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arXiv:1403.1428 · International Conference Laser Optics (ICLO)

Nonlinear Doppler - Free comb-spectroscopy in counter-propagating fields

S. A. Pulkin, Alexey A. Kalinichev, Vasilii Arnautov, Svetlana Uvarova, Svetlana Savel’eva

Published Jun 1, 2014• 0 citations
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Abstract

The method of Doppler - free comb - spectroscopy for dipole transitions was proposed. The calculations for susceptibility spectrum for moving two-level atoms driving by strong counter propagating combs have been done. The used theoretical method based on the Fourier expansion of the components of density matrix on two rows on kv (v-velocity of group of atoms, k-projection of wave vector) and Ω (frequency between comb components). For testing of validity of this method the direct numerical integration was done. The narrow peaks with homogeneous width arise on the background of Doppler counter. The contrast of these peaks is large for largest amplitudes of comb-components. Power broadening is increasing with increase of field amplitudes. The spectral range of absorption spectrum is determined by the spectral range of comb generator and all homogeneous lines arise simultaneously.

DOI
10.1109/lo.2014.6886344

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The method of Doppler - free comb - spectroscopy for dipole transitions was proposed. The calculations for susceptibility spectrum for moving two-level atoms driving by strong counter propagating combs have been done. The used theoretical method based on the Fourier expansion of the components of density matrix on two rows on kv (v-velocity of group of atoms, k-projection of wave vector) and Ω (frequency between comb components). For testing of validity of this method the direct numerical integration was done. The narrow peaks with homogeneous width arise on the background of Doppler counter. The contrast of these peaks is large for largest amplitudes of comb-components. Power broadening is increasing with increase of field amplitudes. The spectral range of absorption spectrum is determined by the spectral range of comb generator and all homogeneous lines arise simultaneously.
The method of Doppler – free comb – spectroscopy for dipole transitions was proposed. The numerical calculations for susceptibility spectrum for two-level system driving by strong counter propagating combs were made. The narrow peaks with homogeneous width arise on the background of Doppler counter. The contrast of these peaks is large for largest amplitudes of comb-components. Power broadening is increasing with increasing of field amplitudes. The amplitudes of peaks depend on the phase difference between carrier frequencies of combs. The spectral range of absorption spectrum is determined by the spectral range of comb generator and all homogeneous lines arise simultaneously. The spectral resolution is determined by the width of homogeneously –broadening lines. The physical nature of narrow peaks is in the existing of multi-photon transitions between manifolds of quasi-energy levels arising for different groups of atoms moving with velocities that satisfy to the resonant conditions 2kv= (n+l)Ω⁄j, where n, l, j-are integers and Ω - frequency difference between comb teeth.
The two-photon transition of 87{}^{87}87Rb ($5{S}_{1/2}\ensuremath{-}4{D}_{3/2}$, $5{S}_{1/2}\ensuremath{-}4{D}_{5/2}$) in a vapor cell is investigated with direct frequency-comb spectroscopy. When strong chirp is imposed on a frequency comb, it is found that the Doppler-free signal amplitude barely degrades despite a significant reduction in peak intensity. In addition, it is found that the Doppler-broadened signal is strongly dependent on the applied chirp. We present a simple model that explains this counterintuitive behavior based on the elongated spatial extent of chirped pulses. Keeping Doppler-free signals almost constant, Doppler-broadened background signals can be strongly suppressed with chirped-pulse excitations. Consequently, in the case of uniformly distributed target atoms, chirped-pulse direct frequency-comb spectroscopy can be a useful method to improve the signal-to-noise ratio in two-photon direct frequency-comb spectroscopy.
In this article, we analyse a new sensitive spectroscopic technique in which a sample cell is irradiated by a two-frequency pump beam (ω + Δ ± δ/2) and a counter-propagating probe beam (ω). The phase-conjugate fields re-emitted at frequencies ω ± δ, via four-wave mixing processes, are detected through their heterodyne beating with the probe field. The properties of the heterodyne beat signal are studied by means of a perturbation calculation of the nonlinear response of the medium, carried out to the third order in the incident fields. In resonant gas media, the emission lineshape exhibits a Doppler-free doublet structure [frequency splitting 3 δ/2 for single-photon resonances, and δ/2 for two-photon transitions]. By using a phase-sensitive detection of the beat signal, one can separately analyse real (dispersion) or imaginary parts (absorption) of the nonlinear susceptibility. For single-photon transitions, the signal phase shift is related to the atomic levels lifetime and allows one to study the relaxation dynamics in gas phase (like quenching collisions, velocity diffusion, etc...). This is particularly interesting for cross-over resonances, in which only the common level contributes. In three-level systems, one also predicts a selective resonant enhancement of the phase-conjugate emission through Raman-type two-photon processes. Most of these predictions have been experimentally verified.
A numerical solution for the polarization of two-level atoms that interact with a polyharmonic field was obtained. An analytical solution for the particular case of a symmetrical position of carrier frequency relative to transition frequency is possible. The results showed that nonlinear effects occur in a polarization spectrum at the small amplitudes of comb components and small frequency distances between them. Consequently, it is necessary to take into account nonlinear effects in comb spectroscopy.
A previously developed theory of spontaneous emission from driven systems has been applied to the case of a Doppler broadened gas of two level atoms radiating into free space. The power spectrum of those photons radiated nearly parallel to the propagation vector of the driving field is predicted to differ from that of the undriven system. The case of zero attenuation coefficient (population equality in the two resonance levels) and the driving field tuned to the center of the Doppler line, is investigated in particular. When the saturation parameter is large there is strong suppression, in an interval about the central frequency comparable to the saturated width, of the spontaneous emission whose spectral components are phased for amplitude modulation relative to the driving field. An amount of power equal to that suppressed, but with spectral components phased for phase modulation relative to the driving field, is radiated in an interval about the central frequency comparable to the homogeneous width.