A group-theoretic approach to the disentanglement of generalized squeezing operators

The disentangled form of unitary operators is an indispensable tool for physical applications such as the study of squeezing properties or the time evolution of quantum systems. Here we derive a closed form disentanglement for the most general element of group ISp(2,R), whose generating Lie algebra is obtained by joining the Heisenberg-Weyl algebra to su(1,1). We attain the disentanglement formula resorting to an extension of the Truax method and check our findings through an independent factorization approach, based on the use of displacement operators. As a result we obtain a new form of factorized squeezing operators, whose action on the light vacuum state is calculated.