Kirk Madison

Associate Professor

Relevant Thesis-Based Degree Programs


Graduate Student Supervision

Doctoral Student Supervision

Dissertations completed in 2010 or later are listed below. Please note that there is a 6-12 month delay to add the latest dissertations.

Development of a cold atom pressure standard (2022)

In this thesis, we report the realization of the world's first cold atom based pressure standardfor the high- and ultra-high vacuum (UHV) regimes, , - the only parameter required to quantify the pressureof background particles given a measurement of the collision rate with a sensor atom.This new quantum measurement standard is fully empirical, based on unchanging andfundamental atomic constants, and does not rely on computations of total collisioncross-sections based on theoretical interaction potentials. We demonstrate, using a sensorensemble of ⁸⁷Rb atoms, that this new quantum pressure standard can be appliedto gases of both atomic species (He, Ar, and Xe) and molecular species (N₂, CO₂, andH₂), surpassing the scope of existing orifice flow pressure standards. The accuracy ofthis new standard was also verified by comparing it with an N₂ calibrated ionizationgauge traced back to an orifice flow standard. They agree within 0.5%. A completeuncertainty analysis of this cold atom pressure standard is provided here. Moreover,using this standard, we are able to observe and quantify the performance limits of twoindustry-standard ionization gauges. Using this universal law, we can precisely measurethe total collision cross-section for the collision system of interest. As anexample, we show a precision measurement of for collisions between Rb and Ar.The experimentally determined value of agrees with the theoretical computationresult within 1.0 %. Next, we demonstrate the use of a magneto-optical trap (MOT) asa transfer pressure standard to extend the operational range of the cold atom pressurestandard by a factor of 100, from P
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Optical synthesis and ultracold reactions of triplet 6Li molecules (2018)

In this thesis, we present the creation, via stimulated Raman adiabatic passage, and pre- liminary lifetime measurements of deeply bound triplet molecules of ⁶Li₂ in several rovi- brabrational levels of the a(³Σ⁺u ) molecular potential, including the lowest lying state in this potential. In addition to being the first experimental demonstration of the formation of these dimers, these results will serve as the basis for our ongoing efforts to reliably determine the rate constants responsible for the finite lifetimes of these ultracold molecules and may shed light on some of the mysteries surrounding the quantum state dependence of chemi- cal reactions in the ultracold regime. Moreover, all of the tools - including a robust laser cooling system for ⁶Li, an ultra-low phase noise Raman laser system and various software recipes for the automation of data collection and analysis - and experimental techniques developed in this study can also be used for the creation of heteronuclear LiRb molecules. Unlike our ⁶Li₂ homonuclear molecules which only have a magnetic dipole moment, the LiRb polar molecules are predicted to also have a large electric dipole in the lowest lying triplet state. These characteristics combined with a three dimensional optical lattice would give us precise control over several degrees of freedom and enable us to perform quantum simulations of exotic condensed matter systems.We also present the design and performance of a coherent source of Lyman-α radiation that was used by the ALPHA collaboration at CERN for laser cooling anti-hydrogen for the purpose of experimentally verifying the predictions of the standard model.

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Photoassociation and Feshbach Resonance Studies in Ultra-Cold Gases of vLi and Rb Atoms (2016)

