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Three-level coherent transient spectroscopy in cesium

Howard Lee, John E. Wessel

Published Apr 26, 1987• 0 citations
OpenAlex

Abstract

Coherent transient spectroscopy is well understood for two-level systems. The effect was demonstrated for a three-level atom a number of years ago.1 However, detailed studies have only recently been initiated. Mossberg’s group2 recently completed studies of three-level coherent transient spectroscopy of ytterbium, which is not subject to complications associated with optical pumping of hyperfine levels. They employed the photon echo technique using an atomic beam to suppress Doppler broadening. Results were complex and required a new dressed atom model of coherent excitation processes.

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The Journal of Chemical Physics•Mar 1, 1983•107 citations
Coherent transient spectroscopy is well understood for two-level systems. The effect was demonstrated for a three-level atom a number of years ago.1 However, detailed studies have only recently been initiated. Mossberg’s group2 recently completed studies of three-level coherent transient spectroscopy of ytterbium, which is not subject to complications associated with optical pumping of hyperfine levels. They employed the photon echo technique using an atomic beam to suppress Doppler broadening. Results were complex and required a new dressed atom model of coherent excitation processes.
We study theoretically ultrafast modulation spectroscopy in Doppler-broadened cascading three-level and four-level systems. The pump beams consist of two frequency components that drive two-pathway excitation. The four-wave mixing (FWM) signal exhibits damping oscillation as the relative time delay τ between the two pump beams is varied, from which the resonant frequencies between energy levels can be deduced. Furthermore, Doppler-free precision in the measurement of the resonant frequencies can be achieved when the pump beams have either narrow-band or broadband linewidths. We study two-photon resonant FWM induced by time-delayed correlated fluctuating fields in a Doppler-broadened cascading three-level system. It is related intrinsically to the sum-frequency trilevel echo when the pump beams have broadband linewidths. However, unlike the corresponding incoherent-light stimulated photon echo, the maximum of the FWM signal is shifted from τ≃0. If we consider the fluctuations of the pump beams, the FWM signal exhibits damping oscillation when the laser frequency is off resonant from the two-photon transition.
The dynamics of nuclear spins in atomic and molecular environments have been examined in exquisite detail over the past 27 years by the methods of pulsed nuclear magnetic resonance. The early discovery of the spin echo by Erwin Hahn and the transient nutation effect by Henry Torrey initiated the field by introducing coherent transient phenomena to radio-frequency spectroscopy. An entire class of coherent spin transients could be observed by a simple variation of the rf pulse sequence, and from the decay characteristics the various spin-dephasing mechanisms could be examined separately. In short, these methods allowed decomposition of the spin-transition linewidth into its broadening components, and also offered new and versatile ways for performing high-resolution rf spectroscopy.
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.
We have developed a general technique for obtaining analytical expressions for coherent transient signals arising from atoms interacting with two or more laser pulses having Gaussian spatial profiles. After deriving the Maxwell-Bloch equations for short laser pulses incident on an ensemble of three-level atoms, we specialize to photon echo spectroscopy. As an example, the stimulated photon echo signal is calculated as a function of the time delay between pulses. Our exact results are compared with both the lowest-order perturbative limit and a calculation in which transit time is treated phenomenologically. We conclude by commenting on the extension of our technique to atoms undergoing velocity-changing collisions. \textcopyright{} 1996 The American Physical Society.
In this series of papers we report on the generation and application of multiple pulse phase coherent sequences in optical spectroscopy. In this paper the effects of intense pulse trains on systems with only two resonant energy levels are analyzed, with particular attention to the effects of extreme inhomogeneous broadening and population depletion to nonresonant levels. It is shown that these effects, which are present in virtually all optical systems, make the simple gyroscopic model of optical coherent transients invalid. Exact calculations show, e.g., that a two-pulse photon echo is not maximized by a 1:2 length ratio for the pulses; that the maximum excited state population is not created by a 180° pulse; and that three equal pulses are almost as effective as a 1:2:1 ratio for producing three pulse echoes. The role of pulse phase is extensively analyzed. Pulse sequences are proposed and experimentally demonstrated which permit optical phase sensitive detection and measurement of ground state relaxation parameters. The experimental results are based on an extension of the acousto-optic modulation and fluoresence detection techniques of Zewail and Orlowski [Zewail et al., Chem. Phys. Lett. 48, 256 (1977); Orlowski et al., ibid. 54, 197 (1978)]. The relative merits of fluorescence and transverse polarization detection are discussed, and fluorescence detection is shown to be more generally useful for these new sequences. Finally, composite pulse trains are shown to be capable of substantially increasing the signal available from highly inhomogenously broadened transitions. In paper II we extend the treatment to multilevel systems with some emphasis on solid state applications.