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Phase-locking transition of coupled low-dimensional superfluids

We study the phase-locking transition of two coupled low-dimensional superfluids, either two-dimensional superfluids at finite temperature, or one-dimensional superfluids at zero temperature. We find that the superfluids have a strong tendency to phase-lock. The phase-locking is accompanied by a sizeable increase of the transition temperature $T_{c}$ (in 2D systems) of the resulting double-layer superfluid to thermal Bose gas transition, compared to the Kosterlitz-Thouless temperature $T_{KT}$ of the uncoupled 2D systems, which suggests a plausible way of observing the Kibble-Zurek mechanism in two-dimensional cold atom systems by rapidly varying the tunneling rate between the superfluids. If there is also interaction between atoms in different layers present we find additional phases, while no sliding phase, characterized by order or quasi long range order (QLRO) either in the symmetric or the antisymmetric sector of the system.