This thesis presents an experimental apparatus capable of producing and studying ultra-cold mixtures of ⁶Li and Rb, and progress towards the creation of ultra-cold ground state ⁶Li₂ and LiRb molecules. Ultra-cold experiments with molecules have applications in many quantum computation and simulation experiments. We discuss elements of the apparatus which are important to these experiments, including electric field plates in air capable of producing fields up to 18 kV/cm, and a laser system for photoassociation spectroscopy based on two Ti:Sapphire lasers phase locked to the same optical frequency comb. With respect to ⁶Li and ⁸⁵Rb mixtures, we report on the observation of six Feshbach resonances, which represent an important step towards molecule production and future experiments in this heteronuclear mixture. In addition, we demonstrate the production of a BEC of ⁶Li₂ Feshbach molecules, a degenerate Fermi gas of ⁶Li and the formation of BCS pairs.In the ⁶Li system, we report on the high resolution spectroscopy of the v'=20-26 vibrational levels of the c(1³∑⁺g) potential and the v'=29-35 vibrational levels of the A(1¹∑⁺u) potential. In the A(1¹∑⁺u) potential, we find that the v'=31 and v'=35 levels have the largest transition strength and are therefore good candidates to use as intermediate states in molecule formation. We demonstrate atom-molecule dark states in the BEC-BCS crossover regime and additionally use dark-state spectroscopy to make extremely high resolution measurements of the least bound N''=0 ro-vibrational levels in the X(1¹∑⁺g) and a(1³∑⁺u) potential. In addition, we present spectroscopy of all ten N''=0 and N''=2 ro-vibrational levels in the a(1³∑⁺u) potential and furnish a preliminary interpretation of the observed energy structure. Finally, we report on the observation of anomalous Autler-Townes and dark-state spectrum. Using an extension to the standard three level model, we show that these anomalous profiles are due to degeneracies that exist in the bound molecular states, and to the choice of polarization of the coupling fields. These results have a direct impact on molecule formation, and provide a clear guide to future experiments.

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Photoassociation spectroscopy of a degenerate Fermi gas of 6Li (2015)

This thesis describes a suite of experimental tools and spectroscopic measurements performed on ultracold ⁶Li molecules. The aim is to create the necessary ingredients for the coherent transfer of the population of ultracold, weakly bound, Feshbach molecules of ⁶Li to deeply bound ro-vibrational levels, making the eventual creation of a Bose-Einstein condensate (BEC) of ground state lithium dimers a reality at the University of British Columbia. Some of the technological milestones include the development of a unique laser system consisting of two Ti:Sapphire lasers frequency stabilized to a femtosecond frequency comb as well as the demonstration of the first in Canada BEC of Feshbach molecules. To determine a suitable path for the coherent transfer using stimulated Raman adiabatic passage (STIRAP) we measure the binding energies of the vibrational levels v''=20-26 of the c(1³Ʃ+g) and v''=29-35 of the A(1¹Ʃ+u) excited states of lithium dimers by the photoassociation of a degenerate Fermi gas of 6Li atoms, achieving accuracy of 600 kHz. For each vibrational level of the triplet potential, we resolve the rotational structure using a Feshbach resonance to enhance the photoassociation rates from p-wave collisions. We also, for the first time, determine the spin-spin and spin-rotation interaction constants for this state. Finally, we are the first to demonstrate exotic dark states in quantum gases of fermionic lithium where atom-molecule coherence is produced between a deeply bound singlet (or triplet) molecular level and atomic pairs in a weakly interacting Fermi gas at zero gauss or in the BEC-BCS crossover regime (i.e. Feshbach molecules or BCS-like pairs). We observe an abrupt and unanticipated change of the classic EIT signature (Electromagnetically Induced Transparency) of the dark-state (i.e. the suppression of single photon absorption to the excited state) in the vicinity of the broad Feshbach resonance at 832.2 gauss potentially indicating new physics notpreviously considered.

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Study of Background Gas Collisions in Atomic Traps (2014)

This thesis describes an investigation and application of the loss of laser cooledatoms from a trap induced by background collisions. The loss rateconstant depends on the density of background gas and the velocity averagedcollisional loss cross section due to collisions. The velocity averagedcollisional loss cross section can be calculated and its dependence on trapdepth was verified using a magneto-optical trap. This verification involvedmeasurements of the loss rate constant for a quadrupole magnetic and amagneto-optical trap and measurement of the density of Ar background gasusing a residual gas analyzer. The second part of the thesis focuses on anapplication of these measurements of the loss rate constant to measure thepressure of the background gas. The experimental progress to date on theatom pressure sensor is provided.

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Master's Student Supervision

Theses completed in 2010 or later are listed below. Please note that there is a 6-12 month delay to add the latest theses.

