Measuring trajectories of environmental noise

Abstract: In classical mechanics, a natural way to simplify a many-body problem is to ``replace'' some of the elements of the composite system with surrogate \textit{force fields}. In the realm of quantum mechanics, however, such a description is rarely compatible with the formalism of the theory. Nevertheless, the quantum version of external field models---the so-called \textit{noise representations}---can be employed in certain circumstances. The mathematics behind these models indicate that the appearing fields typically exhibit random fluctuations, hence, the name \textit{noise field} is more apt. In principle, measuring a classical force field is a trivial task; all that is needed is a probe equipped with an accelerometer that can be moved around while taking the measure of forces that affect it. Unfortunately, an analogous method cannot work in the quantum case. As indicated by the theory, the result of any measurement performed on the quantum system affected by a noise field always appears as an average over fluctuations, therefore, it is impossible to observe the noise fluctuations by measuring the state of the probe. Here, we demonstrate that this limitation can be circumvented and that it is possible to expose the noise field fluctuations to direct observation. This allows one to sample the noise trajectories (stochastic realizations), store them, and later use them to simulate the dynamics of open quantum systems affected by the noise.