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Geometrical properties of intelligent spin states and time evolution of coherent states

Robert Arvieu, P. Rozmej

Published Jan 1, 1999• 6 citations
OpenAlex

Abstract

We remind the properties of the intelligent (and quasi-intelligent) spin states introduced by Aragone et al. We use these states to construct families of coherent wave packets on the sphere and we sketch the time evolution of these wave packets for a rigid body molecule.

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Geometrical properties of intelligent spin states and time evolution of coherent states

Robert Arvieu, P Rozmej

We recall the properties of the intelligent (and quasi-intelligent) spin states introduced by Aragone et al (1974 J. Phys. A: Math. Gen. 7 L149, 1976 J. Math. Phys. 17 1963). We use these states to construct families of coherent wavepackets (WP) on the sphere and we sketch the time evolution of these WP for a rigid-body molecule.

arXiv:quant-ph/9810024•Journal of Physics A Mathematical and General•Jan 1, 1999•7 citations

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A family of angular momentum coherent states on the sphere is constructed using previous work by Aragone et al [1]. These states depend on a complex parameter which allows an arbitrary squeezing of the angular momentum uncertainties. The time evolution of these states is analyzed assuming a rigid body hamiltonian. The rich scenario of fractional revivals is exhibited with cloning and many interference effects.

arXiv:quant-ph/9909022•Sep 7, 1999•0 citations

Relationship between coherent states and intelligent states as applied to spins

I Kolodziejczyk

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

P. Rozmej, Robert Arvieu

The aim of this paper is to present the interference effects that occur during the time evolution of simple angular wave packets (WP's) which can be associated with a diatomic rigid molecule (heteronuclear) or with a quantum rigid body with axial symmetry like a molecule or a nucleus. The time evolution is understood entirely within the framework of fractional revivals discovered by Averbukh and Perelman (Phys. Lett. A 39, 449 (1989); Usp. Fiz. Nauk 161, 41 (1991) [Sov. Phys. Usp. 37, 572 (1991)]), since the energy spectrum is exactly quadratic. Our objectives are to study how these interference effects differ when there is a change of the initial WP. For this purpose we introduce a two-parameter set of angular-momentum coherent states. On the one hand, this set emerges quite naturally from the three-dimensional coherent states of the harmonic oscillator; on the other hand, this set is shown to be built from intelligent spin states. By varying one parameter $(\ensuremath{\eta}),$ a scenario of interferences occurs on the sphere at fractional parts of the revival time that strongly depend on $\ensuremath{\eta}.$ For $\ensuremath{\eta}=\ifmmode\pm\else\textpm\fi{}1$ the WP, which coincides 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 found for the infinite square well in one dimension, and also for a two dimensional rotor. In the context of intelligent spin states it is also natural to study the evolution by changing $\ensuremath{\eta}.$ For $\ensuremath{\eta}=0$ the WP is called linear, and in time produces a set of rings with axial symmetry over the sphere. The WP's for other values of $\ensuremath{\eta}$ are called elliptic, and sets of fractional waves are generated which make a transition between two symmetries. We call these fractional waves ``mutants.'' For specific times a clone is produced that stands among the mutants. Therefore the change in $\ensuremath{\eta}$ produces a change in the quantum spread on the sphere. We have also constructed simple coherent states for a symmetric rotor which are applicable to molecules and nuclei. Their time evolution also shows a cloning mechanism for the rational ratio of moments of inertia. For irrational values of this ratio, the scenario of partial revivals completed by Bluhm, Kostelecky, and Tudose [Phys. Lett. A 222, 220 (1996)] is valid.

arXiv:quant-ph/9801018•Physical Review A•Dec 1, 1998•16 citations

su(3) intelligent states as coupledSU(3) coherent states

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We extend previous work on intelligent states and show how to construct su(3) intelligent states by coupling Su(3) coherent states. We also discuss some properties of the resulting states.

arXiv:1110.4995•Journal of Physics A Mathematical and Theoretical•May 30, 2012•0 citations

On the quantum dynamics of the rigid rotor

K. Kowalski, Jakub Rembieliński, J Zawadzki

The dynamics is investigated of a free particle on a sphere (rigid rotor or rotator) that is initially in a coherent state. The instability of coherent states with respect to the free evolution leads to nontrivial temporal development of averages of observables representing the position of a particle on a sphere that can be interpreted as quantum beats of the rotor. The beats are related to occuring quantum coherent state wave packet revivals on a sphere.

Journal of Physics A Mathematical and Theoretical•Dec 17, 2014•3 citations
The aim of this paper is to present the interference effects that occur during the time evolution of simple angular wave packets (WP's) which can be associated with a diatomic rigid molecule (heteronuclear) or with a quantum rigid body with axial symmetry like a molecule or a nucleus. The time evolution is understood entirely within the framework of fractional revivals discovered by Averbukh and Perelman (Phys. Lett. A 39, 449 (1989); Usp. Fiz. Nauk 161, 41 (1991) [Sov. Phys. Usp. 37, 572 (1991)]), since the energy spectrum is exactly quadratic. Our objectives are to study how these interference effects differ when there is a change of the initial WP. For this purpose we introduce a two-parameter set of angular-momentum coherent states. On the one hand, this set emerges quite naturally from the three-dimensional coherent states of the harmonic oscillator; on the other hand, this set is shown to be built from intelligent spin states. By varying one parameter $(\ensuremath{\eta}),$ a scenario of interferences occurs on the sphere at fractional parts of the revival time that strongly depend on $\ensuremath{\eta}.$ For $\ensuremath{\eta}=\ifmmode\pm\else\textpm\fi{}1$ the WP, which coincides 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 found for the infinite square well in one dimension, and also for a two dimensional rotor. In the context of intelligent spin states it is also natural to study the evolution by changing $\ensuremath{\eta}.$ For $\ensuremath{\eta}=0$ the WP is called linear, and in time produces a set of rings with axial symmetry over the sphere. The WP's for other values of $\ensuremath{\eta}$ are called elliptic, and sets of fractional waves are generated which make a transition between two symmetries. We call these fractional waves ``mutants.'' For specific times a clone is produced that stands among the mutants. Therefore the change in $\ensuremath{\eta}$ produces a change in the quantum spread on the sphere. We have also constructed simple coherent states for a symmetric rotor which are applicable to molecules and nuclei. Their time evolution also shows a cloning mechanism for the rational ratio of moments of inertia. For irrational values of this ratio, the scenario of partial revivals completed by Bluhm, Kostelecky, and Tudose [Phys. Lett. A 222, 220 (1996)] is valid.