Squeezing enhancement for the light interacting with a polarizable confined system

Abstract

With the development of crystal growth technologies, it has become possible to investigate cavity embedded interacting electron systems [l]. The quantum well exciton-cavity system has some fundamental differences with respect to the much simpler two level atom-single mode cavity system; however, coherent linear dynamics of the two systems is very similar dispite the complexity of the electronic states of the semiconductor. In fact, a weak light beam of a given wave vector can excite only one-exciton states, and, owing to the conservation of the in-plane momentum k, only the exciton state with the same wave vector of incident light interacts. Instead, nonlinear dynamics does not mantain the simple picture of two (linearly) coupled fields. However, a simplified model could account the excitonic nonlinearity, coming from Coulomb interaction between electrons, by introducing a Kerr-type term for the exciton mode in the Hamiltonian [2]. Hence, denoting with a the radiation mode and with b the exciton mode, the Hamiltonian we wish to consider is