DECOMPOSITION FORMULAS FOR SU(1,1) AND SU(2) LIE-ALGEBRAS AND THEIR APPLICATIONS IN QUANTUM OPTICS

Generalized normal- and antinormal-order decomposition formulas are derived for exponential functions of the generators of su(1, 1) and su(2) Lie algebras. The expectation values of analytic functions of these generators are calculated in terms of the generalized decomposition formulas, allowing su(1, 1) and su(2) fluctuations and their squeezing properties to be discussed. The second-order correlation functions are also considered. It is shown that the Mach-Zehnder interferometer, which is described by su(2) Lie algebra, is equivalent to a three-dimensional rotation and is characterized by the quantum counterparts of the classical Euler angles.