## PhD Projects

We would love to hear from you if you are interested in a PhD position. Please get in touch and we can discuss options. Further details of possible opportunities are given below (click for details of each):

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School of Physics and Astronomy, University of St Andrews.

We would love to hear from you if you are interested in a PhD position. Please get in touch and we can discuss options. Further details of possible opportunities are given below (click for details of each):

In this project you will work towards building theoretical models of a chemical reaction happening inside a cavity. The cavity is able to confine electromagnetic radiation that can induce a transition between electronic or vibrational states of the molecule(s). However, even when the cavity is unpopulated with photons, vacuum fluctuations could still modify the eigenstates of the molecule-photon system, and in turn this may change the rates and outcome of a chemical reaction.

We recently invented a new technique for studying the dynamics of small open quantum systems, in which the dynamics of quantum system strongly coupled to one or more environments can be modelled. We have shown our method is extremely efficient and able to simulate a very wide range of models. We are now working on how we might extend these models to accurately capture the very large number of molecules that might be involved in a chemical reaction. By using and developing such techniques further, you will model the dynamics of the molecules inside a cavity, treating the cavity modes and molecular vibrations as strongly coupled environments.

We also plan to propose and describe experiments that aim to demonstrate cavity-induced chemical catalysis that are being performed by our collaborators and the Universities of Sheffield and Milan. These might include efforts to improve transport characteristics in a transistor, and altering the progress of an isomerization reaction.

Related literature:
PT-MPO techniques - the new methods we have developed to describe strongly coupling open systems:

[1] Efficient non-Markovian quantum dynamics using time-evolving matrix product operators
Strathearn et al. Nature Comms. 9 3322 (2018)

[2] Efficient exploration of Hamiltonian parameter space for optimal control of non-Markovian open quantum systems Fux et al. Phys. Rev. Lett. 126 200401 (2021)

[3] Exact dynamics of non-additive environments in non-Markovian open quantum systems, Gribben, Rouse, Iles-Smith et al. https://arxiv.org/abs/2109.08442 (2021)

[4] Numerically-exact simulations of arbitrary open quantum systems using automated compression of environments, Cygorek et al. https://arxiv.org/abs/2101.01653 (2021)

Possible experimental demonstration of this kind of thing:

[5] Tilting a ground-state reactivity landscape by vibrational strong coupling
Thomas et al. Science 363 615 (2019)

A model proposing a way in which reaction rates might be influenced by strong coupling:

[6] Resonant catalysis of thermally-activated chemical reactions with vibrational
polaritons Campos-Gonzalez-Angulo et al. Nat Commun. 10 4685 (2019)

A recent demonstration, using molecules in cavities, of superabsorption, by our group and that of experimentalist collaborators:

[7] Superabsorption in an organic microcavity: towards a quantum battery. Quach et al. Science Advances, in the press (2022); see https://arxiv.org/ftp/arxiv/papers/2012/2012.06026.pdf for an earlier preprint.

No real-world quantum system is truly isolated. This means the dynamics of a quantum system cannot be fully captured by just solving its Schrödinger equation, and instead different approaches need to be developed. If the coupling to an environment is strong, as it often is in solid state or molecular systems, it is not even possible to predict a system's future evolution with a model that only depends on the present time. Rather, the full history of how a system has interacted in the past is needed to know what it will do in the future.

Such ‘non-Markovian’ behaviour is notoriously difficult to simulate. However, in recent years we have developed a suite of groundbreaking new algorithms to tackle this challenge. In particular, we use tensor network approaches to capture the influence of the environment on a system efficiently. This has opened up a new world of predictive power.

In this project, we will exploit and combine powerful features from different and currently complementary tensor network methods and apply them to particular real-world problems. In particular, we will be interested in cases where one or two particles in the environment dominate the effect on the open system, over a broad background of the rest. This might, for example, allow us to design molecular systems that have more efficient energy transfer, and so impact on the future developments in solar cell technology.

Related literature:

PT-MPO techniques - the new methods we have developed to describe strongly coupling open systems:

[1] Efficient non-Markovian quantum dynamics using time-evolving matrix product operators
Strathearn et al. Nature Comms. 9 3322 (2018)

[2] Efficient exploration of Hamiltonian parameter space for optimal control of non-Markovian open quantum systems Fux et al. Phys. Rev. Lett. 126 200401 (2021)

[3] Exact dynamics of non-additive environments in non-Markovian open quantum systems, Gribben, Rouse, Iles-Smith et al. https://arxiv.org/abs/2109.08442 (2021)

[4] Numerically-exact simulations of arbitrary open quantum systems using automated compression of environments, Cygorek et al. https://arxiv.org/abs/2101.01653 (2021)

Our studies of the quantum mechanics of light harvesting in molecular systems:

[5] A. Fruchtman et al. Phys. Rev. Lett. 117 203603 (2016)

[6] K. D. B. Higgins, et al. J. Phys. Chem. C 121 20714 (2017)

[7] K. D. B. Higgins, et al. Nature Communications 5 4705 (2017)

There now exist a suite of different experimental techniques that can be used to image how the excitations of a quantum system change in both space and time. Such methods include transient absorption microscopy, which can probe features of above about 100 nm, and scanning tunnelling microscope luminescence, which can reach features that are smaller than a single molecule.

