Abstract
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, long-time transient states become indistinguishable from those of thermal equilibrium states.
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GENERAL SCIENTIFIC SUMMARY Introduction and background. Understanding the non-equilibrium dynamics of many-body quantum systems is one of the most important problems in physics. It is crucial for understanding fundamental problems such as decoherence and equilibration, as well as developing future quantum technologies such as quantum computers. Yet it presents significant challenges; not only is it difficult to theoretically understand and compute the time evolution of the systems, there is also no general approach known to characterize the resulting states, such as the analogue of order parameters in equilibrium systems.
Main results. In this paper, we analytically study two types of dynamics in one dimension. One is the Ramsey sequence of one-dimensional, two-component bosons and the other is the evolution of interference patterns between two one-dimensional quasi-condensates created from a single condensate through splitting. A novel approach we employ is the characterization of the many-body states through quantum noise, i.e. the distributions of measurement results for an observable, such as spins and interference patterns. We show that the full distributions capture the unique features of one-dimensional dynamics in an intuitive, visual fashion. Moreover, our analysis through quantum noise reveals the phenomenon of prethermalization in these dynamics, where a non-equilibrium state reaches a thermal-like steady state in a time scale much shorter than a true equilibration time.
Wider implications. The characterization of quantum many-body dynamics through noise distributions demonstrated in this work provides a powerful approach to studying non-equilibrium many-body systems. Moreover, prethermalization predicted in the one-dimensional dynamics provides an intriguing alternative path for the equilibration process, which can be directly probed by the full distribution functions of quantum noise.
Figure. Time evolution of the distribution functions for spins in the x–y plane for Ramsey dynamics as a function of integration length, which controls the strength of fluctuations. For short integration length (left), the fluctuations of the spins are small, leading to larger magnitudes of spins. For longer integration length (right), the strong fluctuations of the spins in one-dimensional systems destroy the spin coherence and the magnitude of spins diminishes in time.