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Physical Review A

Understanding of phase modulation in two-level systems through inverse scattering

Andrew Hasenfeld, Sharon Hammes‐Schiffer, Warren S. Warren

Published Sep 1, 1988• 13 citations
Publisher

Abstract

Analytical and numerical calculations describe the effects of shaped radiation pulses on two-level systems in terms of quantum-mechanical scattering. Previous results obtained in the reduced case of amplitude modulation are extended to the general case of simultaneous amplitude and phase modulation. We show that an infinite family of phase- and amplitude-modulated pulses all generate rectangular inversion profiles. Experimental measurements also verify the theoretical analysis.

DOI
10.1103/physreva.38.2678

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Analytical and numerical calculations describe the effects of shaped radiation pulses on two-level systems in terms of quantum-mechanical scattering. Previous results obtained in the reduced case of amplitude modulation are extended to the general case of simultaneous amplitude and phase modulation. We show that an infinite family of phase- and amplitude-modulated pulses all generate rectangular inversion profiles. Experimental measurements also verify the theoretical analysis.
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The effects of pulse shapes with simple phase and frequency modulation (phase proportional to amplitude or intensity, frequency proportional to intensity) are explored numerically. Many such shapes can be generated by combining self-phase-modulation with modern laser pulse-shaping capabilities (which are more flexible for amplitude modulation than for frequency modulation). Even though all of these wave forms begin and end at the same frequency (and hence violate the mathematical conditions for adiabatic inversion), we show that they can generate adiabatic population inversion or suppress intramolecular energy redistribution.
We describe a class of continuously phase-modulated radiation pulses that result in coherent population inversion on resonance as well as over a large range of transition frequencies and radiation field strengths. This is a population-inversion analogy to self-induced transparency. Simulations of the inversion properties of the modulated inversion pulse (MIP) are presented. It is shown that the inversion behavior can be explained by treating the MIP as a highly efficient adiabatic sweep. Criteria for establishing adiabaticity are discussed in detail. Finally, a method is presented for generating a sequence of phase-shifted radio-frequency pulses, from the continuously modulated pulse, which can be implemented on modern NMR and coherent optical spectrometers; experimental confirmation is given.
A theoretical analysis is made of the interaction between a two-level quantum-mechanical system and an electromagnetic field which is frequency- and amplitude-modulated. Attention is drawn to the fact that, subject to certain general assumptions, the usual methods for population inversion in such a system—(2 n + l)π pulses and adiabatic inversion methods—apply also if the pump field is of the wide-band type. Exact solutions are obtained for the nature of the time dependence of the instantaneous field frequency at which a population inversion occurs under nonadiabatic conditions.
Abstract The dynamics of two two-photon absorption (TPA) pathways in a four-level quantum system driven by a laser pulse is investigated in this work. An analytical solution for pulse shaping is proposed to be globally optimal for constructive interference between the two pathways, and accurate spectral boundaries for phase modulation are obtained. The TPA rate can be enhanced by a factor of 8.33 with the optimal pulse instead of the transform limited pulse (TL pulse). Simple control strategies modulating both amplitudes and phases are also designed to increase the TPA amplitude along one pathway while decreasing that along the other simultaneously. The strategies are intuitive and the two pathway amplitudes can differ by two orders of magnitude.
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.