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Title: Pythagorean coupling: Complete population transfer in a four-state system

Abstract

Complete population transfer in a four-coupled-modes system is analyzed from a geometrical point of view. An analytical solution of the dynamics is written by the use of two distinct frequencies, the generalization of the single Rabi frequency of the two-state dynamics. We also present its visualization on two separate Bloch spheres with two independent torque equations. With this scheme we analytically derive the requirements for complete population transfer in a four-state quantum system. Interestingly, the solutions are found to be linked to fundamental number theory, whereas complete population transfer occurs only if the ratios between coupling coefficients exactly match a set of Pythagorean triples.

Authors:
 [1];  [2];  [1];  [3];  [2]
  1. Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot IL-76100 (Israel)
  2. (United States)
  3. Department of Physics and Engineering Physics, Tulane University, New Orleans, Louisiana 70118 (United States) and Brescia University, Division of Mathematics and Natural Sciences, Owensboro, Kentucky 42301 (United States)
Publication Date:
OSTI Identifier:
22051325
Resource Type:
Journal Article
Journal Name:
Physical Review. A
Additional Journal Information:
Journal Volume: 84; Journal Issue: 1; Other Information: (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1050-2947
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 74 ATOMIC AND MOLECULAR PHYSICS; ANALYTICAL SOLUTION; BLOCH THEORY; COUPLING; EQUATIONS; QUANTUM STATES

Citation Formats

Suchowski, Haim, Kavli Institute for Theoretical Physics, Santa Barbara, California 93106, Silberberg, Yaron, Uskov, Dmitry B., and Kavli Institute for Theoretical Physics, Santa Barbara, California 93106. Pythagorean coupling: Complete population transfer in a four-state system. United States: N. p., 2011. Web. doi:10.1103/PHYSREVA.84.013414.
Suchowski, Haim, Kavli Institute for Theoretical Physics, Santa Barbara, California 93106, Silberberg, Yaron, Uskov, Dmitry B., & Kavli Institute for Theoretical Physics, Santa Barbara, California 93106. Pythagorean coupling: Complete population transfer in a four-state system. United States. doi:10.1103/PHYSREVA.84.013414.
Suchowski, Haim, Kavli Institute for Theoretical Physics, Santa Barbara, California 93106, Silberberg, Yaron, Uskov, Dmitry B., and Kavli Institute for Theoretical Physics, Santa Barbara, California 93106. Fri . "Pythagorean coupling: Complete population transfer in a four-state system". United States. doi:10.1103/PHYSREVA.84.013414.
@article{osti_22051325,
title = {Pythagorean coupling: Complete population transfer in a four-state system},
author = {Suchowski, Haim and Kavli Institute for Theoretical Physics, Santa Barbara, California 93106 and Silberberg, Yaron and Uskov, Dmitry B. and Kavli Institute for Theoretical Physics, Santa Barbara, California 93106},
abstractNote = {Complete population transfer in a four-coupled-modes system is analyzed from a geometrical point of view. An analytical solution of the dynamics is written by the use of two distinct frequencies, the generalization of the single Rabi frequency of the two-state dynamics. We also present its visualization on two separate Bloch spheres with two independent torque equations. With this scheme we analytically derive the requirements for complete population transfer in a four-state quantum system. Interestingly, the solutions are found to be linked to fundamental number theory, whereas complete population transfer occurs only if the ratios between coupling coefficients exactly match a set of Pythagorean triples.},
doi = {10.1103/PHYSREVA.84.013414},
journal = {Physical Review. A},
issn = {1050-2947},
number = 1,
volume = 84,
place = {United States},
year = {2011},
month = {7}
}