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Journal of Physics A Mathematical and General

Generalised Glauber states and the T1⊗(εg⊕τ2g) Jahn-Teller effect

C. C. Chancey

Published Jul 11, 1987• 9 citations
Publisher

Abstract

The octahedral Jahn-Teller system T 1 ⊗(ε g ⊕tau 2g ) is studied using generalised Glauber states which are eigenstates of the system in the strong-coupling limit. It is shown that these states become, when limited to a total angular momentum of one, eigenstates in the weak-coupling limit. The lower-branch zero-phonon state is studied using these states and expressions as functions of coupling strength are obtained for the energy and Ham reduction factors. The results compare well with the available numerical calculations.

DOI
10.1088/0305-4470/20/10/019

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•Jan 1, 1999•0 citations
The octahedral Jahn-Teller system T 1 ⊗(ε g ⊕tau 2g ) is studied using generalised Glauber states which are eigenstates of the system in the strong-coupling limit. It is shown that these states become, when limited to a total angular momentum of one, eigenstates in the weak-coupling limit. The lower-branch zero-phonon state is studied using these states and expressions as functions of coupling strength are obtained for the energy and Ham reduction factors. The results compare well with the available numerical calculations.
The octahedral Jahn-Teller system E ⊗ is studied using generalised Glauber states which are strong-coupling eigenstates of the system. It is shown that these Glauber states become, under certain conditions, equivalent to the weak-coupling eigenstates obtainable from standard perturbation theory. Eigenstates are thus obtained for the system which can be applied using perturbative procedures over the complete range of coupling strengths. Expressions which are functions of the coupling strength are obtained for the energies, the ground state Ham factor p and the A to E absorption intensities. The results compare well with the available numerical calculations.
Within the Trotter-Suzuki approximations on ${e}^{\mathrm{\ensuremath{-}}\ensuremath{\beta}H}$, the extended projector method [Phys. Rev. A 36, 4612 (1987)] previously introduced by us is shown to be a valuable technique in investigating the general class of few-level systems coupled both linearly and quadratically to a selected number of harmonic oscillators. As an illustration we compare eigenvalues and Ham-reduction factors with the literature for the cubic linear Jahn-Teller systems T\ensuremath{\bigotimes}\ensuremath{\epsilon} and T\ensuremath{\bigotimes}${\ensuremath{\tau}}_{2}$ as well as for the system E\ensuremath{\bigotimes}\ensuremath{\epsilon} for which a quadratic warping interaction is included. For the latter system a symmetry projector is additionally developed, dealing with the transformation properties of nonlinear combinations of representational basis functions. As another illustration, the low-energy eigenstates of a two-level system quadratically coupled to a single harmonic oscillator are investigated. Within the ground state, the system becomes unstable at high coupling strengths and through the evaluation of time- and frequency-dependent correlation functions we found substantially different ground-state dynamic properties compared with those of a linearly coupled system.
Jahn-Teller systems exhibit strong coupling between the electronic and nuclear degrees of freedom. We analyse how linear and quadratic coupling affect the electron-nuclear entanglement in the E⊗ϵE\otimes \epsilonE⊗ϵ system. A measure of quantum entanglement, recently developed by Shimony [Ann. New York Acad. Sci. 755, 675 (1995)], is used. States in the adiabatic regime with quadratic coupling are analysed. The electron-nuclear entanglement in vibronic states of the linear Exe model is calculated numerically. The physical significance of electron-nuclear entanglement is discussed in terms of reduction factors and magnetic vibrational circular dichroism.