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# Dr Thomas Whitehead

I am a machine learning scientist at Intellegens, a Cambridge-based Artificial Intelligence (AI) company with a unique capability to handle sparse and fragmented data sets. Intellegens is a spin-out company from the University of Cambridge's Cavendish Laboratory, where I recently completed my PhD (more about my research below).

At Intellegens, I lead the application of our novel deep learning approach to a wide variety of industrial applications, including in the materials design, drug discovery, and healthcare sectors. I also help develop the internal suite of tools and algorithms to support our core products.

### PhD research

My PhD, under the supervision of Dr Gareth Conduit, involved two main research strands. The first was accelerating and improving the accuracy of numerical simulations, particularly those using a popular quantum Monte Carlo code called CASINO. This involved developing and deploying model potentials for ultracold atomic gas experiments (schematic picture of such an experiment at the bottom of the page), and also the creation of a new form of correlation factor that more realistically interpolated between the physical symmetries of interacting particles and the symmetries imposed by carrying out simulations in finite, tessellated, volumes.

The second strand of my PhD research involved the investigation of a new kind of superconducting phase for a particular type of condensed matter system, called a 'spin-imbalanced Fermi gas'. The traditional, conventional model of superconductivity in these systems has significant drawbacks, and so we proposed a new form of superconductivity based on groups of particles, rather than just the pairs of conventional theory. See the section below for more on this work.

### Spin-imbalanced superconductivity

The BCS theory of superconducivity has a long and successful history of describing superconducting phenomena. The conventional theory is built by combining together Cooper pairs of bound electrons from opposite sides of the (identical) Fermi seas of the up- and down-spin electrons. In imbalanced systems with different numbers of electrons for the different species this concept of Cooper pairs has previously been stretched into so-called FFLO theory, where the members of the pair just reside on the different Fermi surfaces.

However, FFLO theory has several unattractive properties. Chief amongst these is that, because there are different numbers of particles for the different species, some minority electrons will necessarily not be involved in the FFLO pairs. This wastes their potential for contributing binding energy to the system.

Our proposal for a new superconducting state extends the concept of Cooper pairs to include groups of more than two electrons. For example, if the Fermi surface for the up-spin species is twice as big as that for the down-spin species, we might include two up-spin electrons and one down-spin electron in the state, as shown in the schematic figure. We can compare the binding energy of this state to the FFLO state, and find that our proposal is energetically favourable compared to FFLO theory. The many-particle superconducting state is also under investigation, which has the interesting property of not behaving as a collection of composite bosonic particles in any limit.

*Mathematica* Path Integral Monte Carlo program

For my own edification, education, and entertainment, I have put together a *Mathematica* Package that allows the simulation of ultra-cold atomic gas experiments, at finite temperature and with finite system sizes. It is a reasonably quick, parallel bit of code whose main aim is to be easy to understand and extend. The Package, in whichever version number it currently is, should be available from here, and is distributed under GPL 3.0.

### Notes on superconductivity

I have a couple of notes on aspects of FFLO superconductivity that I have found useful during our investigation of the many-particle superconducting state. I'm making them available here in case anyone else might also find them useful: here is a run-through of the evaluation of the thermodynamic potential for 3D FFLO theory, and here is a calculation of the transition imbalance for 2D FFLO. Hopefully they are of some use!

### Previous Study

Prior to coming to Cambridge I studied for an MPhys at St Hugh's College Oxford. My final year project was investigating the motion of active nematic swimmers, supervised by Prof Julia Yeomans.

In the summer of 2013 I worked at the Met Office as part of the Atmospheric Dispersion and Air Quality group, parameterising low frequency turbulence under the supervision of Dr Helen Webster.

### PhD Thesis

My Thesis, entitled ** Interacting Fermi Gases**, is available online here.

### Publications

*Parameterizing unresolved mesoscale
motions in atmospheric dispersion models*,

Journal of Applied Meteorology and Climatology **57**, 645 (2018).

*Multiparticle instability in a spin-imbalanced Fermi gas*, Physical Review B **97**, 014502 (2018).

Also available at arXiv:1712.09847 and as a pdf (© APS).

*Jastrow correlation factor for periodic systems*, Physical Review B **94**, 035157 (2016).

Also available at arXiv:1607.05921 and as a pdf (© APS).

*Pseudopotential for the two-dimensional contact interaction*, Physical Review A **93**, 042702 (2016).

Also available at arXiv:1603.05001 and as a pdf (© APS).

*Pseudopotentials for an ultracold dipolar gas*, Physical Review A **93**, 022706 (2016).

Also available at arXiv:1601.07746 and as a pdf (© APS).

### Presentations

*A multi-particle superconductor?*, Cavendish Graduate Student Conference, University of Cambridge, 1 December 2016; and Frontiers of Condensed Matter Physics, University of Bristol, 10 January 2017.

*The ν Jastrow factor*, Electronic Structure Discussion Group, TCM, University of Cambridge, 9 March 2016.

*Pseudopotentials for a dipolar ultracold atomic gas*, Electronic Structure Discussion Group, TCM, University of Cambridge, 18 March 2015; and Quantum Cambridge Winter School, St Hugh's College Oxford, 20-23 March 2015.

### Posters

*Pseudopotentials for an ultracold dipolar gas*, New States of Matter and their Excitations, Helmholtz Virtual Institute, 18 June 2015; Physics by the Lake, Cumberland Lodge, 2-15 August 2015; Jesus College Graduate Student Conference, 12 March 2016; and Long-Range Interacting Many-Body Systems: from Atomic to Astrophysical Scales, ICTP, Trieste, 25-29 July 2016.