Critical point behaviour of a measurement-based quantum heat engine

At the critical point (CP), pertaining to quantum phase transition (QPT), the long-range quantum correlation (e.g., entanglement) becomes dominant. We show, in case of an ion-based quantum Otto engine, that such correlation does not necessarily enhance the efficiency of the engine, in the neighborhood of the CP. We choose two trapped ions as the working system, subject to a magnetic field and an internal energy-exchange coupling J₁. During the expansion stage of the engine cycle, the adiabatic decrease of the magnetic field from B_H to B_L leads to certain work. The cooling of the system during the exhaust stage is mimicked by a projective measurement of the system into the ground state. During the compression stage, the magnetic field is adiabatically restored to B_H. We find that the critical point B_L=J₁/2 poses as a minimum threshold for the system to work as a heat engine. Further, the efficiency of the engine increases with increase of the interaction strength J₁. On the contrary, the coupling to any ancillary system deteriorates the efficiency at the critical point, though such coupling enhances entanglement into the system. Our result suggests that long-range correlation may not be beneficial for an efficient quantum heat engine in the realm of QPT.