Photon-added coherent states as nonlinear coherent states

Abstract

The states |α, m , defined asâ †m |α up to a normalization constant and m is a nonnegative integer, are shown to be the eigenstates of f (n, m)â where f (n, m) is a nonlinear function of the number operatorn. The explicit form of f (n, m) is constructed. The eigenstates of this operator for negative values of m are introduced. The properties of these states are discussed and compared with those of the state |α, m . 03.65.Fd; 42.50.Dv Typeset using REVT E X

Photon-added one-photon and two-photon nonlinear coherent states

“…When f (N) ≡ 1, the state | − m, α, f reduces to that studied in Ref. [8]. The sector S 0 , built by the repeated application of…”

“…Sivakumar showed that the photon-added coherent states are nonlinear coherent states [8]. As a generalization we showed a general result that photon-added NLCSs(PANLCSs) are still NLCSs with different nonlinear functions [9].…”

Multi-directional higher-order amplitude squeezing

“…We now proceed to study in detail various higher-order amplitude squeezings in the above constructed fan-states |ξ; K, f F . The problem depends essentially on the concrete form of the nonlinear function f ( n) which differs strongly from one to another physical context (e.g., see [31] for harmonious oscillators, [32] for photon-added coherent states, [1,8,33] for trapped ions, etc.) and requires formidable numerical simulations.…”

Engineering nonlinear coherent states as photon-added and photon-subtracted coherent states

“…A class of such nonlinear coherent states are the standard single-photon-added coherent states [5,6], |α, m = 1…”