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Physical Review A

Rabi oscillations and rapid-passage effects in the molecular-beam CO2 -laser Stark spectroscopy of CH3 F

Allan G. Adam, T. E. Gough, Neil R. Isenor, G. Scoles

Published Sep 1, 1985• 43 citations
Publisher

Abstract

Sub-Doppler molecular-beam laser Stark spectroscopy has been employed to produce high-contrast Rabi oscillations in the ${\ensuremath{\nu}}_{3}$ band of ${\mathrm{CH}}_{3}$F. By varying the intensity of the cw ${\mathrm{CO}}_{2}$ laser, up to five complete oscillations were observed before the phenomenon was washed out by rapid-passage effects and damping mechanisms. Besides being useful in clarifying key features of coherent ir molecular-beam spectroscopy, the observation of Rabi oscillations provides one of the most accurate means of directly measuring transition dipole moments. Analysis of the present data on three rovibrational transitions, Q(1,1) -1\ensuremath{\leftarrow}0, P(1,0) 0\ensuremath{\leftarrow}0, and R(1,1) 0\ensuremath{\leftarrow}1, has yielded a rotationless transition dipole moment of 0.21\ifmmode\pm\else\textpm\fi{}0.01 D for the ${\ensuremath{\nu}}_{3}$=1\ensuremath{\leftarrow}0 vibration. This result is in agreement with values estimated from both band-intensity and absorption-coefficient data in the literature.

DOI
10.1103/physreva.32.1451

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Sub-Doppler molecular-beam laser Stark spectroscopy has been employed to produce high-contrast Rabi oscillations in the \ensuremathν3{\ensuremath{\nu}}_{3}\ensuremathν3​ band of CH3{\mathrm{CH}}_{3}CH3​F. By varying the intensity of the cw CO2{\mathrm{CO}}_{2}CO2​ laser, up to five complete oscillations were observed before the phenomenon was washed out by rapid-passage effects and damping mechanisms. Besides being useful in clarifying key features of coherent ir molecular-beam spectroscopy, the observation of Rabi oscillations provides one of the most accurate means of directly measuring transition dipole moments. Analysis of the present data on three rovibrational transitions, Q(1,1) -1\ensuremath{\leftarrow}0, P(1,0) 0\ensuremath{\leftarrow}0, and R(1,1) 0\ensuremath{\leftarrow}1, has yielded a rotationless transition dipole moment of 0.21\ifmmode\pm\else\textpm\fi{}0.01 D for the \ensuremathν3{\ensuremath{\nu}}_{3}\ensuremathν3​=1\ensuremath{\leftarrow}0 vibration. This result is in agreement with values estimated from both band-intensity and absorption-coefficient data in the literature.
We shall report on the observation of Rabi oscillations for the DeltaM=−1\\Delta M = -1DeltaM=−1, Q(1, 1) component of the upsilon3\\upsilon_{3}upsilon3​ band of methyl fluoride (CH3F)(CH_{3}F)(CH3​F) in the 10mum10 \\mu m10mum spectral region. This coherence phenomenon has been observed in a beam produced by a supersonic expansion. The transition is detected by measuring, with a low temperature bolometer, the energy contents of the molecules in the beam downstream from the laser excitation region. A Stark field is used to shift the transition into resonance with a CO2CO_{2}CO2​ laser line thereby circumventing the need for a tunable source. This work is preliminary to further observations of multiple excitation region coherence phenomena (e.g. Ramsey fringes) and their perturbation by molecular collisions.
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.
Well-resolved Ramsey fringes have been demonstrated using laser Stark spectroscopy of CH3{\mathrm{CH}}_{3}CH3​F in a molecular beam with two interaction regions. Fringe separations as low as 155 kHz were obtained. The interaction regions were produced by masks containing slits placed in the Gaussian-profile beam of a cw CO2{\mathrm{CO}}_{2}CO2​ laser. Population inversion resulting from a frequency sweep associated with the curvature of the slit-diffracted wave fronts has limited the observations at high laser-power values. An imaging system has been shown to eliminate this effect. Experiments with three and five laser-molecular beam crossings were also conducted to demonstrate the feasibility of using multiple interaction regions as a tool for high-resolution spectroscopy. The results have been modeled using the optical Bloch equation for a two-level system. Good agreement with the experiment has been obtained.
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Two level systems can interact coherently with infrared laser radiation giving rise to Rabi oscillations. The description of the interaction can in most cases, be cast in terms of the optical Bloch equations, as was shown by Feynmann et al.' Experimentally the interaction may be displayed using apparatus such as that described in reference 2. A molecular beam is generated from a supersonic expansion, crosses the output of a frequency stabilised carbon dioxide laser and impinges on a 2K bolometer. A Stark field is used to tune vibrational transitions of the beam molecules into resonance with the laser: the degree of vibrational excitation can be measured by monitoring the change in resistance of the bolometer as the molecules are tuned through resonance.