Quantum noise thermometry for bosonic Josephson junctions in the mean-field regime

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 $k_{B}T$. 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.

Figure 1

Coherence factor $\alpha$ vs temperature for several values of $\Lambda =N^2{E}_C/4E_J$ (logarithmic scale).

Figure 2

Variance of the normalized population imbalance $⟨{\widehat{z}}^2⟩$ vs temperature for various values of $\Lambda =N^2{E}_C/4E_J$. The gray dashed lines indicate the “low temperature” approximation (15).