Quantum Effects in Light Propagation through a Nonlinear Medium

Abstract

We consider the quantum theory of partially polarized light propagating through a Kerr like medium. Using the usual form of the induced polarisation P = A(E. E*)E + B(E.E)E*, the theory can be formulated in terms of an effective Hamiltonian

$$H = p\left( {{a^{ + 2}} + {b^{ + 2}}} \right)\left( {{a^2} + {b^2}} \right) + q:{\left( {{a^ + }a + {b^ + }b} \right)^2}:$$

where p and q are related to the third order nonlinearity A and B and a and b are the annihilation operators for two orthogonally polarized modes and:: denote normal ordering of the operators. Exact solutions in closed form for the Heisenberg equations of motion are obtained. These solutions are used to evaluate the physical behaviour of varios observables as the field propagates through nonlinear medium. We also present explicit results for the time evolution of the input coherent and Fock states of the field. We show the generation of states which are macroscopic superposition of coherent states. We also find that if the input field is completely polarized, then, due to quantum effects the output field becomes partially polarized. This is in contrast to the classical prediction and can have an important bearing on the question like topological phases of light propagating through a nonlinear medium. Numerical results for the energy in each mode, the correlation between two modes and the higher order correlations will be presented. The input photon statistics is found to make considerable difference in the dynamics.

For detailed results, see G.S. Agarwal and R. R. Puri, Phys. Rev. (to appear, 1989).