LAUSR

Abstract In this paper, we introduce the f –deformed photon–added–then–subtracted S U ( 1 , 1 ) and S U ( 2 ) displaced number states by applying both nonlinear coherent states and group theoretical approaches. In other words, we find the f –deformed formalism of photon addition/subtraction to/from a quantum state of light by considering the nonlinear coherent states associated with nonlinear oscillator algebra. In addition, we establish a connection between displaced Fock states and a particular class of Gilmore–Perelomov–type of S U ( 1 , 1 ) and a class of S U ( 2 ) coherent states. It is shown that various types of nonclassical states can be obtained by selecting properly the controlling parameters in both linear and nonlinear regimes. Furthermore, the nonclassicality features of the quantum states of interest are evaluated by means of photon statistics, quadrature squeezing, and the Wigner–Weyl quasi–probability distribution function. Indeed, the nonclassicality of the states is numerically examined to understand the effects of deformation functions, photons added and subtracted, and photon number occupied in the Fock state on physical properties. It is deduced that the depth as well as the domain of the nonclassicality features can appropriately be controlled by adopting the suitable parameters.