Squeezed states of light in a cavity with a local two-photon absorber

Squeezed states of light are theoretically investigated in a system with a locally placed two-photon absorption medium. We assume that the two-photon absorption process is caused by elementary excitations in the medium (such as biexcitons). Many eigenmodes of photons and those of the elementary excitations are taken into account because of the locality of the absorber. Multi-mode Wigner functions are defined and used for representation of the density operator of the electromagnetic field. The Wigner functions exhibit multi-variable Gaussian distribution and the quantum states of photons are multi-mode quadrature squeezed states. We also discuss effects on squeezing due to detuning of the incident light, the size of the medium, the position of a photo-detector, and damping rates of photons and the elementary excitations.