Deformed photon-added nonlinear coherent states and their nonclassical properties

In this paper, we will try to present a general formalism for the construction of {\it deformed photon-added nonlinear coherent states} (DPANCSs) $|\alpha, f, m>$, which in special case lead to the well-known photon-added coherent state (PACS) $|\alpha, m>$. Some algebraic structures of the introduced DPANCSs are studied and particularly the resolution of the identity, as the most important property of generalized coherent states, is investigated. Meanwhile, it will be demonstrated that, the introduced states can also be classified in the $f$-deformed coherent states, with a special nonlinearity function. Next, we will show that, these states can be produced through a simple theoretical scheme. A discussion on the DPANCSs with negative values of $m$, i.e., $|\alpha, f, -m>$, is then presented. Our approach, has the potentiality to be used for the construction of a variety of new classes of DPANCSs, corresponding to any nonlinear oscillator with known nonlinearity function, as well as arbitrary solvable quantum system with known discrete, nondegenerate spectrum. Finally, after applying the formalism to a particular physical system known as P\"oschl-Teller (P-T) potential and the nonlinear coherent states corresponding to a specific nonlinearity function $f(n)=\sqrt n$, some of the nonclassical properties such as Mandel parameter, second order correlation function, in addition to first and second-order squeezing of the corresponding states will be investigated, numerically.