Paul Siddons

Light propagation through atomic vapours

This tutorial presents the theory necessary to model the propagation of light through an atomic vapour. The history of atom–light interaction theories is reviewed, and examples of resulting applications are provided. A numerical model is developed and results presented. Analytic solutions to the theory are found, based on approximations to the numerical work. These solutions are found to be in excellent agreement with experimental measurements.

Absolute absorption on rubidium D lines: comparison between theory and experiment

We study the Doppler-broadened absorption of a weak monochromatic probe beam in a thermal rubidium vapour cell on the D lines. A detailed model of the susceptibility is developed which takes into account the absolute linestrengths of the allowed electric dipole transitions and the motion of the atoms parallel to the probe beam. All transitions from both hyperfine levels of the ground term of both isotopes are incorporated. The absorption and refractive index as a function of frequency are expressed in terms of the complementary error function. The absolute absorption profiles are compared with experiment, and are found to be in excellent agreement provided a sufficiently weak probe beam with an intensity under one thousandth of the saturation intensity is used. The importance of hyperfine pumping for open transitions is discussed in the context of achieving the weak-probe limit. Theory and experiment show excellent agreement, with an rms error better than 0.2% for the D2 line at 16.5 degrees C.

A gigahertz-bandwidth atomic probe based on the slow-light Faraday effect

The ability to control the speed and polarisation of light pulses will allow for faster data flow in optical networks of the future. Optical delay and switching have been achieved using slow-light techniques in various media, including atomic vapour. Most of these vapour schemes utilise resonant narrowband techniques for optical switching, but suffer the drawback of having a limited frequency range or high loss. In contrast, the Faraday effect in a Doppler-broadened slow-light medium allows polarisation switching over tens of GHz with high transmission. This large frequency range opens up the possibility of switching telecommunication bandwidth pulses and probing of dynamics on a nanosecond timescale. Here we demonstrate the slow-light Faraday effect for light detuned far from resonance. We show that the polarisation dependent group index can split a linearly polarised nanosecond pulse into left and right circularly polarised components. The group index also enhances the spectral sensitivity of the polarisation rotation, and large rotations of up to 15π rad are observed for continuous-wave light. Finally, we demonstrate dynamic broadband pulse switching, by rotating a linearly polarised nanosecond pulse from vertical to horizontal with no distortion and transmission close to unity. The phenomenon of reduced optical group velocity (slow light) is a topic of burgeoning interest [1]. In a slow-light medium, the group refractive index, ng, (the ratio of the speed of light in vacuo to the pulse velocity) is many orders of magnitude larger than the phase index, n. Hence an optical pulse propagates much more slowly than a monochromatic light beam. Large group indices of ∼ 10 are achievable in resonant optical processes, such as electromagnetically induced transparency (EIT), accompanied by a refractive index that is of the order of unity [2]. Such large group indices are the result of a rapid change

Absolute absorption on the rubidium D1 line including resonant dipole?dipole interactions

Here we report on measurements of the absolute absorption spectra of dense rubidium vapour on the D1 line in the weak-probe regime for temperatures up to 170 °C and number densities up to 3 × 1014 cm−3. In such vapours, modifications to the homogeneous linewidth of optical transitions arise due to dipole–dipole interactions between identical atoms, in superpositions of the ground and excited states. Absolute absorption spectra were recorded with a deviation of 0.1% between experiment and a theory incorporating resonant dipole–dipole interactions. The manifestation of dipole–dipole interactions is a self-broadening contribution to the homogeneous linewidth, which grows linearly with number density of atoms. Analysis of the absolute absorption spectra allows us to ascertain the value of the self-broadening coefficient for the rubidium D1 line: β/2π = (0.69 ± 0.04) × 10−7 Hz cm3, in excellent agreement with the theoretical prediction.

Faraday dichroic beam splitter for Raman light using an isotopically pure alkali-metal-vapor cell

We present an application of the Faraday effect to produce a narrowband dichroic beam splitter using an alkali metal vapor. Two Raman beams detuned in frequency by the ground-state hyperfine splitting in (87)Rb are produced using an electro-optic modulator and then separated using the Faraday effect in an isotopically pure (85)Rb thermal vapor. An experimental transmission spectra for the beam splitter is presented along with a theoretical calculation. The performance of the beam splitter is then demonstrated and characterized using a Fabry-Perot etalon. For a temperature of 70 degrees C and a longitudinal magnetic field of 80 G, a suppression of one frequency of 18 dB is achieved, limited by the quality of the polarizers.

Off-resonance absorption and dispersion in vapours of hot alkali-metal atoms

We study the absorptive and dispersive properties of Doppler-broadened atomic media as a function of detuning. Beginning from the exact lineshape calculated for a two-level atom, a series of approximations to the electric susceptibility are made. These simplified functions facilitate direct comparison between absorption and dispersion, and show that dispersion dominates the atom-light interaction far from resonance. The calculated absorption and dispersion are compared to experimental data, showing the validity of the approximations.We study the absorptive and dispersive properties of Doppler-broadened atomic media as a function of detuning. Beginning from the exact lineshape calculated for a two-level atom, a series of approximations to the electric susceptibility are made. These simplified functions facilitate direct comparison between absorption and dispersion, and show that dispersion dominates the atom–light interaction far from resonance. The calculated absorption and dispersion are compared to experimental data for Rb vapour on the D1 transition, showing the validity of the approximations.

Measuring the Stokes parameters for light transmitted by a high-density rubidium vapour in large magnetic fields

Here we report on measurements of the absolute absorption and dispersion of light in a dense rubidium vapour on the D2 line in the weak-probe regime with an applied magnetic field. A model for the electric susceptibility of the vapour is presented which includes both dipole–dipole interactions and the Zeeman effect. The predicted susceptibility is comprehensively tested by comparison to experimental spectra for fields up to 800 G. The dispersive properties of the medium are tested by comparison between experimental measurements and theoretical prediction of the Stokes parameters as a function of the atom–light detuning.

Optical control of Faraday rotation in hot Rb vapor.

We demonstrate controlled polarization rotation of an optical field conditional on the presence of a second field. Induced rotations of greater than

Optical preparation and measurement of atomic coherence at gigahertz bandwidth

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Optical control of the Faraday Effect in a Slow-light Medium

rad are seen with a transmission of