Amplification of squeezing and anti-bunching in the output beams from a degenerate parametric amplifier: linear and nonlinear coherent state approaches

Nonlinear optical phenomena have noticeable importance in quantum computation and quantum information processing. The optical nonlinearity leads to the generation of new frequency components possessing nonclassical properties. In this paper, we have investigated nonclassical properties of output beams from a degenerate parametric amplifier (DPA) based on both linear and nonlinear coherent state approaches. Considering the rotating wave approximation, solutions of the Heisenberg equations of motion associated with the standard coherent and nonlinear coherent radiation fields are compared. Nonclassical properties including the first- and second-order squeezing, anti-bunching and photon statistics are investigated for the signal mode starting with different input field states. The calculations based on both approaches confirm the existence of the first-order squeezing in position quadrature ( \(\hat{x}_1(\hat{X}_1)\) ${\widehat{x}}_1({\widehat{X}}_1)$ for linear(nonlinear) approach) of the field with no squeezing in momentum quadrature, while the second-order squeezing occurs in the momentum quadrature of the field ( \(\hat{x}_2(\hat{X}_2)\) ${\widehat{x}}_2({\widehat{X}}_2)$ for linear(nonlinear) approach) with no squeezing in position quadrature. In addition, photon statistics has been studied wherein anti-bunching has been observed using both approaches. The comparison of the obtained results from the two approaches confirms that in the nonlinear approach the nonclassical properties of the output beams are more amplified.