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Faraday Rotation of Pulsed and Continuous-wave Light in Atomic Vapour

Paul Siddons

Published Jan 1, 2011• 1 citation
OpenAlex

Abstract

The absorptive and dispersive properties of a Doppler-broadened vapour of rubidium atoms is investigated. A detailed model of the atom-light interaction is developed and found to be in excellent agreement with experiment in the regime where the interacting light field is sufficiently weak such that it does not significantly alter the medium through which it propagates. The importance of using a weak beam to probe atomic systems is discussed, and a method of characterising how weak such a beam has to be is provided. The theoretical model is applied to both situations of illumination by continuous-wave and pulsed light, the latter situation providing a demonstration of the slow light effect. This phenomenon is a manifestation of the dispersive properties of the medium and is shown to exist over a particularly large frequency range, compared to the absorption spectrum, in thermal vapours. Off-resonant interactions are studied, in which incident laser-light is detuned from resonance to such a degree that Doppler-broadening can be neglected. We quantify the extent to which the light needs to be detuned to be in this regime, and provide approximations to the line-shape function developed in earlier parts of the thesis. The approximate line-shapes are much easier to manipulate and allow a more intuitive understanding of the atom-light interaction. In the second part of the thesis we study the Faraday effect and related phenomena which are an expression of the birefringent properties of the atom-light system. Beginning with a theoretical and experimental investigation of the Faraday rotation of a weak continuous-wave beam, we move on to the consideration of pulsed light. Optically-induced birefringence via the application of an intense continuous-wave pumping field is demonstrated experimentally, and the theoretical plausibility of controlling the polarisation state of a weak pulsed field mediated via intense pulsed light is shown.

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This thesis presents both a computational and experimental investigation into light propagation in hot alkali-metal vapours, with a particular focus on utilizing the Faraday effect for practical applications. A model to calculate various spectra for a weak-probe laser beam in an atomic medium with an applied axial magnetic field is presented. A computer program (ElecSus) was developed which implements this model efficiently. Using ElecSus we design optical devices such as Faraday filters and laser frequency stabilizing references. The design of Faraday filters utilizing compact vapour cells is shown, along with excellent agreement with experiment. The importance of including the effect of self broadening in the model is shown for these short path length vapour cells. Also, a Faraday filter is presented that can potentially be used for quantum optics experiments on the caesium D$_1$ line (894~nm). The filter displays the highest ratio of transmission to equivalent noise bandwidth to date for a linear Faraday filter, demonstrating the power of computerized optimization for this application. Furthermore, a Faraday filter is presented for use as an intra-cavity element in an external-cavity diode laser. A proof-of-principle experiment is demonstrated which shows that using a short external cavity with the Faraday filter eliminates mode-hops. Experimentally and theoretically the Faraday effect is investigated in large magnetic fields where alkali-metal atoms enter the hyperfine Paschen-Back regime. This hyperfine Paschen-Back Faraday effect is shown to allow a direct measure of the refractive indices for left and right circular polarized light. Furthermore, fitting the weak-probe spectra using ElecSus is found to give measures of the magnetic field with a fractional precision of the order of $10^{-4}$. In addition we study slow-light pulse propagation in a high density rubidium vapour, showing that our theoretical model for the electric susceptibility is valid for short pulses as well as continuous-wave light. This shows that the model is accurate for predicting weak-probe pulse propagation.

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Weller, L, Dalton, T, Siddons, P +3 more

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

Lee Weller, Toryn Dalton, Paul Siddons +2 more

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.

