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Journal of the Optical Society of America B

Susceptibility for Doppler-broadened two-level atoms in pump–probe spectroscopy: analytical solutions revisited

Heung‐Ryoul Noh

Published Feb 5, 2016• 6 citations
Publisher

Abstract

We present an analytical study of susceptibility in pump–probe laser spectroscopy for an atomic medium composed of two-level atoms in the Doppler-broadened limit. We derive an accurate analytical formula for susceptibility up to the first (arbitrary) order at the Rabi frequency of the probe (pump) beam. This is expressed in a succinct single term rather than as a complicated summation, as presented in previous papers. We also derive analytical solutions for the linewidth and peak value of the absorption spectrum of the probe beam.

DOI
10.1364/josab.33.000308

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Journal of the Optical Society of America B•Jun 23, 2016•3 citations
We present an analytical study of susceptibility in pump–probe laser spectroscopy for an atomic medium composed of two-level atoms in the Doppler-broadened limit. We derive an accurate analytical formula for susceptibility up to the first (arbitrary) order at the Rabi frequency of the probe (pump) beam. This is expressed in a succinct single term rather than as a complicated summation, as presented in previous papers. We also derive analytical solutions for the linewidth and peak value of the absorption spectrum of the probe beam.
We present an analytical calculation of the susceptibility in Doppler-broadened three-level atomic systems using a diagrammatic method. The optical coherences responsible for the susceptibility of the probe field are obtained from the optical Bloch equations for Ladder (lower or upper transition probed), V and Λ-type three-level atoms up to the first (arbitrary) order in the probe (coupling) field Rabi frequency, and are then averaged over a Maxwell–Boltzmann velocity distribution. Finally, we obtain analytical solutions of the susceptibility for four different three-level atomic systems. In particular, the general expressions of the susceptibility are obtained where the wavelengths of the probe and coupling fields are different from each other.
We present an analytic calculation for linear susceptibility in pump-probe spectroscopy for a Doppler broadened atomic vapor. The analytic form of the population of each magnetic sublevel of a 87Rb^{87}\mathrm{Rb}87Rb atom, illuminated by a weak circularly polarized pump beam, was calculated for the lowest order of laser intensity and used in the calculation for the susceptibility of a counterpropagating (copropagating) probe beam. The obtained analytic results for the susceptibility can be used for calculating the absorption or the refractive index of the probe beam as functions of pump beam diameter and intensity.
We present the analytic solutions of the saturated absorption spectrum for an atomic medium composed of two-level atoms and describe the effects of saturation and optical pumping on the spectrum. The background-subtracted Doppler-free spectrum is Lorentzian-shaped with an amplitude and width given by 1 − {1 + s 0 [1 + (γ 2 t /2)]} −1/2 and γ t [1 + {1 + s 0 [1 + (γ 2 t /2)]} 1/2 ], respectively, where γ t is the transverse decay rate, γ 2 is the decay rate to energy levels other than the ground state, s 0 is the saturation parameter and t is the interaction time of the atoms with laser beams. Analytic results are compared with numerical results and show good agreement with one another. This paper is intended for graduate students who have started to study basic atomic physics.
An analytical expression for the degenerate four-wave mixing signal produced in a medium composed of two-level atoms by pump and probe lasers of arbitrary intensities and parallel linear polarization, suffering negligible absorption and depletion, has been derived. The Abrams–Lind approach [Opt. Lett.2, 94 and 3, 205 (1978)] for deriving the phase-matched polarization has been extended to find all the other higher-order polarization terms contributing to the signal. The signal field amplitude is expressed as an infinite series whose convergence rate depends on the intensity of the input fields and their detuning from resonance. The solution is successfully verified by comparison with a full numerical nonperturbative calculation and is found to be equivalent to the Abrams–Lind result in the limit of weak probe intensity. The result is used to calculate the saturation effects on spectral line shape that are relevant to simulation of molecular spectra obtained by degenerate four-wave mixing with saturating pump and probe fields. The result is extended to treat atomic motion in the case of forward geometry of the input beams.