  As a quantum device, a quantum heat engine (QHE) is described by a Hermitian
Hamiltonian.However, since it is an open system, reservoirs have to be imposed
phenomenologically without any description in the context of quantum mechanics.
A non-Hermitian system is expected to describe an open system which exchanges
energy and particles with external reservoirs. Correspondingly,such an exchange
can be adiabatic in the context of quantum mechanics. We first propose a
non-Hermitian QHE by a concrete simple two-level system, which is an S = 1/2
spin in a complex external magnetic field. The non-Hermitian PT -symmetric
Hamiltonian, as a self-contained one,describes both working medium and
reservoirs. A heat-engine cycle is composed of completely quantum adiabatic
processes. Surprisingly, the heat efficiency is obtained to be the same as that
of Hermitian quantum Otto cycle. A classical analogue of this scheme is also
presented. Our finding paves the way for revealing what the role of a
non-Hermitian Hamiltonian plays in physics.
