Exponential and Laguerre Squeezed States for su(1,1) Algebra and Calogero-Sutherland Model

Abstract

A class of squeezed states for the su(1,1) algebra is found and expressed by the exponential and Laguerre-polynomial operators acting on the vacuum states. As a special case it is proved that the Perelomov's coherent state is a ladder-operator squeezed state and therefore a minimum uncertainty state. The theory is applied to the two-particle Calogero-Sutherland model. We find some new squeezed states and compared them with the classical trajectories. The connection with some su(1,1) quantum optical systems (amplitude-squared realization, Holstein-Primakoff realization, the two mode realization and a four mode realization) is also discussed.