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arXiv:quant-ph/0207092 · Physical Review A

Frequency modulation and pulse compression by coherent multimode molecular motion

Fam Le Kien, K. Hakuta, Alexei V. Sokolov

Published Nov 21, 2002• 8 citations
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Abstract

We study the beating of a probe field with a time-varying susceptibility in a coherently prepared Raman medium. We consider the general case of an arbitrary variation of the susceptibility, which corresponds to a superposition of an arbitrary number of excited Raman transitions. We derive a general analytical solution and conservation relations for this process. We show that the interference between Raman polarizations may substantially affect frequency modulation and pulse compression for the probe field.

DOI
10.1103/physreva.66.055802

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We study the beating of a probe field with a time-varying susceptibility in a coherently prepared Raman medium. We consider the general case of an arbitrary variation of the susceptibility, which corresponds to a superposition of an arbitrary number of excited Raman transitions. We derive a general analytical solution and conservation relations for this process. We show that the interference between Raman polarizations may substantially affect frequency modulation and pulse compression for the probe field.
We present a general analysis for the interaction of a probe-laser radiation with a coherently prepared molecular Raman medium. We describe a general formalism that includes dispersive effects, such as group velocity and group-velocity dispersion (GVD). When dispersion is negligible, the analysis is especially simple and insightful. We show that molecular oscillations result in a modulated instantaneous susceptibility of the medium. The effect of the time-varying susceptibility on a probe-laser pulse is twofold: the output frequency becomes modulated because of the time-varying phase velocity, and the pulse shape becomes deformed because of the time-varying group velocity. We identify two mechanisms for pulse compression: (1) Frequency chirping with subsequent pulse compression by normal linear GVD (possibly in the same medium) and (2) Compression due to the time-varying group velocity. We analyze various aspects of pulse compression in the coherent Raman medium and derive conservation relations for this process. When we consider a probe-laser pulse that is much shorter than the molecular oscillation period, we observe frequency chirping, compression, or stretching of this pulse, depending on its relative timing with respect to the molecular oscillations. Based on our analysis, we propose a method for selective compression or frequency conversion of single ultrashort pulses.
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 model of two-level weakly interacting quantum systems is used to demonstrate that the phase of molecular vibrations excited through stimulated Raman scattering can be controlled by the relative phase of time-separated laser pulses, allowing synchronization and amplitude control of coherence excitation in a medium. For transients with a phase relaxation time less than the field cycle, the field half-cycle can serve as a subfemtosecond probe of coherent vibrations. In this regime, the high-frequency field-induced modulation of molecular dipole moments gives rise to a detectable modulation of the optical response of a medium at the frequency $2\ensuremath{\omega}$, $\ensuremath{\omega}$ being the frequency of the laser field.
We have observed self-modulation and self-compression of a femtosecond laser pulse after passing the beam through a Raman-active medium of hydrogen. Femtosecond pulses produce Stokes emissions of ortho-hydrogen and para-hydrogen, depending on the input beam conditions. The shape of the output pulses drastically changed as a function of the intensity of the Stokes emissions and the total width of the spectrum. This is attributed to nonlinear modulation of the wave form induced by coherent rotational motions of hydrogen molecules in the time domain.
We present a detailed experimental investigation into the off-resonant preparation of a vibrational coherence for multiorder Raman generation. In particular, the importance of the balance between the conflicting requirements for generating a strong coherence and for adiabatic evolution of the system are examined. For the parameters accessible in our experiment, we find that the strongest frequency modulation occurs under conditions for which there is some nonadiabatic behavior, and the coherence is less than the peak value obtainable. We investigate the modulation of a narrowband probe pulse, and an ultrashort probe pulse, in the coherently prepared medium, and demonstrate efficient modulation of both probe pulses resulting in the generation of 360THz360\phantom{\rule{0.3em}{0ex}}\mathrm{THz}360THz bandwidth fields. This system therefore has an application in the field of subfemtosecond pulse generation.