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Chinese Journal of Physics

Rabi Oscillations in a Two-Level Atomic System with a Pseudo-Hermitian Hamiltonian: A Path Integral Approach

Rima Rekik, Farida Halimi, Mekki Aouachria

Published Jun 1, 2015• 2 citations
Publisher

Abstract

The time development of a two-level system with a pseudo-Hermitian Hamiltonian is studied using the spin coherent state path integral. The propagator is first written in the standard form by replacing the spin by a unit vector aligned along the polar and azimuthal directions (θ,φ). Then it is determined exactly using perturbation methods. The metric of the pseudo-Hermitian Hamiltonian and its bi-orthonormal basis of system states are deduced.

DOI
10.6122/cjp.20150304

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The time development of a two-level system with a pseudo-Hermitian Hamiltonian is studied using the spin coherent state path integral. The propagator is first written in the standard form by replacing the spin by a unit vector aligned along the polar and azimuthal directions (θ,φ). Then it is determined exactly using perturbation methods. The metric of the pseudo-Hermitian Hamiltonian and its bi-orthonormal basis of system states are deduced.
Rabi oscillations of a two-level atomic system with damping effects are described by the use of a pseudo-Hermitian Hamiltonian. The Rabi frequency and the amplitudes for being in the upper and lower level depend in the present system on both the Hermitian resonant interaction between the em field and the atomic dipole and on damping effects. The time development of the two-level system is studied by using the metric of the pseudo-Hermitian Hamiltonian and its bi-orthonormal basis of states. The special characteristics of the present system are related to PT (parity-time reversal) and C (generalized conjugation operator) invariant properties of the pseudo-Hermitian Hamiltonian.