Prospect for measuring work statistics in quantum coherent systems

Abstract: Quantum thermodynamics is concerned with heat and work exchange between a quantum coherent system and heat reservoirs or work agents. In stochastic thermodynamics a key object of interest is the statistics of these quantities, but it is notoriously difficult to measure it in general systems. Here we discuss the prospect for measuring work statistics in electronic devices, via a study of a transmon-microcavity system. The microwave cavity acts as a work agent, exchanging work with the transmon. We formulate a protocol to measure the first moments of work $\langle W^n \rangle$ via photon number detection. We find conditions for capturing quantum coherence in the work statistics. Interestingly, by measuring higher moments one can verify the Jarzynski equality $\langle e^{-W/T} \rangle = 1$ including quantum interference. Our work opens a way for measuring work statistics in nontrivial quantum systems.