Measuring work in quantum many-body systems using a dynamical "work agent"

We consider a generic quantum many-body system initiated at thermal equilibrium and driven by an external parameter, and discuss the prospect for measuring the work done by the varying parameter on the system. While existing methods are based on a full control of the system's Hamiltonian and are thus limited to few-level quantum systems, measuring work in many-body quantum systems remains challenging. Our approach relies on transforming the external parameter into a dynamical ``work agent", for which we consider an harmonic oscillator in a semiclassical coherent state with a large photon number. We define a work generating function which coincides with the standard two-point measurement protocol for work measurement in the limit of a large photon number. While \emph{in principle} it allows to relate the moments of work $\langle W^n \rangle$ to observables of the work agent, we focus on the average work, which is obtained from energy conservation by the change of the energy of the agent, which can be measured using photon number detection. We illustrate this concept on a transmon-microcavity system, which displays various quantum coherent effects including Landau-Zener St\"{u}kelberg interference and collapse and revival of Rabi oscillations. We discuss how our setup allows to measure work in a variety of quantum many-body systems.