The dynamics and prethermalization of one-dimensional quantum systems probed through the full distributions of quantum noise

Quantum noise correlations have been employed in several areas of physics, including condensed matter, quantum optics and ultracold atoms, to reveal the non-classical states of the systems. To date, such analyses have mostly focused on systems in equilibrium. In this paper, we show that quantum noise is also a useful tool for characterizing and studying the non-equilibrium dynamics of a one-dimensional (1D) system. We consider the Ramsey sequence of 1D, two-component bosons, and obtain simple, analytical expressions for time evolutions of the full distribution functions for this strongly correlated, many-body system. The analysis can also be directly applied to the evolution of interference patterns between two 1D quasi-coindensates created from a single condensate through splitting. Using the tools developed in this paper, we demonstrate that 1D dynamics in these systems exhibits the phenomenon known as 'prethermalization', where the observables of non-equilibrium, longtime transient states become indistinguishable from those of thermal equilibrium states.