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Modelling and experimental control of hot rubidium vapour in hollow-core fibres

Daniel R Häupl

Published Sep 15, 2025• 0 citations
Publisher

Abstract

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.

DOI
10.25593/open-fau-2273

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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.
[Truncated] This thesis concerns a new photonic technology based on hollow-core photonic-crystal fibre (HC-PCF) that has been loaded with an atomic vapour. It was demonstrated that this technology may have important applications in the fields of metrology and quantum optics. Furthermore, the small size and robustness of HC-PCF allows these devices to potentially be miniaturised for possible commercial and industrial applications. By filling the HC-PCF with an atomic vapour, excellent light-atom coupling can be attained as both the atoms and light are confined within the same volume. The small transverse dimensions of the fibre’s optical mode leads to high intensities at low input powers, enabling efficient driving of non-linear transitions which would otherwise be difficult with free-space optical systems. Additionally, long interaction lengths, obtained through an arbitrary length of HC-PCF, lead to large optical depths on these typically weak non-linear transitions. The non-linear transition employed here is the 5S1/2 → 5D5/2 rubidium (Rb) two-photon transition. This system is of great interest due to its non-linearity, long excited state lifetime, efficient excitation and large optical depth attained within the HC-PCF. A number of methods for loading a HC-PCF with Rb are discussed, along with proposed ideas for making this process more efficient. Spectroscopic techniques were used to investigate the effect of the fibre’s confined geometry upon the atomic spectra. Extensive theoretical modelling was employed to confirm the observed spectra and give insight to the mechanisms behind the observations. Using this experimental and theoretical knowledge, two applications were targeted: optical atomic frequency standards; and cross phase modulation for quantum logic gates.
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.
Abstract We present a new type of compact and all-glass based vapour cell integrating hollow-core photonic crystal fibres. The absence of metals, as in a traditional vacuum chamber and the much more compact geometry allows for fast and homogeneous heating. As a consequence we can fill the fibres on much faster timescales, ranging from minutes to hours. Additionally the all-glass design ensures optical access along the fibre. This allows live monitoring of the diffusion of rubidium atoms inside the hollow-core by measuring the frequency-dependent fluorescence from the atoms. The atomic density is numerically retrieved using a five-level system of Bloch-equations.
We present a new type of compact and all-glass based vapour cell integrating hollow-core photonic crystal fibres. The absence of metals, as in a traditional vacuum chamber and the much more compact geometry allows for fast and homogeneous heating. As a consequence we can fill the fibres on much faster timescales, ranging from minutes to hours. Additionally the all-glass design ensures optical access along the fibre. This allows live monitoring of the diffusion of rubidium atoms inside the hollow-core by measuring the frequency-dependent fluorescence from the atoms. The atomic density is numerically retrieved using a 5-level system of Bloch-equations.
This thesis reports on the design and fabrication of an experimental platform for in-fibre laser cooling of Rb and atom optics. By in-fibre laser cooling, we mean the long term aim of laser cooling thermal Rb atoms of a Photonic MicroCell (PMC), and subsequently developing what would be cold-atom photonic crystal fibre (PCF). The platform was designed to harbor several experiments on cold and thermal atom guidance and in-fibre spectroscopy so to address several open questions related for example to the effect of the core inner-wall surface on the atom energy structure and on selective fibre mode excitation for atom trapping and cooling. The completed platform comprises a specific and large ultra-high vacuum (UHV) chamber and a set of lasers for both atom cooling and atom guiding inside highly tailored hollow-core PCF (HC-PCF). The UHV chamber was designed to accommodate several HC-PCFs and two magneto-optical traps (MOT). The HC-PCF were designed, fabricated and post-processed to exhibit different core diameter, modal content and core inner surface material. For example, the mode field diameters range from ~30 µm to ~80 µm for the fundamental Gaussian-like core mode, and the surface materials include pure silica, a layer of Aluminosilicate or a layer of PDMS so to provide a large parameter space in assessing the effect of surface on the fibre-confined atoms. The system has been constructed and characterized. The cooling/repumping laser was frequency-stabilized, with measured Allan variance deviation of σ(τ)=3.8×10^(-11)/√τ. With the system we generated MOT with both isotopes of the Rb atom, with a cooling temperature as low as 7 µK. The platform is now operational to undertake the first atom guidance and explore the feasibility of atom cooling inside a HC-PCF.
This thesis describes developments in atomic vapour loading in hollow core photonic crystal fibre (HC-PCF) for fabrication of atomic vapour loaded photonic microcells (PMC). These developments have been targeted at addressing some of the issues associated with loading atomic vapours in confined waveguiding geometries such as increased dephasing and physio-chemical wall absorptions. Atomic vapour loaded HC-PCF and PMC’s have applications in laser metrology, coherent optics and magneto optical spectroscopy. State of the art HC-PCF have been fabricated for loading with atomic vapour including both photonic bandgap (PBG) guiding and inhibited coupling (IC) hypocycloidal core shape Kagome HC-PCF. Record loss of 70 dB/km has been achieved in IC hypocycloid core shape Kagome HC-PCF in the spectral region centred at 800 nm. This fibre retains excellent single mode propagation combined with large core and increased optical bandwidth in comparison with specialist PBG HC-PCF optimised for operation around 800 nm. Aluminosilicate sol-gel coatings have been developed and successfully applied to the inner core wall of HC-PCF’s to reduce the atomic vapour surface interaction. Confining atomic vapours in micron scaled HC-PCF results in increased dephasing rates because of the frequent atom wall collisions. Anti relaxation coating materials have been applied to the inner core wall and the longitudinal relaxation time has been measured in coated and uncoated fibres utilising a magneto optical technique. Additionally sub Doppler transparencies are investigated in anti relaxation coated and uncoated HC-PCF.