Quantum thermodynamics under observation: The influence of periodic quantum measurements

Abstract

Within a quantum-thermodynamical approach a single subsystem can be shown to relax to a thermal state if appropriately embedded in a quantum environment. This picture appears to be at variance with the foundations of statistical mechanics, according to which thermal properties emerge either as a long-time or ensemble average. Here we argue that periodic measurements on the environment may establish the missing link: we consider a two-level system (TLS) coupled to an environment consisting of many spins, the magnetization of which is measured periodically. These measurements destroy system-environment correlations and influence the state of the TLS due to so-called co-jumps, which lead to quasi-classical trajectories for the TLS. We derive an analytical solution for the ensemble-averaged attractor state reached after many measurements. Reinterpreting the setup as an indirect measurement process for the TLS also sheds new light on the properties of such periodic indirect measurements.