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Journal of Physics Conference Series

Rabi oscillation in a damped rotating magnetic field: A path integral approach

Mekki Aouachria

Published Apr 26, 2013• 4 citations
Publisher

Abstract

In this paper we consider a spin 1/2 particle interacting with a damped rotating magnetic field using path integral formalism. The propagator is first of all written in the standard form by replacing the spin by two fermionic oscillators via the Schwinger's model; then it is determined exactly thanks to the introduction of a particular rotations in coherent state space which has eliminated the rotation angle of the magnetic field and has simplified the Hamiltonian of the considered system. Thus, the Rabi formula are deduced.

DOI
10.1088/1742-6596/435/1/012021

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In this paper we consider a spin 1/2 particle interacting with a damped rotating magnetic field using path integral formalism. The propagator is first of all written in the standard form by replacing the spin by two fermionic oscillators via the Schwinger's model; then it is determined exactly thanks to the introduction of a particular rotations in coherent state space which has eliminated the rotation angle of the magnetic field and has simplified the Hamiltonian of the considered system. Thus, the Rabi formula are deduced.
Exact solutions of the neutral spinning particle in interaction with rotating magnetic field and a scalar potential using path integral formalism have been found. The propagator is first written in the standard Feynman form by replacing the spin by a unit vector aligned along the polar and azimuthal directions (θ φ). Then we use the phase-space and rotations in the space of spin coherent states to simplify the calculations. Thus the exact energy spectrum with a corresponding wave functions are deduced.
Using the coherent states representation and the Schwinger boson model, the propagator of a spinning particle in interaction with an arbitrary magnetic field is derived in the framework of the path integral formalism. To show the relevance of the formalism to some applications, the Green function of spinning particle s=1/2 in special configuration of magnetic field is calculated. The transition amplitude and Berry’s phase for an arbitrary spin and time dependent magnetic field are deduced. The case of half integer spin is also considered.