Two-qubit charger-battery system subject to weak, continuous measurements with quantum point contacts

Abstract Quantum batteries modeled as two-qubit systems coupled to Markovian thermal reservoirs have been shown to benefit from measurement-assisted charging, where projective measurements enhance the charging rate at an infinite thermodynamic resource cost. In this work, we consider weak, continuous measurements implemented via quantum point contact detectors (QPCs), which enhance the charging rate at a definite and quantifiable resource cost. We analyze three measurement configurations, namely, a single QPC, two independent QPCs, and a series-coupled (coherent) two- QPC scheme, and study their effect on the peak transient charging rate, defined as the rate of energy flow from the charger qubit to the battery qubit, relative to the unmeasured baseline. We find that the charging rate enhancement is non-monotonic as a function of the temperature and potential gradients required to drive the QPCs, exhibiting a plateau of near-optimal enhancement. Comparing the three configurations, the plateau of optimal enhancement contracts toward lower temperature and chemical potential for both cases with two QPCs compared to the single-QPC case. The coherent measurement further shows a lowering of the resource requirement relative to the two-independent-QPC case for achieving the same enhancement. The hierarchy is coherent > two independent QPCs > single QPC with respect to both the magnitude of the peak transient charging rate enhancement and the minimization of measurement cost which is quantified in terms of the operating point of the detector.