SU(1,1)-displaced coherent states, photon counting, and squeezing

Abstract

We revisit the Perelomov SU(1,1)-displaced coherent states as possible quantum states of light. We disclose interesting statistical aspects of these states in relation to photon counting and squeezing. In the non-displaced case, we discuss the efficiency of the photodetector as inversely proportional to the parameterϰof the discrete series of unitary irreducible representations of SU(1,1). In the displaced case, we study the counting and squeezing properties of the states in terms ofϰand the number of photons in the original displaced state. We finally examine the quantization of a classical radiation field based on these families of coherent states. The procedure yields displacement operators that might allow to prepare such states in the way proposed by Glauber for standard coherent states.