We explore the dependence of the performance bounds of heat engines andrefrigerators on the initial quantum state and the subsequent evolution oftheir piston, modeled by a quantized harmonic oscillator. Our goal is toprovide a fully quantized treatment of self-contained (autonomous) heatmachines, as opposed to their prevailing semiclassical description thatconsists of a quantum system alternately coupled to a hot or a cold heat bath,and parametrically driven by a classical time-dependent piston or field. Hereby contrast, there is no external time-dependent driving. Instead, theevolution is caused by the stationary simultaneous interaction of two heatbaths (having distinct spectra and temperatures) with a single two-level systemthat is in turn coupled to the quantum piston. The fully quantized treatment we put forward allows us to investigate workextraction and refrigeration by the tools of quantum-optical amplifier anddissipation theory, particularly, by the analysis of amplified or dissipatedphase-plane quasiprobability distributions. Our main insight is that quantumstates may be thermodynamic resources and can provide a powerful handle, orcontrol, on the efficiency of the heat machine. In particular, a pistoninitialized in a coherent state can cause the engine to produce work at anefficiency above the Carnot bound in the linear amplification regime. In therefrigeration regime, the coefficient of performance can transgress the Carnotbound if the piston is initialized in a Fock state. The piston may be realizedby a vibrational mode, as in nanomechanical setups, or an electromagnetic fieldmode, as in cavity-based scenarios.
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