Multiphoton supercoherent states

In this paper we are going to build the multiphoton supercoherent states for the supersymmetric harmonic oscillator as eigenstates of the $m$-th power of a special form (but still with a free parameter) of the Kornbluth-Zypman supersymmetric annihilation operator. They become expressed in terms of the multiphoton coherent states for the standard harmonic oscillator. The Heisenberg uncertainty relation and some statistical properties for these states will be studied. Since the multiphoton supercoherent states turn out to be periodic, then the associated geometric phases will be as well evaluated.