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Chemical Physics Letters

Velocity dependent pump-probe spectroscopy for a five-level system: An application to Rb D2 transitions

Dipankar Bhattacharyya, Amitava Bandyopadhyay, Shrabana Chakrabarti, Biswajit Ray, Pradip Narayan Ghosh

Published Apr 9, 2007• 14 citations
Publisher
DOI
10.1016/j.cplett.2007.04.007

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Theory of pump-probe spectroscopy using an amplitude approach

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The relative intensities of the Doppler-free signals of the 85Rb and Cs D2 lines in saturation spectroscopy, velocity-selective optical pumping (VSOP) spectroscopy, and polarization spectroscopy were calculated theoretically, taking into accont the optical pumping process in the Zeeman sublevels and arbitrary polarization combinations for pump and probe beams. Both circular and linear optical anisotropy induced by the pump beam were considered in the theoretical calculation. The magnitude and sign of the Doppler-free resonances in each spectroscopic method were quite different owing to the polarizations of the pump and probe beams. The theoretical results obtained from a single-cycle optical pumping in a four-level approximation were in good agreement with recent experimental reports.
We investigate coherent pump–probe spectroscopy of a medium of atoms in Λ configuration with a closely placed adjacent excited level. The presence of the additional level results in two simultaneous Λ resonances excited by the same pair of pump and probe fields. A master equation framework is used to discuss the probe absorption spectrum and dispersion in the absence/presence of inhomogeneous broadening, and the results are illustrated by using a model four-level system in the D2 transition of 85Rb. The system is observed to exhibit additional interference effects arising from two competing Λ resonances. These effects manifest in terms of linewidths of the triplet dressed state spectrum and suppression of the subnatural peak for the stationary atoms. The effect on electromagnetically induced transparency is discussed in the light of its shape, position and linewidth. The discussion is further augmented by the study of a six-level model as applicable to the D2 transition of 85Rb. The analysis presented here provides a realistic theoretical description of the pump–probe spectroscopy of hyperfine transitions of alkali atoms.
Abstract We theoretically and experimentally investigate the Doppler-broadened absorption spectrum of the D2-line (52 S 1/2 → 52 P 3/2) in thermal (room-temperature) Rb vapour over a wide range of probe intensity, probe diameter, and vapour cell temperature to understand the effect of hyperfine pumping and transit-relaxation on the absorption lineshape. We present a relatively simple but comprehensive five-level rate equation model which incorporates optical pumping of the atomic population into the other ‘dark’ ground hyperfine level (leading to absorption saturation), including contributions of the three closely spaced (within one Doppler linewidth) hyperfine levels in the excited state 52 P 3/2 (allowed by the dipole transition selection rules). D2-line transmission spectra predicted by our model show excellent agreement (rms error < 5 % ) with the experimental data for a wide range of probe intensities (from ∼ 0.001 I s a t 0 all the way up to ∼ 10 I s a t 0 , where I sat0 is the usual two-level saturation intensity for the respective atomic transition), vapour cell temperatures (24.2°C–53.5 °C) and beam diameters (1/e 2 width ∼ 1 − 6 mm). Our model also takes into account the finite transit time of atoms across the probe beam cross-section, and correctly predicts the dependence of effective saturation intensity on probe diameter (up to ∼ 10 × lower saturation intensity as compared to I sat0 for few-mm beam sizes). This ab initio five-level model can thus predict accurate Doppler lineshapes for any given experimental parameter set for a linearly polarized probe without any fitting parameters, and can be easily applied to any other atomic system by an appropriate change of the atomic constants in the rate equations.