We analyze the effects of 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 visibility and the fluctuation of the on-site occupation number and study them as functions of temperature. We show that, contrary to naive expectations, when the boson–boson interaction is suitably chosen thermal effects can increase the coherence visibility and reduce the on-site number fluctuation.
Bosonic Josephson junctions can be realized by confining ultracold gases of bosons in multiwell traps and studied theoretically with the
M-site Bose-Hubbard model. We show that canonical equilibrium states of the
M-site Bose-Hubbard model may be approximated by mixtures of coherent states, provided the number of atoms is large and the total energy is comparable to
kBT. Using this approximation, we study thermal fluctuations in bosonic Josephson junctions in the mean-field regime. Statistical estimates of the fluctuations of relative phase and number, obtained by averaging over many replicates of an experiment, can be used to estimate the temperature and the tunneling parameter or to test whether the experimental procedure is effectively sampling from a canonical thermal equilibrium ensemble.
We investigate the finite-temperature properties of a bosonic Josephson junction composed of N interacting atoms confined by a quasi-one-dimensional asymmetric double-well potential, modeled by the two-site Bose-Hubbard Hamiltonian. We compute numerically the spectral decomposition of the statistical ensemble of states, the thermodynamic and entanglement entropies, the population imbalance, the quantum Fisher information, and the coherence visibility. We analyze their dependence on the system parameters, showing in particular how finite temperature and on-site energy asymmetry affect the entanglement and coherence properties of the system. Moreover, starting from a quantum phase model which accurately describes the system over a wide range of interactions, we develop a reliable description of the strong tunneling regime, where thermal averages may be computed analytically using a modified Boltzmann weight involving an effective temperature. We discuss the possibility of applying this effective description to other models in suitable regimes.