Pokrovsky-Talapov transition with two Ramsey-tunnel-coupled 1D-Bose gases

The high flexibility of ultracold atoms allows for the design, control and investigation of quantum matter. In this work we consider two one-dimensional Ramsey tunnel-coupled Bose gases and show that the low-energy effective theory of this system is described by the quantum Prokrovsky-Talapov model. We study the ground state with variational wave-functions and elaborate on the modification of the quantum phase transition due to a finite system size. Finally, we consider the non-equilibrium evolution determined by quench from an uncoupled Bose gases to the Ramsey tunnel coupled case and predict the experimental relevant evolution of phase correlations.