Quantum Heat Engine With Multi-Level Quantum Systems
  By reformulating the first law of thermodynamics in the fashion of quantum-mechanical operators on the parameter manifold, we propose a universal class of quantum heat engines (QHE) using the multi-level quantum system as the working substance. We obtain a general expression of work for the thermodynamic cycle with two thermodynamic adiabatic processes, which are microscopically quantum adiabatic processes. We also classify the conditions for a 3-level QHE to extract positive work from a heat bath. Our result is counter-intuitively different from that of a 2-level system. As a more realistic illustration, a 3-level atom system with dark state configuration manipulated by classical light is used to demonstrate our central idea. 
H. T. Quan, P. Zhang and C. P. Sun