Squeezing of coherent light coupled to a periodically driven two-photon anharmonic oscillator

The electromagnetic field coupled to a (2l-1) order of nonlinear medium leads to the model of a 2lth anharmonic oscillator, l >= 2 being an integer. The oscillator with l=2 corresponds to the model of a quartic anharmonic oscillator. In spite of the huge advancement of mathematical physics, we are still in search of exact analytical solution to the lowest order (i.e., l=2) of anharmonic oscillator. There are few interesting reports where the approximate solutions to the classical and quantum quartic oscillator problems are explored. In the present investigation, the exact analytical solutions of the quartic anharmonic oscillator under rotating wave approximation and hence the two-photon anharmonic oscillator with periodic forcing are exhibited. The solutions corresponding to the quantized two-photon anharmonic oscillator with periodic forcing is used to calculate the second-order variances of the canonically conjugate quadrature in terms of the initial coherent state. The effects of the forcing parameters on the second-order variances and hence on the squeezing effects are examined for various photon numbers and the dimensionless interaction constants. In these studies, we assume that the oscillator is in on-resonance with those of the external forcing term. The off-resonant contribution is found to be small and is neglected.