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Two interacting spins in external fields. Four‐level systems
Author(s) -
Bagrov V.G.,
Baldiotti M.C.,
Gitman D.M.,
Levin A.D.
Publication year - 2007
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.200610231
Subject(s) - galileo (satellite navigation) , global positioning system , physics , relativistic quantum chemistry , theory of relativity , satellite , general relativity , observer (physics) , classical mechanics , computer science , aerospace engineering , geodesy , astronomy , telecommunications , quantum mechanics , geography , engineering
In the present article, we consider the so‐called two‐spin equation that describes four‐level quantum systems. Recently, these systems attract attention due to their relation to the problem of quantum computation. We study general properties of the two‐spin equation and show that the problem for certain external backgrounds can be identified with the problem of one spin in an appropriate background. This allows one to generate a number of exact solutions for two‐spin equations on the basis of already known exact solutions of the one‐spin equation. Besides, we present some exact solutions for the two‐spin equation with an external background different for each spin but having the same direction. We study the eigenvalue problem for a time‐independent spin interaction and a time‐independent external background. A possible analogue of the Rabi problem for the two‐spin equation is defined. We present its exact solution and demonstrate the existence of magnetic resonances in two specific frequencies, one of them coinciding with the Rabi frequency, and the other depending on the rotating field magnitude. The resonance that corresponds to the second frequency is suppressed with respect to the first one.