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Physical Review A

Modulated coherent Raman beats

Eric W. Van Stryland, R. L. Shoemaker

Published Oct 1, 1979• 8 citations
Publisher

Abstract

The authors study the phenomenon of coherent Raman beats in $^{15}\mathrm{N}$${\mathrm{H}}_{3}$ using a C${\mathrm{O}}_{2}$ laser and Stark switching. In particular, a three-level system in which the two upper levels always remain split by a few MHz is prepared by switching the transitions into resonance with a short Stark pulse whose bandwidth is large enough to coherently excite both transitions. When one of the coherently excited levels remains in resonance with the laser after the Stark pulse, this system exhibits a qualitatively new effect which has not been seen heretofore. For Stark shifts on the order of the upper-state splitting or smaller, the Raman beat is amplitude modulated at a frequency related to the optical nutation frequency. This is interpreted as being due to an interaction between the two-photon coherent Raman beat process and a single-photon optical nutation process which occurs simultaneously. Numerical calculations as well as a simple analytic model are presented to support this interpretation. By reducing the laser power, one can make the modulation of the Raman beat disappear. From the Raman signal in this regime the permanent electric dipole moment of $^{15}\mathrm{N}$${\mathrm{H}}_{3}$ in an excited vibrational state is determined and the Raman beat decay rate measured. By comparing the latter result with a delayed optical nutation measurement we show that phase-changing collisions are negligible for the transition studied.

DOI
10.1103/physreva.20.1376

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Physical Review Letters•Jul 20, 1981•12 citations
The authors study the phenomenon of coherent Raman beats in ^{15}\mathrm{N}$${\mathrm{H}}_{3} using a CO2{\mathrm{O}}_{2}O2​ laser and Stark switching. In particular, a three-level system in which the two upper levels always remain split by a few MHz is prepared by switching the transitions into resonance with a short Stark pulse whose bandwidth is large enough to coherently excite both transitions. When one of the coherently excited levels remains in resonance with the laser after the Stark pulse, this system exhibits a qualitatively new effect which has not been seen heretofore. For Stark shifts on the order of the upper-state splitting or smaller, the Raman beat is amplitude modulated at a frequency related to the optical nutation frequency. This is interpreted as being due to an interaction between the two-photon coherent Raman beat process and a single-photon optical nutation process which occurs simultaneously. Numerical calculations as well as a simple analytic model are presented to support this interpretation. By reducing the laser power, one can make the modulation of the Raman beat disappear. From the Raman signal in this regime the permanent electric dipole moment of ^{15}\mathrm{N}$${\mathrm{H}}_{3} in an excited vibrational state is determined and the Raman beat decay rate measured. By comparing the latter result with a delayed optical nutation measurement we show that phase-changing collisions are negligible for the transition studied.
The phenomenon of coherent Raman beats observed recently by Shoemaker and Brewer is analyzed through solutions of the coupled Maxwell-Schr\"odinger equations. The effect arises in coherently prepared molecular samples where the level degeneracy is suddenly removed by Stark-pulse switching. The problem divides into two parts: (a) a steady-state preparative regime whereby the initially degenerate quantum levels are placed in superposition by a resonant laser field, and (b) a transient regime in which coherent forward Raman scattering decays in the presence of the same laser field during a nonresonant condition. The laser and Raman light thus propagate together and produce at a detector a coherent beat with a frequency that corresponds to the level splitting between initial and final states. The beat signal possesses the remarkable property of being entirely independent of longitudinal molecular velocity in the case of a plane-wave laser beam and of being almost so for milliradian divergence. It follows that relaxation involving velocity-changing collisions and that Doppler dephasing effects are absent in coherent Raman beats, in agreement with experimental measurements of the decay rate. The effect of off-resonance excitation on the dephasing time and on the period of the beat signal is also discussed, and the possibility of a small rotation of the plane of polarization of the scattered light is included. The subject presents a new aspect of Raman scattering which can now yield precise radio-frequency splittings directly and offers a selective way of examining relaxation phenomena.
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 present a theoretical treatment of the coherent three-level beat signals occurring in the transient response of a Doppler-broadened molecular system with coupled closely spaced levels resonating with an intense monochromatic cw laser field. When the degenerate levels of the molecular system are suddenly split by means of an external Stark or Zeeman field, the transmitted laser radiation exhibits decaying beats at frequencies related to the level splitting or Raman frequency. This effect has been the subject of earlier theoretical analyses, but some relevant aspects such as the velocity integration, were not taken into account. A perturbation treatment, complete to third order in laser field strength, is used to calculate the velocity-integrated induced polarization and the corresponding reradiated field. The calculation takes into account both Raman-type processes, which lead to transient oscillations at the Raman frequency ${\ensuremath{\omega}}_{21}$, and population-saturation effects. In particular, population-induced transient oscillations at half the Raman frequency, $\frac{{\ensuremath{\omega}}_{21}}{2}$, are predicted. The relative importance of the various oscillations is analyzed as a function of the laser detuning and other parameters, including velocity-changing collisions. The relationship between the three-level beat signals and the well-known quantum-beat effect studied in fluorescence is explored.
The superposition of vibrational states produced in gaseous 13C^{13}\mathrm{C}13CH3{\mathrm{H}}_{3}H3​F by 9.6-\ensuremath{\mu}m infrared laser radiation results in anomalous echo-envelope and free precession-beat effects. The effects arise when pulsed Stark electric fields alter the state mixing among nearly degenerate spin-rotation states. The initial eigenstates are governed by the internal spin-rotation interaction and by applied dc bias Stark electric and Zeeman magnetic fields. Unresolved modulation of the photon echo envelope caused by sudden changes of state mixtures is confirmed by analytic theory. Separate measurement of ground- and excited-state spinrotation interactions is possible for future investigations with increase in apparatus resolution. A new anomalous coherent Raman beat also caused by altering the state mixtures is investigated. The reduction of state mixing by local collisional electric fields which increase with gas pressure is qualitatively confirmed.
Optical nutation under Raman excitation accompanied by considerable (up to inverted) population changes was observed. The Raman-active 6P1/2–6P3/2 transition of thallium atoms was excited by picosecond pulses of a dye and an Nd : YAG laser. Transition polarization and upper level population were probed by delayed pulses at a fixed time by means of coherent Raman scattering and third harmonic generation schemes, respectively. Optical nutation manifested itself in corresponding changes of anti-Stokes and third harmonic signal energies as functions of the product of the pump pulses energies. As a result of the a.c. Stark shift, the nutation picture strongly depended on the sign of wavenumber detuning from the transition wavenumber. Copyright © 2000 John Wiley & Sons, Ltd.
Photon-echo interference damping and anomalous coherent Raman beats are observed due to the spin-rotation interaction from laser-excited vibration-rotation transitions in 13C^{13}\mathrm{C}13CH3{\mathrm{H}}_{3}H3​F at 9.6\ensuremath{\mu}m. Pulsed Stark fields superimposed upon a constant magnetic field control the intrinsic mixture of spin-rotation states. The spin-rotation interaction for spin I=12I=\frac{1}{2}I=21​ is confirmed from photon-echo measurement and theory.