Linear Light Amplifier and Amplification of N-Photon States

We consider a linear quantum amplifier consisting of NA two-level atoms and study the problem of amplification of N-photon states. The N-photon states are associated with N-quantum states of the harmonic oscillator. We show that the process of interaction of the electromagnetic field with atoms can be associated with some transformation of the phase space and functions defined on this phase space. We consider the Husimi functions QN(q, p) of N-quantum states of the harmonic oscillator, which are defined on the phase space, investigate transformation of these functions, and find an explicit form of the density matrix of the amplified N-photon state. © 2019, Springer Science+Business Media, LLC, part of Springer Nature