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Extension of the Rosen-Zener solution to the two-level problem

Extension of the Rosen-Zener solution to the two-level problem We solve the problem of two discrete quantum levels which are coupled by a time-dependent radio-frequency pulse W ( t ) = V ( t ) e i ν t , where the envelope function is of a form suggested by Rosen and Zener: V ( t ) = V 0 sech ( π t T ) . When a level damping constant γ is included, in the manner of Bethe-Lamb theory, the solutions show new features which are not expected on the basis of a sudden-approximation theory, where V ( t ) = const over the pulse duration T . Various transient effects such as "ringing" are not present in the extended Rosen-Zener solution; these effects are related to the large impulsive forces at the step discontinuities in the sudden approximation. The final-state level amplitudes can be quite different depending on the size of the pulse rise time T as compared with the system Bohr period 1 ω . Our results allow a continuous and quantitatively exact comparison between the extremes of the sudden ( ω T ≪ 1 ) and adiabatic ( ω T ≫ 1 ) approximations. A model of a "quasisudden" step function is also constructed, and remarks are made on the validity of a certain conjecture by Rosen and Zener. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review A American Physical Society (APS)

Extension of the Rosen-Zener solution to the two-level problem

Physical Review A , Volume 17 (1) – Jan 1, 1978
14 pages

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Publisher
American Physical Society (APS)
Copyright
Copyright © 1978 The American Physical Society
ISSN
1094-1622
DOI
10.1103/PhysRevA.17.247
Publisher site
See Article on Publisher Site

Abstract

We solve the problem of two discrete quantum levels which are coupled by a time-dependent radio-frequency pulse W ( t ) = V ( t ) e i ν t , where the envelope function is of a form suggested by Rosen and Zener: V ( t ) = V 0 sech ( π t T ) . When a level damping constant γ is included, in the manner of Bethe-Lamb theory, the solutions show new features which are not expected on the basis of a sudden-approximation theory, where V ( t ) = const over the pulse duration T . Various transient effects such as "ringing" are not present in the extended Rosen-Zener solution; these effects are related to the large impulsive forces at the step discontinuities in the sudden approximation. The final-state level amplitudes can be quite different depending on the size of the pulse rise time T as compared with the system Bohr period 1 ω . Our results allow a continuous and quantitatively exact comparison between the extremes of the sudden ( ω T ≪ 1 ) and adiabatic ( ω T ≫ 1 ) approximations. A model of a "quasisudden" step function is also constructed, and remarks are made on the validity of a certain conjecture by Rosen and Zener.

Journal

Physical Review AAmerican Physical Society (APS)

Published: Jan 1, 1978

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