Quantum simulation of expanding space-time with tunnel-coupled condensates

We consider two weakly interacting quasi-1D condensates of cold bosonic atoms. It turns out that a time-dependent variation of the tunnel-coupling between those condensates is equivalent with the spatial expansion of a one-dimensional toy-Universe with regard to the dynamics of the relative phase field. The dynamics of this field is governed by the quantum sine-Gordon equation. Thus, this analogy could be used to 'quantum simulate' the dynamics of a scalar, interacting quantum field on an expanding background. We discuss, how to observe the freezing out of quantum fluctuations during an accelerating expansion in a possible experiment. We also discuss an experimental protocol to study the formation of sine-Gordon breathers in the relative phase field out of quantum fluctuations.