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Journal of Modern Optics

Direct multi-level density matrix calculation of nonlinear optical rotation spectra in rubidium vapour

N. Korneev, Olena Benavides

Published May 29, 2009• 4 citations
Publisher

Abstract

We propose a rapid solution algorithm for the calculation of the full density matrix evolution for a multi-level atom. The calculation principle is similar to the split-step algorithm widely used for modelling the nonlinear propagation in media with Kerr-type nonlinearity, optical fibres in particular. The spectrum of nonlinear Faraday rotation in the D2 natural rubidium line is calculated and compared with the experiment. Good agreement is obtained.

DOI
10.1080/09500340902990023

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We propose a rapid solution algorithm for the calculation of the full density matrix evolution for a multi-level atom. The calculation principle is similar to the split-step algorithm widely used for modelling the nonlinear propagation in media with Kerr-type nonlinearity, optical fibres in particular. The spectrum of nonlinear Faraday rotation in the D2 natural rubidium line is calculated and compared with the experiment. Good agreement is obtained.
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Abstract We study non-linear absorption of intense monochromatic light through a dense natural rubidium (Rb) vapour. We measure transmission through a 10 cm long heated vapour cell for atom densities up to 3 × 1019 m−3 and saturation parameters up to 104, for linear and circular polarisation, close to resonance on the 87Rb D2 F = 1 → F′ = 0, 1, 2 transition. The strong absorption at low intensity is frustrated by an interplay of optical non-linearities (saturation and optical pumping) and non-linear effects due to the high atom density (collisional broadening and collisional depumping). To understand the results of the transmission measurements, we developed a model that incorporates these non-linear effects into the optical absorption. The model takes into account the absolute line strengths of all transitions from both hyperfine levels of the ground state of both isotopes of naturally abundant Rb. Doppler and collisional broadening are included in the Voigt profiles for the resonances. We show the effect of each of the non-linear processes on the calculation results of the model, and from comparison with experiment we conclude that all non-linear effects are necessary for a quantitative agreement.
Rubidium vapor cells play a key role in contemporary quantum optics since they have strong nonlinear interactions with a low-power incident laser light. The simplest nonlinear interaction is the Kerr effect. Although most calculations concentrate on the unsaturated Kerr effect, the saturated Kerr effect has been measured in many materials including 85Rb and 87Rb vapor. Moreover, entanglement-generating vapor cells often operate in the saturated regime. Here, the calculation of the saturated Kerr effect for rubidium vapor at the D2 line uses a density matrix formulation that includes two hyperfine-split levels and all magnetic sublevels in each of the ground and excited states to account for incomplete optical pumping: the transit time of the atoms through the beam is too short to reach a final population distribution. The calculation shows a rapid qualitative change at low optical power, in semiquantitative agreement with experimental data.
Abstract We present a theoretical and experimental study of the polarization rotation of a linearly polarized probe beam scanning across all of the neighboring hyperfine levels ( F e = 1 and 2) with a circularly polarized pumping beam resonant on the F g = 2 → F e = 3 transition of the D2 line of 87 Rb atoms. The experimental results match well with the results calculated from the full-level density matrix equations considering laser phase noise, which hinders observations of narrow lines with linewidths of ∼90 kHz, as calculated in polarization rotation spectra for the first time.
We theoretically and experimentally study the effects of Faraday rotation, optical polarization of self-rotation, and their overlapping rotation. In our theoretical simulation, we set up a simple and effective theoretical model for the three kinds of rotations. In our experiment, the atomic vapor is placed in a magnetic shielding cavity to shield the earth magnetic field. Doppler-free spectrum configuration is used and the F=2 F'=3 transition of 87Rb D2 line is chosen. We observe the three kinds of rotations, separately. Experimental results and theoretical simulations are in good agreement.