In this paper, a quantum theory of an inversionless laser is presented
. The gain medium is considered to consist of three-level atoms in a c
losed LAMBDA configuration, with a lower-level microwave coupling. By
deriving an equation of motion for the reduced density matrix for the
two modes of the field, gain and diffusion are studied. In particular,
two mechanisms through which inversionless amplification takes place
in the context of this model, namely, the suppression of absorption an
d mode coupling, are discussed. Stable conditions for inversionless am
plification and the attendant phase diffusion are discussed and a comp
arison is made with conventional, inversion-based lasers. It is shown
that lasing without inversion does not necessarily result in a reduced
linewidth compared to a conventional laser.