Quantum heat engines and refrigerators

A quantum heat engine is a device that generates power from the heat flow between hot and cold reservoirs. The operation mechanism of the engine can be described by the laws of quantum mechanics. The first realization of a quantum heat engine was pointed out by Scovil and Schulz-DuBois in 1959, showing the connection of efficiency of the Carnot engine and the 3-level maser. Quantum refrigerators share the structure of quantum heat engines with the purpose of pumping heat from a cold to a hot bath consuming power first suggested by Geusic, Schulz-DuBois, De Grasse and Scovil. When the power is supplied by a laser the process is termed optical pumping or laser cooling, suggested by Wineland and Hänsch. Surprisingly heat engines and refrigerators can operate up to the scale of a single particle thus justifying the need for a quantum theory termed quantum thermodynamics. The three-level-amplifier is the template of a quantum device. It operates by employing a hot and cold bath to maintain population inversion between two energy levels which is used to amplify light by stimulated emission The ground state level (1-g) and the excited level (3-h) are coupled to a hot bath of temperature . The energy gap is . When the population on the levels equilibrate where is the Planck constant and is the Boltzmann constant. The cold bath of temperature couples the ground (1-g) to an intermediate level (2-c) with energy gap . When levels 2-c and 1-g equilibrate then The device operates as an amplifier when levels (3-h) and (2-c) are coupled to an external field of frequency . For optimal resonance conditions . The efficiency of the amplifier in converting heat to power is the ratio of work output to heat input: Amplification of the field is possible only for positive gain (population inversion) This is equivalent to . Inserting this expression into the efficiency formula leads to: where is the Carnot cycle efficiency. Equality is obtained under a zero gain condition .