Ergotropic advantage in a measurement-fueled quantum heat engine

Abstract

This paper investigates a coupled two-qubits heat engine fueled by generalized measurements of the spin components and using a single heat reservoir as sink. Our model extends the proposal of Yi and coworkers [Phys. Rev. E {\bf 96}, 022108 (2017)] where the role of a hot reservoir in a four-stroke cycle was replaced by a quantum measurement apparatus, the other steps being two quantum adiabatic strokes and thermalization with a cold reservoir. We propose a five-stroke cycle, where an ergotropy extracting stroke is introduced following the measurement stroke, and study the effect of measurements of different spin components on the performance of the machine. For measurements along z-z directions, we find two possible occupation distributions that yield an active state and the ergotropic stroke improves the performance of the engine over the four-stroke cycle. Further, the three-stroke engine ( {without the adiabatic strokes}) yields the same performance as the five-stroke engine. For arbitrary working medium and non-selective measurements, we prove that the total work output of a five-stroke engine is equal to the sum of the work outputs of the corresponding four-stroke and three-stroke engines. For measurement directions other than z-z, there may be many possible orderings of the post-measurement probabilities that yield an active state. However, as we illustrate, for specific cases (e.g. x-x), a definite ordering may be obtained with the projective measurements. Thus, we find that the five-stroke engine exploiting ergotropy outperforms both its four-stroke as well as three-stroke counterparts.