Quantum fluctuations in atomic Josephson junctions: the role of dimensionality

In this thesis we investigate the role of quantum fluctuations in atomic Josephson junctions in dimension D=1,2,3. In particular, we study the impact of these fluctuations on two key quantities: the Josephson frequency and the critical strength of macroscopic quantum self-trapping. Initially, we investigate the inter-atomic potential in the s-wave scattering approximation, exploring the relationship between contact and finite-range coupling constants with the s-wave scattering length and the effective range in dimensions D=1,2,3. In the second chapter, we illustrate the mean-field behavior of Josephson junction systems and the calculation of key parameters, namely the Josephson frequency and the critical strength of macroscopic quantum self-trapping (MQST). After that, we present the derivation of quantum fluctuations correction to the grand potential of a bosonic system considering also a finite range term in the potential. This is done systematically for a system of dimension D=1,2,3. Finally, in the last two chapters, we investigate the effects of quantum fluctuations on the Josephson frequency and the critical strength of macroscopic quantum self-trapping beyond the mean-field approximation, respectively with and without finite range correction to the potential. Our main findings reveal that, when compared to the mean-field Josephson frequency, the Josephson frequency is higher in 2D and 3D, while it is lower in 1D. On the other hand, the MQST critical strength is higher in 1D and lower in 2D and 3D. These results highlight the crucial role of quantum fluctuations in determining the properties of atomic Josephson junctions and show that the behavior of these systems is different in different dimensions.