Photon-added and photon-depleted "semi"-coherent field: Non-classical properties

In this paper, we introduce photon-added and photon-subtracted "semi"-coherent field states. These states are constructed via the boson operator actions on the semi-coherent states (P.M. Mathews, K. Eswaran, Nuovo Cimento B 17, 332 (1973)). These are not a family of the f -deformed coherent states, however they can be considered as superpositions of two distinguishable components of the photon-added and photon-depleted coherent states. The physical properties of these states, like the sub-Poissonian statistics and the normal-order squeezing effect are discussed analytically. An exact analytic expression for their optical tomogram is derived in terms of the Hermite and Laguerre polynomials. Finally, we propose a scheme to generate the photon-add semi-coherent states.