Coherent states and symmetric spaces. II

M. I. Monastyrskiǐ, A. M. Perelomov

Michael Martin Nieto, L. M. Simmons

We apply our minimum-uncertainty coherent-states formalism, which is physically motivated by the classical motion, to two confining one-dimensional systems: the harmonic oscillator with centripetal barrier and the symmetric P\"oschl-Teller potentials. The minimum-uncertainty coherent states are discussed in great detail, and the connections to annihilation-operator coherent states and displacement-operator coherent states are given. The first system discussed provides an excellent bridge between the harmonic oscillator and more general potentials because, even though it is a nonharmonic potential, its energy eigenvalues are equally spaced. Thus, its coherent states have many, but not all, of the properties of the harmonic-oscillator coherent states.

Olshanetsky, A. M. Perelomov

S. Twareque Ali, Stephan De Bièvre

Ching Tsung Lee

A sufficient condition for nonclassical two-mode states in terms of three probabilities, (n2+1)p(n1-1, n2+1)2n1p(n1, n2)+(n1+1)p(n1+1, n2-1)2n2p(n1, n2)<1, is established as a new type II criterion. This criterion is applied to the two-mode coherent state, the two-mode squeezed vacuum state, and the pair coherent state to show how easily it can be used. It is also applied to the photon-added two-mode thermal state and the mixing of two two-photon states by a symmetric beam splitter to show that the type II criterion is superior to its type I counterpart in at least these two examples.

Jean-Pierre Antoine, Bagarello, Fabio, Jean‐Pierre Gazeau