Spin Coherent State Path Integral for the Interaction of Two-Level System with Time Dependent Non-Uniform Magnetic Field

Authors: Rekik Rima, Aouachria Mekki

Abstract:

We study the movement of a two-level atom in interaction with time dependent nonuniform magnetic filed using the path integral formalism. The propagator is first written in the standard form by replacing the spin by a unit vector aligned along the polar and azimuthal directions. Then it is determined exactly using perturbation methods. Thus the Rabi formula of the system are deduced.

Keywords: Path integral, Formalism, Propagator, Transition probability.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1091342

References:

[1] C. Grosche and F. Steiner, Handbook of Feynman Path Integrals, Springer-Verlag (1998).
[2] M. Aouachria, L. Chetouani, Eur. Phys. J. C 25, 333 (2002).
[3] M. Aouachria, L. Chetouani, Chinese. J. Phys. 40, 496 (2002).
[4] M. Aouachria, L. Chetouani, Can. J. Phys. 87, 389 (2009).
[5] A. M. Perelomov, Generalized Coherent states and Their Application (Springe-Verlag, Berlin, 1986). I. I. Rabi, Phys. Rev. 51, 652 (1937).
[6] A. Alscher, H. Grabert, J. Phys. A. 32, 4907 (1999).
[7] J. R. Klauder, Ann. Phys. (NY) 11, 123 (1960).
[8] Y. Ohnuki, T. Kashiwa, Prog. Theor. Phys. 60, 548 (1978).
[9] T. Boudjedaa, A. Bounames, L. Chetouani, T. F. Hammann, J. Math. Phys. 36, 1602 (1995).
[10] A. M. Perelomov, Commun. Math. Phys. 26, 22 (1972).