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arXiv:quant-ph/0207091 · Physical Review A

Pulse compression by parametric beating with a prepared Raman coherence

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

Published Aug 16, 2002• 27 citations

Abstract

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.

DOI: 10.1103/physreva.66.023813

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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.

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.

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.

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.

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.

A quasi-transparent propagation phenomenon is presented for a pair of frequency-modulated laser pulses in an optically thick medium of cold atomic gas. The noninteracting, identical lambda-structured atoms are driven by two classical laser fields, which are frequency-chirped in the same way around the corresponding atomic transition frequencies, maintaining two-photon (Raman) resonance. It is shown by numerical analysis that after propagating over a relatively short distance (determined by the absorption length), the frequency-chirped pulse pair is affected by the atoms in such a way that instead of exciting the atoms (as it would happen in an optically dilute medium), they create a certain coherent superposition of the ground states (which can be varied by the parameters of the incoming fields), and they propagate in the remainder of the medium without significant further losses. This quasi-lossless propagation effect of the Raman-resonant frequency-chirped pulses, described above, is not only interesting in the point of view of the laser fields, but the on-demand creation of coherent superpositions among atomic states along the optically thick medium may also find applications in quantum optical experiments and quantum informatics.