Optimizing photoassociation signals in small magneto-optical traps and evaporative cooling schemes for shallow optical dipole traps (2023)

This thesis presents work done on two projects that contribute to the study of ultracold atoms in the QDG lab.First, we present a study of the dependence of photoassociation on the trap parameters of a magneto-optical trap. Photoassociation spectroscopy of ultracold atoms has emerged as a powerful tool to measure the energetic and scattering properties of atoms and molecules. The photoassociation process is seen to be strongly affected by the intensity of the cooling laser as well as its detuning. Potential mechanisms, with emphasis on optical shielding bythe trapping lasers, are presented that account for these observations. Considerations presented therein should guide the enhancement of photoassociation signals in atomic species that have constraints on trap sizes.We then present the development of a direct simulation Monte Carlo approach to model evaporative cooling in an optical dipole trap. Simple proof-of-principle results are presented to showcase its utility. Potentially useful applications are outlined for future experiments in our lab.

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Progress towards a portable cold-atom pressure standard (2022)

All existing pressure standards (classical and quantum-based) are large apparatuses - typically, the size of a van or larger. In this thesis, we report on the progress towards building a portable version of a cold-atom based pressure standard which can easily transported by a van instead. Specifically, we discuss - the flexible laser design that can produce 780 nm pump light anywhere in a 26 GHz range and repump light anywhere in a +/- 6.8 GHz range within 14 mL/s of 10 C to 15 C water is available.- the low-outgassing vacuum chamber that can supply rubidium for measurement while minimizing contamination in the chamber under test.- preliminary results characterizing the performance of its rubidium source and magneto-optical trap.- future plans for the apparatus.This pressure standard leverages the linear relationship between the pressure of a vacuum chamber and loss rate of atoms from a magnetic trap in that chamber. Using the universality of loss rates with respect to trap depth, we can use this apparatus to measure the total collision cross section between the trapped rubidium and any species of collision partner. We can also take advantage of the flexible design of its laser system to quickly alternate measurements between ⁸⁵Rb and ⁸⁷Rb to confirm the universal behaviour of both isotopes. We plan to take the apparatus to Physikalisch-Technische Bundesanstalt in the coming months to compare the cold-atom based standard against their orifice flow standard.

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Determination of the atom's excited-state fraction in a magneto-optical trap (2018)

This thesis introduces an empirical method for determining and controlling the excited-state fraction of atoms in a magneto-optical trap (MOT), which is essential for the use of cold atoms as a sensor when they are held in a MOT since their interactions with other particles and fields are quantum state dependent. A four-level theoretical atomic model was used to describe the transitions of the atoms in a MOT, and the fluorescence emitted from a fixed number of atoms under different laser conditions were measured to determine the saturation parameters empirically. Two saturation parameters P_sat= 1.15 (0.06) mW and P_r,sat= 2.05 (0.59) mW were successfully extracted from the model, and the excited-state fraction in the four-level model was accurately calculated as a function of the MOT trap parameters, which ranges from 0.045 to 0.415 for the experimental settings currently available. We also observed minor deviations from the four-level model for the photon scattering rate, and a hypothesis of atom pinning under high powers was proposed to explain the problem. We plan to use this simple excited-state fraction determination method to distinguish the ground and excited state collision cross section of Rubidium atoms with species in residual gas of the vacuum. This is the first step to establishing atom loss rates from a MOT as an atomic primary pressure standard.

