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Proceedings of the Estonian Academy of Sciences Physics Mathematics

THE BERRY PHASE OF AN E Θe SYSTEM

G E Drăgănescu, N.M. Avram

Published Feb 14, 1995• 0 citations
Publisher

Abstract

In this paper, we consider an EQ®e-type Jahn-Teller system described by а twõ-rhode Hamiltonian.The Berry phase method enables the calculation of the probabilities of non-adiabatic transitions.We have calculated the Berry phase for an Ege Jahn-Teller system.The results are two types of transitions, one modifying ) and the other one leaving j constant.

DOI
10.3176/phys.math.1995.2/3.10

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In this paper, we consider an EQ®e-type Jahn-Teller system described by а twõ-rhode Hamiltonian.The Berry phase method enables the calculation of the probabilities of non-adiabatic transitions.We have calculated the Berry phase for an Ege Jahn-Teller system.The results are two types of transitions, one modifying ) and the other one leaving j constant.
Jahn-Teller systems and the Jahn-Teller effect are discussed in terms of cavity QED models. By expressing the field modes in a quadrature representation, it is shown that certain setups of a two-level system interacting with a bimodal cavity are described by the Jahn-Teller $E\ifmmode\times\else\texttimes\fi{}\ensuremath{\epsilon}$ Hamiltonian. We identify the corresponding adiabatic potential surfaces and the conical intersection. The effects of a nonzero geometrical Berry phase, governed by encircling the conical intersection, are studied in detail both theoretically and numerically. The numerical analysis is carried out by applying a wave packet propagation method, more commonly used in molecular or chemical physics, and analytic expressions for the characteristic time scales are presented. It is found that the collapse-revival structure is greatly influenced by the geometrical phase and as a consequence, the field intensities contain direct information about this phase. We also mention the link between the Jahn-Teller effect and the Dicke phase transition in cavity QED.