Squeezed and coherent states of fractional photons

Abstract

We define k’-photon uncertainties Δ$X_{\left(k\mathcal{’}\right)}$,Δ$P_{\left(k\mathcal{’}\right)}$ in k-photon states, and show that all such calculations can be correlated using a fractional photon index r≡k’/k. We exemplify by choosing as k-photon states the coherent states of the k-photon generalized harmonic oscillator, and also the group-theoretic coherent states corresponding to Holstein-Primakoff realizations of SU(2) and SU(1,1). We compute the squeezing obtained in these cases, and show that they have a common limit.