Optics and Photonics Society of Iran

The four-photon coherent states have been already studied. In this article the four-photon nonlinear coherent states are presented as the eigenstates of the fourth power of deformed photon annihilation operator and their non-classical properties are investigated. In the physical realization of the resulted states by considering the deformation function related to the Kerr nonlinear medium and the trapped ion system, it was found that unlike the corresponding linear states, such states indicate sub-Poissonian photon statistics as a non-classical property in the wide range of the field amplitude. Moreover the study of the higher-order squeezing as well as amplitude-squared squeezing shows that the domain of the squeezing (domain of the non-classical feature) for such states is greater than that for linear states. Finally it is concluded that the negativity of Wigner distribution function of the presented nonlinear states, in the extensive region of the phase space, implicate the non-classicality nature of such states.