Boson inverse operators and associated coherent states

Abstract

Making use of the recently introduced inverses of boson creation and annihilation operators, the authors show that the 'photon-added coherent states' are eigenstates of the operator (a^{Dagger m} aa^{Dagger -m}) and also of the operator (a-ma^{Dagger -1}) with eigenvalue alpha . The authors discuss completeness of these states. They obtain another family of photon-added coherent states which are proportional to a^-m mod alpha ), where m is a positive integer and mod alpha ) is a coherent state. They show that these are the eigenstates of the operator (a^-ma^m+1) with eigenvalue alpha . Analogously, the authors introduce 'photon-depleted coherent states', a^{Dagger -m} mod alpha ), and show that these are the eigenstates of the operator (a+ma ^Dagger-1) with eigenvalue alpha . The conditions for squeezing and antibunching of photons have also been discussed.