Dynamic symmetry and coherent states of quantum systems

Vladimir G. Makhankov

Rui-hua Xie, Gong-ou Xu

Dynamical symmetry and squeezing effect have been investigated in a classically chaotic quantum system [M. Ku\ifmmode \acute{s}\else \'{s}\fi{}, Phys. Rev. Lett. 54, 1343 (1985)] when it is restricted to the following initial condition: the atom in its SU(2) coherent state and the field in the vacuum state. In the regime of classically regular motion, dynamical symmetry and squeezing effects have been exposed under proper choice of the atomic coherent state; but, in that of classically chaotic motion, the symmetry is destroyed thoroughly and the squeezing effect disappears. \textcopyright{} 1996 The American Physical Society.

Constantin Brif, A. Mann, M. Revzen

We consider quantum systems, whose dynamical symmetry groups are semisimple Lie groups, which can be split or decay into two subsystems of the same symmetry. We prove that the only states of such a system that factorize upon splitting are the generalized coherent states. Since Bell's inequality is never violated by the direct product state, when the system prepared in the generalized coherent state is split, no quantum correlations are created. Therefore the generalized coherent states are the unique Bell states, i.e., the pure quantum states preserving the fundamental classical property of satisfying Bell's inequality upon splitting.

Anthony Brinton Wolbarst

Alexander V. Gorokhov

A problem of the coherent control of a quantum system in an external electromagnetic field is considered. We use the technique of dynamical symmetry Lie groups and relevant coherent states. The general approach is illustrated by examples of qubit and qudit dynamics in an external classical field, and transitions between the Rydberg states of a hydrogen-like atom with the fixed principal quantum number. The problem of generalization of the approach for taking into account additional interaction with a large dissipative environment is discussed.