Quantum fields in a cold atomic simulator: relaxation and phase locking in tunnel-coupled 1D bosonic quasi-condensates

We consider a prime example of simulating interacting relativistic QFT with cold atoms: the realisation of the sine-Gordon model by tunnel-coupled quasi-1D Bose gases. While experiments have shown that it can realise the sine-Gordon model in equilibrium, studies of non-equilibrium dynamics have revealed a phase-locking behaviour that stands in contrast to predictions from sine-Gordon field theory. Here, we examine a one-dimensional field-theoretic model of the system and find that the phase-locking behaviour can be understood in terms of the presence of the longitudinal harmonic trap, and that the additional degrees of freedom known to be present in the experiment do not appear to play a significant role. Therefore, the experimental setup provides a good simulator of the sine-Gordon quantum field theory, even out of equilibrium, if the inhomogeneous background induced by the trap is taken into account. Furthermore, our results support the idea that modifying the longitudinal trap to a box shape should result in agreement with standard sine-Gordon dynamics. The main remaining open issues are to account for 3D corrections and model the effect of the boundaries.