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Canadian Journal of Physics

Berry's phase for U(1/1) coherent states

H. A. Schmitt, A. Mufti

Published Jul 1, 1991• 0 citations
Publisher

Abstract

Berry's geometrical phase is calculated for the coherent states of the compact unitary supergroup U(1/1). With properly chosen parameters, these coherent states are shown to be eigenstates of the nonresonant two-level Jaynes–Cummings Hamiltonian.
DOI
10.1139/p91-141

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We study the total (dynamical plus geometrical (Berry)) phase of cyclic quantum motion for coherent states over homogeneous Kähler manifolds X = G/H, which can be considered as the phase spaces of classical systems and which are, in particular cases, coadjoint orbits of some Lie groups G. When the Hamiltonian is linear in the generators of a Lie group, both phases can be calculated exactly in terms of classical objects. In particular, the geometric phase is given by the symplectic area enclosed by the (purely classical) motion in the space of coherent states. I.
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