Such techniques are very exciting since they open a new window on how complex quantum mechanical processes work and what their function is in real devices. For example, they allow us to track how absorbed energy moves around in a solar cell, thus enabling us to design more efficient devices. In addition, imaging biomolecules in this way will allows us a greater understanding the fundamental mechanisms of life — and to probe the key role of non-equilibrium dynamics in biology.

It is vital then, to develop theoretical tools that are able to model the quantum dynamics of systems like molecules, which are typically strongly coupled to an environment of vibrational modes. Such open quantum systems undergo non-Markovian dynamics, in which the behaviour of a system cannot be predicted from its current state alone. What it has done in the past, too, affects what it will do in the future.

We have developed a set of ground-breaking new tools that enable the ultra-efficient modelling of such systems. Our tools are based on tensor networks, and are ideally suited for extracting the kinds of spatio-temporal information that modern experiments are now able to provide. In this project your aim will be to identify and model the signals that are generated in these experiments.

In the longer term, this work will help to identify better device designs for solar energy harvesting, In addition, we hope to understand how quantum allostery—i.e. signalling between different parts of a protein that triggers a biological function — works.

Related literature:

Tensor network methods we we have developed to describe strongly coupling open systems:

[1] Unveiling non-Markovian spacetime signaling in open quantum systems with long-range tensor network dynamics Lacroix, Dunnett, Gribben, Lovett, and Chin Phys. Rev. A 104 052204 (2021)

[2] Efficient non-Markovian quantum dynamics using time-evolving matrix product operators
Strathearn et al. Nature Comms. 9 3322 (2018)

[3] Efficient exploration of Hamiltonian parameter space for optimal control of non-Markovian open quantum systems Fux et al. Phys. Rev. Lett. 126 200401 (2021)

[4] Exact dynamics of non-additive environments in non-Markovian open quantum systems, Gribben, Rouse, Iles-Smith et al. https://arxiv.org/abs/2109.08442 (2021)

[5] Numerically-exact simulations of arbitrary open quantum systems using automated compression of environments, Cygorek et al. https://arxiv.org/abs/2101.01653 (2021)

Experimental methods probing spatio-temporal correlations:

[6] Probing intramolecular vibronic coupling through vibronic-state imaging Kong et al. Nature Comms. 12 1280 (2021)

[7] Transient absorption microscopy: Technological innovations and applications in materials science and life science Zhu and Cheng J. Chem, Phys. 152 020901 (2020)

[8] Microcavity-like exciton-polaritons can be the primary photoexcitation in bare organic semiconductors Pandya, et al. Nature Comms. 12 6519 (2021)

Allostery:

[9] Energy Flow in Proteins Leitner, Ann. Rev. Phys. Chem. 59 233 (2008)

The generation of indistinguishable single photons on demand is a key requirement for many kinds of future quantum technologies, such as secure communication and optical quantum computing [1]. Being able to make coherent quantum light sources in solid state systems would enable us to create on-chip photonic circuits that would enable this technology. It is therefore of the utmost importance to understand what effect a solid state environment has on the fidelity of emitted photons.

In this project, you will exploit and developing a groundbreaking new technique our group has created for simulating open quantum systems [2]. Based on a combination of Feynman's path integrals [3,4] and matrix product states [5], it has already enabled calculations impossible by more traditional means. You will study how the technique might be used to calculate the photon correlation functions that characterise a single photon source, in the presence of a strongly-coupled environment of vibrational modes of the crystal. You will go on to study how a photonic cavity might be used to improve the performance of such a device.

[1] I. Aharonovich. D. Englund and Milos Toth, Nature Photonics 10 631 (2016)

[2] A. Strathearn, P. Kirton, D. Kilda, J. Keeling, and B. W. Lovett, Nature Communications 9 3322 (2018)

[3] R. P. Feynman, and F. L. Vernon, Jr., Ann. Phys. 24 118 (1963)

[4] N. Makri and D. E. Makarov. The Journal of Chemical Physics J. Chem. Phys. 102 4600 (1995)

[5] R. Orús, Annals of Physics 349 117 (2014)

While we do not have any positions available at present, Brendon is happy to advise with applications for fellowships. Some relevant links are below. Other schemes exist, particularly international.

Royal Society Dorothy Hodgkin Fellowship

The Royal Commission for the Exhibition of 1851 Fellowships

Royal Society Newton International Fellowships

Leverhulme Trust Early Career Fellowships