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 in physics including condensed matter, quantum optics and ultracold atom to reveal non-classical states of the systems. So far, such analysis mostly focused on systems in equilibrium. In this paper, we show that quantum noise is also a useful tool to characterize and study the non-equilibrium dynamics of one dimensional system. We consider the Ramsey sequence of one dimensional, two-component bosons, and obtain simple, analytical expressions of 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 one dimensional quasi-condensates created from a single condensate through splitting. Using the tools developed in this paper, we demonstrate that one dimensional dynamics in these systems exhibits the phenomenon known as "prethermalization", where the observables of {\it non-equilibrium}, long-time transient states become indistinguishable from those of thermal {\it equilibrium} states.