Abstract
By applying a transformation from fermion pair operators to boson operators which preserves the Fermi commutation rules for exciton operators, we introduce the correlation effects neglected in the crude boson approximation. We apply this method to describe saturation effects in cavity polaritons under resonant optical pumping. The reduction in Rabi splitting with increasing pump intensity and the non-linear behaviour of the input-output characteristics are described. Finally, by applying the linearized theory of fluctuations, we obtain an analytic expression for the normalized second-order correlation function for the transmitted light which exhibits photon antibunching even in the limit of weak pump power. The photon antibunching behaviour is inversely proportional to the number of states available for exciton formation.
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