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Journal of Physics B Atomic Molecular and Optical Physics

Concerning the 'asymmetrized Rosen-Zener model'

Edward J. Robinson

Published Mar 28, 1995• 2 citations

Abstract

In the concluding paragraph of a recent paper on two-state atoms driven by transients, Vitanov (1994) raised two questions. First, he queried whether or not, at non-zero detuning, there exist asymmetric pulses of arbitrary smoothness that can restore the system to its initial level. Second, he asked whether one could find symmetric pulses that fail to restore the system to its initial state, regardless of pulse area. In this letter, we respond to these speculations. We show that pulses with shapes that are hyperbolic secants modified by powers of the hyperbolic tangent can arbitrarily approach the restoring condition, while the existence of a symmetric pulse incapable of restoration implies unitarity violation. We also draw a distinction between the infinitely large set of restoring pulse areas that exist for symmetric pulses, as compared to the small number (typically no more than one) that can be found in the asymmetric case.

DOI: 10.1088/0953-4075/28/6/003

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In the concluding paragraph of a recent paper on two-state atoms driven by transients, Vitanov (1994) raised two questions. First, he queried whether or not, at non-zero detuning, there exist asymmetric pulses of arbitrary smoothness that can restore the system to its initial level. Second, he asked whether one could find symmetric pulses that fail to restore the system to its initial state, regardless of pulse area. In this letter, we respond to these speculations. We show that pulses with shapes that are hyperbolic secants modified by powers of the hyperbolic tangent can arbitrarily approach the restoring condition, while the existence of a symmetric pulse incapable of restoration implies unitarity violation. We also draw a distinction between the infinitely large set of restoring pulse areas that exist for symmetric pulses, as compared to the small number (typically no more than one) that can be found in the asymmetric case.

We have found new analytic results for a wide variety of atomic excitation processes which involve the use of amplitude-and frequency-modulated laser pulses: (1) We have unified all the previously known solutions including those of Rosen and Zener,1 Landau2 and Zener,3 Rabi,4 Bambini and Berman,5 Demkov,6 McCall and Hahn,7 Allen and Eberly,8 and Hioe,9 among others, and have significantly extended it with expressions involving three free parameters and an arbitrary function to an infinite variety of amplitude-and frequency-modulated laser pulses.10 We have found a simple condition which the three essential parameters in the amplitude-and frequency-modulation functions must satisfy in order to achieve a complete population inversion, or to achieve a complete population restoration as in the case of self-induced transparency7 or soliton propagation.

It is shown that any pulse with a time-asymmetric envelope and a constant non-zero detuning excites a two-level quantum system with a probability of nearly one-half provided the pulse is very asymmetric, adiabatic in the slowly rising part of its envelope, sudden in the steep part and the peak Rabi frequency is much greater than the detuning. Three particular cases are considered analytically: the asymmetric hyperbolic-secant, the Bambini-Berman and the exponential pulse, which illustrate the general conclusions. The results are applied to a special three-level 'vee' system whose two transitions are driven by two asymmetric laser pulses of the same Rabi frequencies and the same detunings. Analysis shows that if such a system is prepared initially in its ground state, effective population depletion of this state can be achieved, the results being quite insensitive to variations in the Rabi frequency and the detuning.