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Title: Two-level systems: Exact solutions and underlying pseudo-supersymmetry

Abstract

Chains of first-order SUSY transformations for the spin equation are studied in detail. It is shown that the transformation chains are related with a polynomial pseudo-supersymmetry of the system. Simple determinant formulas for the final Hamiltonian of a chain and for solutions of the spin equation are derived. Applications are intended for a two-level atom in an electromagnetic field with a possible time-dependence of the field frequency. For a specific form of this dependence, the time oscillations of the probability to populate the excited level disappear. Under certain conditions this probability becomes a function tending monotonously to a constant value which can exceed 1/2.

Authors:
 [1];  [1];  [2]
  1. Department of Quantum Field Theory, Tomsk State University, 36 Lenin Ave., 634050 Tomsk (Russian Federation)
  2. Institute of Physics, USP (Brazil). E-mail: gitman@dfn.if.usp.br
Publication Date:
OSTI Identifier:
20976755
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics (New York); Journal Volume: 322; Journal Issue: 5; Other Information: DOI: 10.1016/j.aop.2006.05.004; PII: S0003-4916(06)00116-3; Copyright (c) 2006 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ELECTROMAGNETIC FIELDS; EQUATIONS; EXACT SOLUTIONS; EXCITED STATES; HAMILTONIANS; POLYNOMIALS; PROBABILITY; SPIN; SUPERSYMMETRY; TIME DEPENDENCE; TRANSFORMATIONS

Citation Formats

Shamshutdinova, V.V., Samsonov, Boris F., and Gitman, D.M. Two-level systems: Exact solutions and underlying pseudo-supersymmetry. United States: N. p., 2007. Web. doi:10.1016/j.aop.2006.05.004.
Shamshutdinova, V.V., Samsonov, Boris F., & Gitman, D.M. Two-level systems: Exact solutions and underlying pseudo-supersymmetry. United States. doi:10.1016/j.aop.2006.05.004.
Shamshutdinova, V.V., Samsonov, Boris F., and Gitman, D.M. Tue . "Two-level systems: Exact solutions and underlying pseudo-supersymmetry". United States. doi:10.1016/j.aop.2006.05.004.
@article{osti_20976755,
title = {Two-level systems: Exact solutions and underlying pseudo-supersymmetry},
author = {Shamshutdinova, V.V. and Samsonov, Boris F. and Gitman, D.M.},
abstractNote = {Chains of first-order SUSY transformations for the spin equation are studied in detail. It is shown that the transformation chains are related with a polynomial pseudo-supersymmetry of the system. Simple determinant formulas for the final Hamiltonian of a chain and for solutions of the spin equation are derived. Applications are intended for a two-level atom in an electromagnetic field with a possible time-dependence of the field frequency. For a specific form of this dependence, the time oscillations of the probability to populate the excited level disappear. Under certain conditions this probability becomes a function tending monotonously to a constant value which can exceed 1/2.},
doi = {10.1016/j.aop.2006.05.004},
journal = {Annals of Physics (New York)},
number = 5,
volume = 322,
place = {United States},
year = {Tue May 15 00:00:00 EDT 2007},
month = {Tue May 15 00:00:00 EDT 2007}
}