Non-linear squeezing of the vacuum and the one-photon states as realizations of the<i>SU</i>(1,1) group

Abstract

We introduce a class of non-linear squeezed vacuum and one-photon states. Under conditions on the non-linearity function, these states are realizations of the SU(1,1) group. However, when a condition is removed, these states are defined as eigenstates of certain operators. Some of the properties of these states are investigated for the case of trapped ions. In particular, the Mandel q number, the photon number distribution, the phase properties, the Husimi–Kano Q-function and the Wigner–Moyal W-function of the non-linear squeezed one-photon states are discussed.