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Physical Review A

Two-photon transient phenomena

D. G. Gold, Erwin Louis Hahn

Published Jul 1, 1977• 32 citations
Publisher

Abstract

The first observations of two-photon free-precession and driven transient coherence by Hatanaka et al. are extended by an experimental NMR verification of the Brewer-Hahn exact solutions for two-photon resonance.
DOI
10.1103/physreva.16.324

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A class of molecular two-photon processes, occurring under transient or steady-state conditions, is analyzed exactly for certain cases using a density-matrix formalism. Our results are relevant to the recently observed phenomena of transient coherent Raman beats and steady-state two-photon absorption of oppositely directed laser beams. Lowest-order perturbation theories have shown that these processes are insensitive to the Doppler effect, and consequently the linewidth is unaffected by Doppler broadening and by elastic collisions that change molecular velocity. The solutions presented here are of the same form for the Raman and two-photon problems and reveal significant power-dependent frequency shifts and line broadening that correct the ideal Doppler-free solutions. For the transient case, we assume a molecular three-level quantum structure that can be switched in or out of optical resonance with cw laser radiation by means of a pulsed dc Stark field, but the solutions also apply when resonant optical pulses are introduced. During the resonant condition when the Stark pulse is on, the three levels are prepared in coherent superposition, and during the nonresonant condition following the Stark pulse, the laser field(s) stimulates the coherently prepared sample in a transient two-photon process. One of these processes, the Ramanbeat effect, has been observed in forward scattering, but the second one, transient two-photon emission, should be observable in backward scattering. Bloch-like equations are derived for this three-level problem that facilitate an exact pulse solution for state preparation. Following the pulse, transient decay is well-approximated by a perturbation calculation. For the steady-state case, an exact solution is also obtained and is of interest for continuous-wave spectroscopy or for transient experiments requiring an initial preparation of quantum states, prior to Stark switching. These solutions exhibit a power-dependent line broadening and a frequency shift of magnitude $\ensuremath{\sim}\frac{\ensuremath{\Delta}({\ensuremath{\alpha}}^{2}\ensuremath{-}{\ensuremath{\beta}}^{2})}{({\ensuremath{\Delta}}^{2}+\frac{1}{{T}_{2}^{2}})}$, in agreement with our earlier estimate, where $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ are the Rabi flopping frequencies for the two intermediate transitions and $\ensuremath{\Delta}$ is the off-resonance tuning behavior for one of them.

Physical Review A•May 1, 1975•341 citations
Abstract Soon after the discovery of the principal phenomenon of nuclear magnetic resonance (NMR) by Purcellet al.[1] and Blochet al.[2] , it was Hahn [ 3] who realized that spin precession can be observed directly in the rotating frame as a transient phenomenon called free induction decay (FID). In linear response theory, both phenomena, the continuous wave (c.w.) observation and the free precession are related to each other by Fourier transformation. Within the same year, however, Hahn realized that there is more to the motion of spins than just a linear response to radiofrequency field excitation and discovered the spin echo phenomenon [ 4] which led to the foundation of modern NMR spectroscopy and nonlinear optical spectroscopy. In this contribution we want to present a special view on how these early principles of Hahn influenced the development of Optical Excitation and Detection of Spin Precession. For this purpose we consider a very simple physical system, namely an atomic vapour. In optical pumping spectroscopy it is well known that the transmitted light intensity is modulated by irradiating the system with resonant radiofrequency (r.f.) fields [5-8]. By monitoring the transmission of light as a function of the r.f., sublevel splittings of the optically connected states can thus be measured, which are usually not resolved in the Dopplerbroadened optical spectrum.
The Stark-pulse technique of Brewer and Shoemaker allows one to observe phenomena such as optical free-induction decay, optical nutation, and two-photon superradiance. In this paper, we develop a theoretical treatment of these phenomena under the appropriate experimental conditions. The calculations of the free-induction decay and the corresponding optical nutation are shown to be in excellent agreement with experiment. We also discuss the two-photon superradiance phenomenon of Brewer and Shoemaker as a Raman effect appearing in first-order perturbation theory. The analysis illustrates the essential features of the experimental observation.
A class of molecular two-photon processes, occurring under transient or steady-state conditions, is analyzed exactly for certain cases using a density-matrix formalism. Our results are relevant to the recently observed phenomena of transient coherent Raman beats and steady-state two-photon absorption of oppositely directed laser beams. Lowest-order perturbation theories have shown that these processes are insensitive to the Doppler effect, and consequently the linewidth is unaffected by Doppler broadening and by elastic collisions that change molecular velocity. The solutions presented here are of the same form for the Raman and two-photon problems and reveal significant power-dependent frequency shifts and line broadening that correct the ideal Doppler-free solutions. For the transient case, we assume a molecular three-level quantum structure that can be switched in or out of optical resonance with cw laser radiation by means of a pulsed dc Stark field, but the solutions also apply when resonant optical pulses are introduced. During the resonant condition when the Stark pulse is on, the three levels are prepared in coherent superposition, and during the nonresonant condition following the Stark pulse, the laser field(s) stimulates the coherently prepared sample in a transient two-photon process. One of these processes, the Ramanbeat effect, has been observed in forward scattering, but the second one, transient two-photon emission, should be observable in backward scattering. Bloch-like equations are derived for this three-level problem that facilitate an exact pulse solution for state preparation. Following the pulse, transient decay is well-approximated by a perturbation calculation. For the steady-state case, an exact solution is also obtained and is of interest for continuous-wave spectroscopy or for transient experiments requiring an initial preparation of quantum states, prior to Stark switching. These solutions exhibit a power-dependent line broadening and a frequency shift of magnitude $\ensuremath{\sim}\frac{\ensuremath{\Delta}({\ensuremath{\alpha}}^{2}\ensuremath{-}{\ensuremath{\beta}}^{2})}{({\ensuremath{\Delta}}^{2}+\frac{1}{{T}_{2}^{2}})}$, in agreement with our earlier estimate, where $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ are the Rabi flopping frequencies for the two intermediate transitions and $\ensuremath{\Delta}$ is the off-resonance tuning behavior for one of them.