We theoretically investigate a bosonic Josephson junction by using the path-integral formalism with relative phase and population imbalance as dynamical variables. Starting from a Lagrangian of a Bose Josephson junction, we derive an action only in terms of relative phase by performing functional integration over the population imbalance. We then analyze the quantum only-phase action, which formally contains all of the quantum corrections. To the second order in the derivative expansion and to the lowest order in $\hbar$, we finally obtain the quantum correction to the Josephson frequency of oscillation in the Josephson regime . The identical quantum correction is found also by adopting an alternative approach. While the estimated quantum correction to the Josephson frequency is relatively small based on current experimental setups, we expect that the correction can be significant by appropriately tuning some parameters such as the onsite interaction strength in an atomic Josephson junction or the capacitance in a superconducting Josephson circuit. Our predictions would be a useful theoretical tool for experiments with atomic or superconducting Josephson junctions.
 K. Furutani, J. Tempere, and L. Salasnich, Phys. Rev. B 105, 134510 (2022).
|Presenter name||Koichiro Furutani|
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