Photon-added coherent states as nonlinear coherent states

Abstract

The states $|\alpha ,m>$, defined as ${a^{†}}^m|\alpha >$ up to a normalization constant and $m$ is a nonnegative integer, are shown to be the eigenstates of $f(\hat{n},m)\hat{a}$ where $f(\hat{n},m)$ is a nonlinear function of the number operator $\hat{n}$. The explicit form of $f(\hat{n},m)$ 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 $|\alpha ,m>$.

Rev Tex file with two figures as postscript files attached. Email: [email protected]

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