Critical transport across a finite temperature bosonic Josephson junction : resistive superflow dynamics, vortex ring generation and thermal damping

Abstract

A Josephson junction consists of two-weakly coupled quantum fluids through a barrier and is an ideal environment for studying coherent quantum transport and its breakdown due to dissipation, depending on whether or not the superfluid velocity exceeds a critical value. Motivated by a recent experiment with 6Li (in the Bose-Einstein condensation limit) at LENS (Florence), in this thesis we firstly characterised the dynamical regimes observed experimentally for an elongated three-dimensional bosonic Josephson junction: the coherent dynamics Josephson ‘plasma’ oscillations regime and the dissipative one. Our analysis is based on both zero-temperature mean-field theory (Gross-Pitaevskii equation), and its finite temperature kinetic theory generalisation, in which the condensate is coupled to a dynamical thermal cloud, described by a quantum Boltzmann equation (Zaremba Nikuni-Griffin method), and reveals excellent agreement with experimental findings. Secondly, we showed a direct connection between resistive superfluid current and vortex ring (VR) nucleation, through the mechanism of phase slips, thus demonstrating a close analogy with the phase-slippage phenomenon in superfluid helium. Specifically, we identify the origin of dissipation as the transfer of the incompressible kinetic energy from the axial flow to the VR swirling flow, and the phonon emission during vortex propagation. Performing a detailed study of the VR dynamics in our three-dimensional inhomogeneous superfluid, we highlighted the role of trap asymmetry on the emergence of elliptical VRs exhibiting Kelvin wave excitations. The dissipation due to relative condensate-thermal motion (at fixed condensate number, well below the transition temperature) was found to have no effect at early times but it becomes relevant at longer timescales, affecting both the oscillatory relative population dynamics and the VR dynamics. Exploring a wider range of barrier heights/widths beyond the experimental parame ters, we constructed an extended phase diagram for the elongated trap, including –beyond Josephson ‘plasma’ and dissipative regimes discussed above – also the expected Macro scopic Quantum Self-Trapping regime. Confirmation of the emergence of an analogous phase diagram in a spherical trap, demonstrates unequivocally that all three regimes should be observable in carefully-tailored ultracold experiments. Studying the role of finite temperature, we distinguished two regimes: at relatively low temperatures, where condensate mean field dynamics dominates, the relative population imbalance oscillates with two main frequencies: in this regime, the thermal cloud is driven by the condensate, with its presence damping the condensate motion and decreasing its frequency. However, when the temperature becomes such that the thermal cloud mean ki netic energy exceeds the barrier height, the thermal cloud oscillates with its own frequency, and begins to drive the condensate, significantly affecting its observable dynamics.