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We use the Bose-Hubbard Hamiltonian to study quantum fluctuations in canonical equilibrium ensembles of bosonic Josephson junctions at relatively high temperatures, comparing the results for finite particle numbers to the classical limit that is attained as $N$ approaches infinity. We consider both attractive and repulsive atom-atom interactions, with especial focus on the behavior near the T=0 quantum phase transition that occurs, for large enough $N$, when attractive interactions surpass a critical level. Differences between Bose-Hubbard results for small $N$ and those of the classical limit are quite small even when $N sim 100$, with deviations from the limit diminishing as 1/N.
We investigate the dynamics of bosonic atoms in elongated Josephson junctions. We find that these systems are characterized by an intrinsic coupling between the Josephson mode of macroscopic quantum tunneling and the sound modes. This coupling of Jos
We extend a recent method to shortcut the adiabatic following to internal bosonic Josephson junctions in which the control parameter is the linear coupling between the modes. The approach is based on the mapping between the two-site Bose-Hubbard Hami
We calculate the first two moments and full probability distribution of the work performed on a system of bosonic particles in a two-mode Bose-Hubbard Hamiltonian when the self-interaction term is varied instantaneously or with a finite-time ramp. In
We analyze the effects of the temperature on a bosonic Josephson junction realized with ultracold and dilute atoms in a double-well potential. Starting from the eigenstates of the two-site Bose-Hubbard Hamiltonian, we calculate the coherence visibili
We analyze phase interferometry realized with a bosonic Josephson junction made of trapped dilute and ultracold atoms. By using a suitable phase sensitivity indicator we study the zero temperature junction states useful to achieve sub shot-noise prec