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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.
Physical Review A – American Physical Society (APS)
Published: Jan 1, 1978
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