  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.
