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Optics Letters

Coherent Raman beats: high-order interference effects

Dieter Suter, Thomas Marty

Published Oct 1, 1993• 1 citation
Publisher

Abstract

Light propagating through an optically anisotropic resonant medium excites coherent Raman fields that propagate together with the original wave; the interference between the two fields generates the well-known Raman beats. We solve the coupled-wave equations for finite optical path lengths and show how the coherent exchange of energy between the two fields leads to interference effects that distort the observed signal for different detection schemes. Theoretical analysis is compared with experimental results from the Na D1 transition.

DOI
10.1364/ol.18.001663

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Light propagating through an optically anisotropic resonant medium excites coherent Raman fields that propagate together with the original wave; the interference between the two fields generates the well-known Raman beats. We solve the coupled-wave equations for finite optical path lengths and show how the coherent exchange of energy between the two fields leads to interference effects that distort the observed signal for different detection schemes. Theoretical analysis is compared with experimental results from the Na D1 transition.
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.
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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.
In coherent Raman beat experiments a laser field coherently scatters off a material excitation that evolves under the internal Hamiltonian of the system. The Raman signal, which is observed as a beat signal between the test laser and the scattered Raman field, provides information on energy-level splittings and dephasing rates. We propose a modification of this technique, which allows, in contrast to the conventional method, the excitation of coherent Raman beats also in systems with large sublevel splittings and small oscillator strengths. For this purpose, we use a bichromatic laser field to excite the coherent superposition in the medium. We calculate the evolution of the coherence during the laser excitation analytically and discuss its dependence on various experimental parameters. We compare the theoretical results with experimental data from Pr3+{\mathrm{Pr}}^{3+}Pr3+:YAlO3{\mathrm{YAlO}}_{3}YAlO3​.
A theory of quantum beats in a Stokes signal observed in pump-probe experiments upon excitation of four-level atoms with two close upper lying levels by femtosecond laser pulses is developed. Quantum beats arise in the intensity of the Stokes field due to the interference of two atomic wave packets generated by ultrashort pump and probe pulses. An analytical solution of the non-steady-state Maxwell-Bloch equations is obtained, and the dependence of the Stokes radiation intensity on the delay time between two laser pulses is investigated. The theoretical results describe qualitatively well the observed features of quantum beats.
By using spontaneous Raman processes in the high gain regime, we produce two independent Raman Stokes fields from an atomic ensemble. Temporal beating is observed between the two directly generated Stokes fields in a single realization. The beat frequency is found to be a result of an AC Stark frequency shift effect. However, due to the spontaneous nature of the process, the phases of the two Stokes fields change from one realization to another so that the beat signal disappears after average over many realizations. On the other hand, the beat signal is recovered in a two-photon correlation measurement, showing a two-photon interference effect. The two-photon beat signal enables us to obtain dephasing information in the Raman process. The dephasing effect is found to depend on the temperature of the atomic medium.