SU(2) and SU(1,1) algebra eigenstates: A unified analytic approach to coherent and intelligent states

摘要

We introduce the concept of algebra eigenstates which are defined for anarbitrary Lie group as eigenstates of elements of the corresponding complex Liealgebra. We show that this concept unifies different definitions of coherentstates associated with a dynamical symmetry group. On the one hand, algebraeigenstates include different sets of Perelomov's generalized coherent states.On the other hand, intelligent states (which are squeezed states for a systemof general symmetry) also form a subset of algebra eigenstates. We develop thegeneral formalism and apply it to the SU(2) and SU(1,1) simple Lie groups.Complete solutions to the general eigenvalue problem are found in the bothcases, by a method that employs analytic representations of the algebraeigenstates. This analytic method also enables us to obtain exact closedexpressions for quantum statistical properties of an arbitrary algebraeigenstate. Important special cases such as standard coherent states andintelligent states are examined and relations between them are studied by usingtheir analytic representations.