Ultracold Atom-Atom Scattering with R-Matrix Methods

Novel experimental methods have allowed for the routine production of ultracold (sub-Kelvin) atoms and small molecules. This has facilitated the study of chemical reactions involving only a small number of partial waves, allowing for unprecedented control over ultracold chemical reactions. This thesis describes work towards a new set of theories, based on Wigner's R-matrix methodology, which are adapted for so-called heavy particle scattering, and in particular atom-atom scattering. From these new theories a new set of methods are constructed to accurately simulate scattering observables such as scattering lengths, cross-sections, and resonances for atom-atom scattering events at ultracold temperatures by producing high resolution plots of these observables. The methods utilise software built for high-accuracy diatomic spectra, such as Duo, to provide molecular eigenenergies and wavefunctions of the bound system at short internuclear distances (in a region known as the inner region), only requiring as input a matrix of diatomic internuclear potential energy curves and couplings. These methods then act as 'harnesses', allowing this information to be used to perform an R-matrix propagation at long internuclear distances (in a region known as the outer region) using R-matrix propagation codes such as PFARM. The result of this propagation is then used to produce the aforementioned scattering observables. In this work these new R-matrix methods are applied to the case of a particle scattering off a Morse potential, to elastic argon-argon collisions, and to the intramultiplet mixing of oxygen when impacted by helium. This work also serves as a basis for the future simulation of more complex scattering events, such as atom-diatom collisions and higher polyatomic collisions

Low-temperature chemistry using the R-matrix method

Techniques for producing cold and ultracold molecules are enabling the study of chemical reactions and scattering at the quantum scattering limit, with only a few partial waves contributing to the incident channel, leading to the observation and even full control of state-to-state collisions in this regime. A new R-matrix formalism is presented for tackling problems involving low- and ultra-low energy collisions. This general formalism is particularly appropriate for slow collisions occurring on potential energy surfaces with deep wells. The many resonance states make such systems hard to treat theoretically but offer the best prospects for novel physics: resonances are already being widely used to control diatomic systems and should provide the route to steering ultracold reactions. Our R-matrix-based formalism builds on the progress made in variational calculations of molecular spectra by using these methods to provide wavefunctions for the whole system at short internuclear distances, (a regime known as the inner region). These wavefunctions are used to construct collision energy-dependent R-matrices which can then be propagated to give cross sections at each collision energy. The method is formulated for ultracold collision systems with differing numbers of atoms.Comment: Presented at Faraday Discussion on the Theory of Chemical Reactions Published in Faraday Discussion

Low temperature scattering with the R-matrix method: argon-argon scattering

Results for elastic atom-atom scattering are obtained as a first practical application of RmatReact, a new code for generating high-accuracy scattering observables from potential energy curves. RmatReact has been created in response to new experimental methods which have paved the way for the routine production of ultracold atoms and molecules, and hence the experimental study of chemical reactions involving only a small number of partial waves. Elastic scattering between argon atoms is studied here. There is an unresolved discrepancy between different argon-argon potential energy curves which give different numbers of vibrational bound states and different scattering lengths for the argon-argon dimer. Depending on the number of bound states, the scattering length is either large and positive or large and negative. Scattering observables, specifically the scattering length, effective range, and partial and total cross-sections, are computed at low collision energies and compared to previous results. In general, good agreement is obtained, although our full scattering treatment yields resonances which are slightly lower in energy and narrower than previous determinations using the same potential energy curve.Comment: 26 pages, 9 figures, 3 table

The influence of the symmetry of identical particles on flight times

In this work, our purpose is to show how the symmetry of identical particles can influence the time evolution of free particles in the nonrelativistic and relativistic domains. For this goal, we consider a system of either two distinguishable or indistinguishable (bosons and fermions) particles. Two classes of initial conditions have been studied: different initial locations with the same momenta, and the same locations with different momenta. The flight time distribution of particles arriving at a `screen' is calculated in each case. Fermions display broader distributions as compared with either distinguishable particles or bosons, leading to earlier and later arrivals for all the cases analyzed here. The symmetry of the wave function seems to speed up or slow down propagation of particles. Due to the cross terms, certain initial conditions lead to bimodality in the fermionic case. Within the nonrelativistic domain and when the short-time survival probability is analyzed, if the cross term becomes important, one finds that the decay of the overlap of fermions is faster than for distinguishable particles which in turn is faster than for bosons. These results are of interest in the short time limit since they imply that the well-known quantum Zeno effect would be stronger for bosons than for fermions.Fermions also arrive earlier than bosons when they are scattered by a delta barrier. Furthermore, the particle symmetry does not affect the mean tunneling flight time and it is given by the phase time for the distinguishable particle.Comment: 25 pages, 1 table, 5 figure

Original research by Young twinkle students (ORBYTS): when can students start performing original research?

Involving students in state-of-the-art research from an early age eliminates the idea that science is only for the scientists and empowers young people to explore STEM (Science, Technology, Engineering and Maths) subjects. It is also a great opportunity to dispel harmful stereotypes about who is suitable for STEM careers, while leaving students feeling engaged in modern science and the scientific method. As part of the Twinkle Space Mission's educational programme, EduTwinkle, students between the ages of 15 and 18 have been performing original research associated with the exploration of space since January 2016. The student groups have each been led by junior researchers—PhD and post-doctoral scientists—who themselves benefit substantially from the opportunity to supervise and manage a research project. This research aims to meet a standard for publication in peer-reviewed journals. At present the research of two ORBYTS teams have been published, one in the Astrophysical Journal Supplement Series and another in JQSRT; we expect more papers to follow. Here we outline the necessary steps for a productive scientific collaboration with school children, generalising from the successes and downfalls of the pilot ORBYTS projects

Bringing pupils into the ORBYTS of research

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A connectome and analysis of the adult Drosophila central brain.

The neural circuits responsible for animal behavior remain largely unknown. We summarize new methods and present the circuitry of a large fraction of the brain of the fruit fly Drosophila melanogaster. Improved methods include new procedures to prepare, image, align, segment, find synapses in, and proofread such large data sets. We define cell types, refine computational compartments, and provide an exhaustive atlas of cell examples and types, many of them novel. We provide detailed circuits consisting of neurons and their chemical synapses for most of the central brain. We make the data public and simplify access, reducing the effort needed to answer circuit questions, and provide procedures linking the neurons defined by our analysis with genetic reagents. Biologically, we examine distributions of connection strengths, neural motifs on different scales, electrical consequences of compartmentalization, and evidence that maximizing packing density is an important criterion in the evolution of the fly's brain