arXiv:1112.3912•Journal of Physics B Atomic Molecular and Optical Physics•Feb 21, 2012•24 citations
The absorptive and dispersive properties of a Doppler-broadened vapour of rubidium atoms is investigated. A detailed model of the atom-light interaction is developed and found to be in excellent agreement with experiment in the regime where the interacting light field is sufficiently weak such that it does not significantly alter the medium through which it propagates. The importance of using a weak beam to probe atomic systems is discussed, and a method of characterising how weak such a beam has to be is provided. The theoretical model is applied to both situations of illumination by continuous-wave and pulsed light, the latter situation providing a demonstration of the slow light effect. This phenomenon is a manifestation of the dispersive properties of the medium and is shown to exist over a particularly large frequency range, compared to the absorption spectrum, in thermal vapours. Off-resonant interactions are studied, in which incident laser-light is detuned from resonance to such a degree that Doppler-broadening can be neglected. We quantify the extent to which the light needs to be detuned to be in this regime, and provide approximations to the line-shape function developed in earlier parts of the thesis. The approximate line-shapes are much easier to manipulate and allow a more intuitive understanding of the atom-light interaction. In the second part of the thesis we study the Faraday effect and related phenomena which are an expression of the birefringent properties of the atom-light system. Beginning with a theoretical and experimental investigation of the Faraday rotation of a weak continuous-wave beam, we move on to the consideration of pulsed light. Optically-induced birefringence via the application of an intense continuous-wave pumping field is demonstrated experimentally, and the theoretical plausibility of controlling the polarisation state of a weak pulsed field mediated via intense pulsed light is shown.
This thesis presents both a computational and experimental investigation into light propagation in hot alkali-metal vapours, with a particular focus on utilizing the Faraday effect for practical applications. A model to calculate various spectra for a weak-probe laser beam in an atomic medium with an applied axial magnetic field is presented. A computer program (ElecSus) was developed which implements this model efficiently. Using ElecSus we design optical devices such as Faraday filters and laser frequency stabilizing references. The design of Faraday filters utilizing compact vapour cells is shown, along with excellent agreement with experiment. The importance of including the effect of self broadening in the model is shown for these short path length vapour cells. Also, a Faraday filter is presented that can potentially be used for quantum optics experiments on the caesium D1_11​ line (894~nm). The filter displays the highest ratio of transmission to equivalent noise bandwidth to date for a linear Faraday filter, demonstrating the power of computerized optimization for this application. Furthermore, a Faraday filter is presented for use as an intra-cavity element in an external-cavity diode laser. A proof-of-principle experiment is demonstrated which shows that using a short external cavity with the Faraday filter eliminates mode-hops. Experimentally and theoretically the Faraday effect is investigated in large magnetic fields where alkali-metal atoms enter the hyperfine Paschen-Back regime. This hyperfine Paschen-Back Faraday effect is shown to allow a direct measure of the refractive indices for left and right circular polarized light. Furthermore, fitting the weak-probe spectra using ElecSus is found to give measures of the magnetic field with a fractional precision of the order of 10−410^{-4}10−4. In addition we study slow-light pulse propagation in a high density rubidium vapour, showing that our theoretical model for the electric susceptibility is valid for short pulses as well as continuous-wave light. This shows that the model is accurate for predicting weak-probe pulse propagation.
This thesis deals with the study of propagation effects experienced by weak light pulses as they propagate in atomic media driven by strong pulses. We explore both the ultra-short and long pulse regime and investigate the phenomena that arise at these different time scales. In the short pulse regime, a strongly driven two level atomic system presents transient light shifts, and non-adiabatic transitions occur between these adiabatic levels. We have studied a method to probe these light shifts in real time by propagating a weak probe through the medium. The light shifts enrich the spectrum of the probe and the probe gets shaped as a result. In this way a strongly driven two-level system can act as an active pulse shaper, and can introduce oscillations in the temporal profile of an ultra-short pulse at a time scale shorter than the pulse duration. We also show that by driving the system with two time delayed non-resonant strong fields, the non-adiabatic effects can be rendered phase dependent. This gives very sensitive phase control of the excited state population and can be used to formulate new techniques in interferometry. In the long pulse regime we present a new method of slowing light that can be realized in a double two-level system interacting with two orthogonally polarized light pulses that propagate along different axis. Spatio-temporal dependence of the total polarization induces a grating in the ground Zeeman coherence. The stronger of the two fields (the control field) is diffracted from this grating into the direction of the weak probe field compensating for the absorption of this latter field. A transparency window is thus created in the absorption spectrum of the probe leading to the slowing down of light. The transparency window exhibits characteristics similar to the one obtained by EIT (electromagnetic induced transparency) method. However, the important difference between our method and the traditional EIT method, is that ours doesn't rely on realizing dark state in the system. This may open the possibility of slowing down light in more complex atomic media. Moreover, when the linear absorptive response of the medium is cancelled in this manner, the nonlinear response becomes more important. In the situation where fields propagate in the same direction and have same frequency, two regimes have been investigated. For small optical depths, the effective susceptibility behaves as chi_lin exp[2 i phi] (with phi the phase difference between two fields). This renders phase control of the medium response, and the medium can be changed from an absorber to an amplifier, with normal or anomalous dispersion, by adjusting the relative phase phi.  In the regime of large optical thickness, phase saturation takes place and the effective susceptibility turns into chi_lin*, changing an absorber into an amplifier without effecting the dispersive response (chi_lin is linear susceptibility).
Continuous wave extended cavity diode lasers are used to measure the absorptive and dispersive properties of the 5 2S1/2 → 5 (^2)Рз/2 resonance, at 780 nm, in Rubidium (Rb) vapour. The Doppler-broadened hyperfine transitions are studied both with and without a pump beam. The investigation concentrates on three-level Л-systems, realized in the presence of a pump beam, exhibiting Electromagnetically Induced Transparency (EIT). Electromagnetically Induced Absorption (EIA) IS also seen. The EIT and EIA resonances can be several orders of magnitude narrower than the natural line width of the atomic transitions in the absence of the pump beam. Further, the EIT resonances are sensitive to applied magnetic fields. The narrowest resonances measured in this work have a full-width at half- maximum of 〜 80 kHz. This is limited by the transit time of the atoms through the probe and pump beams. Predictions of theoretical calculations and models are compared to experimental results. The theory of beam splitters and interferometers is developed to enable the implementation of a Sagnac interferometer in a novel "biased" alignment. This allows the dispersion of atomic resonances to be measured directly. The direct measurement of the dispersion of the narrow EIT features in a "biased" Sagnac interferometer is presented. Such a signal is ideally suited to precision measurement applications such 88 inertial sensing and magnetometry.
This thesis presents theoretical models and results of numerical simulations describing the propagation of optical pulses through dense, thermal atomic vapours. In particular we investigate the nonlinear effects of optical solitons due to self-induced transparency (SIT) in two-level systems, optical simultons in V-type three-level systems and electromagnetically induced transparency (EIT) in Λ-type systems, including the storage and retrieval of dark-state polaritons. An investigation is made into two-photon excitation of the 5D states of rubidium in a high-intensity beam including the hyperfine structure of the relevant atomic levels. Decay from these states to the 6P manifolds is ruled out as a cause of experimentally observed fluorescence due to the amount of power broadening associated with intensities necessary to provide any significant level of population in these highly excited states. We combine the nonlinear effects of optical solitons and EIT to explain experimentally observed steepened pulses in a V-type system in a micron-length cell. We explain the behaviour as the early formation of a simulton pulse drawn from a CW probe field by a strong coupling pulse, due to coherent population trapping. We predict that in a longer cell it may be possible to facilitate propagation of matched pulses, even when the transitions in the system have different propagation coefficients, as long as decoherence from collision broadening can be controlled. The fact that weak pulses can propagate with this scheme suggests an approach to achieving transparent propagation of single or few photon pulses distinct from, but related to, both SIT and EIT.
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.
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.