Efficiency at maximum power of quantum-mechanical Carnot engine enhanced by energy quantization

In an adiabatic process, the change in energies of select states may be inhomogenously scaled due to energy quantization. To illustrate this, we introduce a delta barrier turning up (turning down) in an adiabatic expansion (compression). We consider a quantum-mechanical Carnot engine employing a single particle confined in an infinite potential, assuming only the lowest two energy levels to be occupied. This cyclic engine model consists of two isoenergetic strokes where the system is alternatively coupled to two energy baths, and two adiabatic processes where the potential is adiabatically deformed with turning up or down a delta barrier. Having obtained the work output and efficiency, we analyze the efficiency at maximum power under the assumption that the potential moves at a very slow speed. We show that the efficiency at maximum power can be enhanced by energy quantization.