Boson inverse operators and a new family of two-photon annihilation operators

Abstract

We introduce the inverse of the Hermitian operator (ââ^†) and express the Boson inverse operators â^-1 and â^†-1 in terms of the operators â, â^† and (ââ^†)^-1. We show that these Boson inverse operators may be realized by Susskind-Glogower phase operators. In this way, we find a new two-photon annihilation operator and denote it as â²(ââ^†)^-1. We show that the eigenstates of this operator have interesting non-classical properties. We find that the eigenstates of the operators (ââ^†)^-1 â², â(ââ^†)^-1 â and â²(ââ^†)^-1 have many similar properties and thus they constitute a family of two-photon annihilation operators.