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Progress Towards a Primary Pressure Standard With Cold Atoms (2017)

This thesis describes a method of using an ultra-cold ensemble of atoms confined in a trap as an atomic primary pressure standard. The development of the standard and its current status are described in detail. This standard uses a 3D MOT to trap ⁸⁷Rb and then transfer them to a quadrupole magnetic trap where the atoms undergoes collisions with a background gas. By measuring the number of atoms left in the magnetic trap as a function of time one extract a loss rate and from this rate determine the background gas density. This loss rate is a product of the density of the background, multiplied by the loss cross section averaged over the velocity distribution of the background gas. By computing the average loss cross section in the magnetic trap and measuring the loss rate, the density of the background gas can be determined. This gives a calibration free measurement of density of a background gas in the UHV range (10-⁶ ‑ 10-⁹) Torr or (10-⁴ - 10-⁷) Pa which allows for it to be used as a standard. In conjunction with this, preparation of the atoms prior to the loss rate measurement is investigated to ensure accuracy and reproducibility of the standard. Finally a comparison between UBC's atomic standard and NIST's (National Institute for Standards and Technology) orifice flow standard is conducted via an ionization gauge which employed as a transfer standard.All measurement are carried out using Argon gas as the background gas of study.

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The study of field programmable gate array based servos in atomic, molecular and optical physics experiments (2017)

The use of Field Programmable Gate Array (FPGA) is becoming increasingly popular in new designs for instrumentation tools. Among them, the FPGA-based servo is emerging as a replacement for the traditional analog servo as a more versatile, automated and remotely controllable alternative. Despite the demonstration of FPGA servos for the control of lasers in the literature, the practical constraints of an FPGA servo have not yet been fully investigated. This work presents an open-source FPGA servo design that is capable of reaching a total signal latency of 200 ns including both conversion delay and computation delay. This work also investigates various limitations inherent in a digital implementation of a servo arising from the computation precision of an Infinite Impulse Response (IIR) filter and the effect that signal quantization has on the transfer function that a digital servo can implement. These technical details are not widely discussed, but are important both for the design and the operation of the FPGA servo. Applying the FPGA servo in an intensity stabilization application allows direct tests of these limitations. In particular, this work compares the performance of the FPGA servo and a high-performance commercial analog servo with a focus on key specifications including the closed-loop bandwidth, noise floor and the resolution of the transfer functions. For closed-loop control scenario with a bandwidth below 1 MHz, we achieve better performance with the FPGA servo than the analog servo through the use of more complex transfer functions including a Proportional and Integral Cubed (PI3) and a Proportional Integral and Integral (PII) with lag-lead.

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Tools for Trapping and Detecting Ultracold Gases (2016)

We construct a vertical imaging system designed to image along the quantization axis of the experiment. We demonstrate that it has a resolution on the order of 1-2μm which is on par with previous characterizations of the constituent components. We find that the inclusion of the vertical imaging system has a detrimental effect on the atom loading performance of the MOT. We show that this decrease is by approximately a factor of 2 down to 6.5×10⁶ atoms per second and 8.1×10⁷ atoms respectively. We subsequently detail the design of a novel lattice apparatus capable of tuning the lattice spacing by many orders of magnitude on the timescale of a typical experimental cycle. A proof-of-principle for this so-called dilating lattice is realized and the mechanism for variable lattice spacing is shown to work. Lastly, we cover our efforts towards measuring the effect of Feshbach resonances on collisional decoherence rates in ⁶Li. To this end, we show that the Rabi frequency we can create given our current tools is approximately 100Hz. A unknown strong mechanism for decoherence obstructs our experimental signature and a brief discussion of our attempts to discover its origin is presented.

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An experimental apparatus for the laser cooling of lithium and rubidium (2014)

We demonstrate a two species effusive source and Zeeman slower for lithium 6 and rubidium 85. The fluxes produced by this slower allow for magneto-optical trap loading rates in excess of 10⁸ atoms per second for both species. A detailed model is developed to predict the emission properties of the effusive source along with the flux of cold atoms produced by the slower. Novel to this design is the mating of Zeeman slower magnetic field to the field produced by trapping coils which increases the effective length over which atoms are slowed. This allows for a smaller, more compact slower, without a sacrifice in performance. Details relating to the design and performance of the vacuum system and magnetic field producing coils are also covered. The apparatus can be easily adapted to operate with different atomic species making it well suited for ultracold atomic physics experiments studying mixtures or as starting point for the creation of hetero-nuclear molecules.

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