Universal Rephasing Dynamics after a Quantum Quench via Sudden Coupling of Two Initially Independent Condensates

We consider a quantum quench in which two initially independent condensates are suddenly coupled, and study the subsequent "rephasing" dynamics. For weak couplings, the time-evolution of physical observables is predicted to follow universal scaling laws, connecting the short-time dynamics to the long-time non-perturbative regime. We first present a two-mode model valid in two and three dimensions and then move to one dimension, where the problem is described by a gapped Sine-Gordon theory. Combining analytical and numerical methods, we compute universal time-dependent expectation values, allowing a quantitative comparison with future experiments.