaction strength on the scattering length in the different dimensions.