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Journal of the Optical Society of America B

Coherent Raman beats from dark states

Ken-ichi Harada, Koji Motomura, 隆典 越水, Hirotaka Ueno, Masaharu Mitsunaga

Published May 1, 2005• 7 citations
Publisher

Abstract

We have observed coherent Raman beat signals from a Lambda-type three-level system in a sodium atomic vapor. The sample is first prepared in a coherent superposition state of the ground-state hyperfine levels, or a dark state, by resonant bichromatic radiation. A following sudden frequency shift of one of the excitation beams causes the beat signals. Detailed analytical calculations based on the three-level Liouville equations are presented and are compared with experimental results. This simple technique is particularly suited for the obtaining of information on the generated sublevel coherence, including magnitude, phase, and decay time.

DOI
10.1364/josab.22.001105

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We have observed coherent Raman beat signals from a Lambda-type three-level system in a sodium atomic vapor. The sample is first prepared in a coherent superposition state of the ground-state hyperfine levels, or a dark state, by resonant bichromatic radiation. A following sudden frequency shift of one of the excitation beams causes the beat signals. Detailed analytical calculations based on the three-level Liouville equations are presented and are compared with experimental results. This simple technique is particularly suited for the obtaining of information on the generated sublevel coherence, including magnitude, phase, and decay time.
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.
The authors study the phenomenon of coherent Raman beats in 15N^{15}\mathrm{N}15NH3{\mathrm{H}}_{3}H3​ 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 15N^{15}\mathrm{N}15NH3{\mathrm{H}}_{3}H3​ 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.
In this paper we develop a three-element vector model to describe the stimulated Raman interaction in a \ensuremath{\Lambda} system. This model is valid over the range of interaction energies for which the excited state follows the ground states adiabatically. We use the model to present simple physical interpretations of the generation of Raman-Ramsey fringes in a separated field excitation, the ac Stark shift in the Raman clock, the ultrahigh-resolution mapping of microwave phase using Raman probes, and the coherent transfer of population by adiabatic passage for atomic beam splitters. The expressions for observables are derived by inspection and agree quantitatively with published experimental results.
We demonstrate the efficient generation of Raman sidebands in a medium coherently prepared in a dark state by continuous-wave low-intensity laser radiation. Our experiment is performed in sodium vapor excited in $\ensuremath{\Lambda}$ configuration on the D1{D}_{1}D1​ line by two laser fields of resonant frequencies ${\ensuremath{\omega}}_{1}$ and ${\ensuremath{\omega}}_{2},$ and probed by a third field ${\ensuremath{\omega}}_{3}.$ First-order sidebands for frequencies ${\ensuremath{\omega}}_{1},$ ${\ensuremath{\omega}}_{2}$ and up to the third-order sidebands for frequency ${\ensuremath{\omega}}_{3}$ are observed. The generation starts at a power as low as 10 \ensuremath{\mu}W for each input field. Dependences of the intensities of both input and generated waves on the frequency difference $({\ensuremath{\omega}}_{1}\ensuremath{-}{\ensuremath{\omega}}_{2}),$ on the frequency ${\ensuremath{\omega}}_{3},$ and on the optical density are investigated.
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.
A sodium atomic beam is deflected by two optical standing-wave fields which excite near resonance Raman transitions. Observed deflections are consistent with theoretical predictions of a long-range dc component of the force on a three-level atom in the \ensuremath{\Lambda} configuration. The low laser intensities (and small detunings) used, combined with observed evidence of damping in the three-level \ensuremath{\Lambda} system, may ultimately lead to the design of high-density, all optical traps wherein the atoms would be mostly in the dark state.