Abstract
We present a detailed analysis of the relaxation dynamics in an extended bosonic Josephson junction. We show that stochastic classical field simulations using Gross-Pitaevskii equations in three spatial dimensions reproduce the main experimental findings of M. Pigneur et al., Phys. Rev. Lett. 120, 173601 (2018). We give an analytic solution describing the short time evolution through multimode dephasing. For longer times, the observed relaxation to a phase locked state is caused by nonlinear dynamics beyond the sine-Gordon model, induced by the longitudinal confinement potential and persisting even at zero temperature. Finally, we analyze different experimentally relevant trapping geometries to mitigate these effects. Our results provide the basis for future experimental implementations aiming to study nonlinear and quantum effects of the relaxation in extended bosonic Josephson junctions.
Highlights
The Josephson effect is a prominent example for the manifestation of macroscopic quantum effects
We gave a detailed discussion of the rich nonlinear dynamics in inhomogeneous extended bosonic Josephson junctions
The short time behavior was well described through the sineGordon model, i.e., the low-energy effective theory for the antisymmetric degrees of freedom of two tunnel-coupled onedimensional superfluids
Summary
The Josephson effect is a prominent example for the manifestation of macroscopic quantum effects. Increased interest over the last decades has been on its application to atomic systems, where two-body interactions enrich the dynamical behavior This has led to a number of ongoing theoretical and experimental studies, from fermionic superfluids [3], macroscopic quantum self trapping [4,5], bosonic Josephson junctions [6,7,8,9,10,11], to different geometries [12,13] from small to extended junction arrays. We show that nonlinear dynamics beyond the sine-Gordon model causes the relaxation of the system to the observed phase-locked state We find this effect to persist even at zero temperature, which highlights the importance of understanding the relevance of classical nonlinear dynamics of thermally fluctuating fields when analyzing complex quantum many-body systems.
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