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.
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 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.
Abstract Laser spectroscopy of hot atomic vapours has been studied extensively. Theoretical models that predict the absolute value of the electric susceptibility are crucial for optimising the design of photonic devices that use hot vapours, and for extracting parameters, such as external fields, when these devices are used as sensors. To date, most of the models developed have been restricted to the weak-probe regime. However, fulfilling the weak-probe power constraint may not always be easy, desired or necessary. Here we present a model for simulating the spectra of alkali-metal vapours for a variety of experimental parameters, most distinctly at intensities beyond weak laser fields. The model incorporates optical pumping effects and transit-time broadening. We test the performance of the model by performing spectroscopy of 87Rb in a magnetic field of 0.6 T, where isolated atomic resonances can be addressed. We find very good agreement between the model and data for three different beam diameters and a variation of intensity of over five orders of magnitude. The non-overlapping absorption lines allow us to differentiate the saturation behaviour of open and closed transitions. While our model was only experimentally verified for the D2 line of rubidium, the software is also capable of simulating spectra of rubidium, sodium, potassium and caesium over both D lines.
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.
We investigate experimentally and theoretically the Faraday effect in an atomic medium in the hyperfine Paschen–Back regime, where the Zeeman interaction is larger than the hyperfine splitting. We use a small permanent magnet and a micro-fabricated vapour cell, giving magnetic fields of the order of a tesla. We show that for low absorption and small rotation angles, the refractive index is well approximated by the Faraday rotation signal, giving a simple way to measure the atomic refractive index. Fitting to the atomic spectra, we achieve magnetic field sensitivity at the 10 −4 level. Finally we note that the Faraday signal shows zero crossings which can be used as temperature insensitive error signals for laser frequency stabilization at large detuning. The theoretical sensitivity for 87 Rb is found to be ∼40 kHz °C −1 .
Having a strong interaction between hot alkali vapour and light is important for Rydberg physics and nonlinear optics. In optical fibres, the tight confinement by the core offers high laser intensities for even moderate powers. With the invention of hollow-core photonic crystal fibres (HC-PCFs), the interaction of alkali atoms with high intensities over long distances could be studied. In the past, setups combining alkali atoms and a HC-PCF have suffered from long waiting times until atoms are evenly distributed along the fibre. The large size of the used vacuum chambers entailed technical challenges when trying to heat the system uniformly. In this thesis, an all-glass vapour cell incorporating a hollow-core fibre is presented. Its compact size allows fast and precise control of the temperature. Measurements have shown that this cell drastically reduces the time required for equilibration to only hours. Furthermore, the cell’s all-glass design permits unobstructed optical access from all sides. The optical access can be used to record the fluorescence emitted by atoms along the inside of the fibre core. In a first experiment, the frequency-dependent fluorescence along the fibre position was monitored while alkali vapour was diffusing out of the fibre. The atomic density was successfully retrieved using a numerical model based on the optical Bloch equations. Promising technical improvements of the cell design using fibre tapers are discussed, which could lead to an all-fibre vapour cell with fibre-integrated light delivery. The high laser intensity inside a HC-PCF can easily exceed the linear spectroscopy regime. Staying below the saturation intensity inside a waveguide might not always be easy—or even desired. However, established numerical software packages, such as ElecSus, are limited to the weak-probe regime. For that reason, an open-source software based on the Lindblad master equation was developed in this work. The software allows predicting the absolute value of the electric susceptibility for many experimental parameters of hot alkali vapours, including the isotope ratio, temperature or magnetic field strength. Most distinctly, it includes the laser intensity and effects such as optical pumping and transit-time broadening. To verify the model accuracy, spectra of 87Rb-filled cells were measured in a magnetic field of 0.6 T. Entering the hyperfine Paschen-Back regime, individual atomic resonances can be addressed, allowing further benchmarking of the model based on open and closed transitions. Comparing the experimental data with simulated spectra, very good agreement for three different beam diameters and for laser intensities over a range of more than five orders of magnitude was found. Finally, Rydberg states of rubidium—with their multitude of possible transitions—are discussed as a possible source of light in the terahertz (THz) region. In contrast to some other existing sources, THz from hot atomic vapour is expected to be very narrowband. In one report, the successful generation of THz in a four-level-system in hot rubidium vapour was observed. Here, a very similar setup was employed, but unfortunately no THz emission was detected. It is unclear if the reason is of fundamental or experimental nature. One potential route to enhance the THz signal strength at the detector is to channel the signal as much as possible by guiding it inside a waveguide. Appropriate waveguides were investigated, which in contrast to optical frequencies use polymers as a material. Using polymers, waveguides using the 3D printing technique were fabricated and guidance of THz light was observed.
We investigate experimentally and theoretically the Faraday effect in an atomic medium in the hyperfine Paschen–Back regime, where the Zeeman interaction is larger than the hyperfine splitting. We use a small permanent magnet and a micro-fabricated vapour cell, giving magnetic fields of the order of a tesla. We show that for low absorption and small rotation angles, the refractive index is well approximated by the Faraday rotation signal, giving a simple way to measure the atomic refractive index. Fitting to the atomic spectra, we achieve magnetic field sensitivity at the 10−4 level. Finally we note that the Faraday signal shows zero crossings which can be used as temperature insensitive error signals for laser frequency stabilization at large detuning. The theoretical sensitivity for 87Rb is found to be ∼40 kHz °C−1.
We present a major update to ElecSus, a computer program and underlying model to calculate the electric susceptibility of an alkali-metal atomic vapour. Knowledge of the electric susceptibility of a medium is essential to predict its absorptive and dispersive properties. In this version we implement several changes which significantly extend the range of applications of ElecSus, the most important of which is support for non-axial magnetic fields (i.e. fields which are not aligned with the light propagation axis). Supporting this change requires a much more general approach to light propagation in the system, which we have now implemented. We exemplify many of these new applications by comparing ElecSus to experimental data. In addition, we have developed a graphical user interface front-end which makes the program much more accessible, and have improved on several other minor areas of the program structure. Program Title: ElecSus Program Files doi: http://dx.doi.org/10.17632/h7cj8bz4bd.1 Licensing provisions: Apache License, Version 2.0 Programming language: Python External routines/libraries: SciPy library [1] 0.15.0 or later, NumPy [1], matplotlib [2], sympy [3], lmfit 0.9.5 or later [4], wxpython (required for GUI only) Nature of problem: Calculating the weak-probe electric susceptibility of an alkali-metal vapour. The electric susceptibility can be used to calculate spectra such as transmission and Stokes parameters. Measurements of experimental parameters can be made by fitting the theory to data. Solution method: The transition frequencies and wavelengths are calculated using a matrix representation of the Hamiltonian in the completely uncoupled basis. A suite of fitting methods are provided in order to allow user supplied experimental data to be fit to the theory, thereby allowing experimental parameters to be extracted. Restrictions: Results are only valid in the weak-probe regime. [1] T. E. Oliphant, Comput. Sci. Eng. 9, 10 (2007). http://www.scipy.org/ [2] J. D. Hunter, Comput. Sci. Eng. 9, 10 (2007). http://matplotlib.org/ [3] A. Meurer et. al, PeerJ Comp. Sci. 3, e103 (2017) http://www.sympy.org/ [4] M. Newville et al., LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python, Zenodo (2014). DOI:10.5281/zenodo.11813 https://lmfit.github.io/lmfit-py/