Clones and other interference effects in the evolution of angular-momentumcoherent states

The aim of this paper is to present the interference effects that occur dur ing the time evolution of simple angular wave packets (WP's) which can be a ssociated with a diatomic rigid molecule (heteronuclear) or with a quantum rigid body with axial symmetry like a molecule or a nucleus. The time evolu tion is understood entirely within the framework of fractional revivals dis covered by Averbukh and Perelman (Phys. Lett. A 39, 449 (1989); Usp. Fit. N auk 161, 41 (1991) [Sov. Phys. Usp. 37, 572 (1991)]), since the energy spec trum is exactly quadratic. Our objectives are to study how these interferen ce effects differ when there is a change of the initial WP. For this purpos e we introduce a two-parameter set of angular-momentum coherent states, On the one hand, this set emerges quite naturally from the three-dimensional c oherent states of the harmonic oscillator: on the other hand, this set is s hown to be built from intelligent spin states. By varying one parameter (et a), a scenario of interferences occurs on the sphere at fractional parts of the revival time that strongly depend on eta. For eta=+/-1 the WP, which c oincides with a WP found by Mostowski [Phys. Lett. A 56, 369 (1976)], is a superposition of Bloch [Phys. Rev. 70, 460 (1946)] or Radcliffe [J. Phys. A 4, 313 (1971)] states, and clone exactly in time according to a scenario f ound for the infinite square well in one dimension, and also for a two-dime nsional rotor. In the context of intelligent spin states it is also natural to study the evolution by changing eta. For eta=0 the WP is called linear, and in time produces a set of rings with axial symmetry over the sphere. T he WP's for other values of eta are called elliptic, and sets of fractional waves are generated which make a transition between two symmetries. We cal l these fractional waves "mutants." For specific times a clone is produced that stands among the mutants. Therefore the change in eta produces a chang e in the quantum spread on the sphere. We have also constructed simple cohe rent states for a symmetric rotor which are applicable to molecules and nuc lei. Their time evolution also shows a cloning mechanism for the rational r atio of moments of inertia. For irrational values of this ratio, the scenar io of partial revivals completed by Bluhm, Kostelecky, and Tudose [Phys. Le tt. A 222, 220 (1996)] is valid. [S1050-2947(98)04012-8].