Theory of Quantum Nanomaterials

Over the last decade, we have developed a transformative new approach to modelling non-Markovian open quantum systems—i.e. quantum systems coupled to external environments where we cannot make standard textbook approximations of assuming weak-coupling to the environment, or that the environment rapidly "forgets" information. These methods are based on the Process Tensor approach [1] and in particular its efficient representation and calculation using matrix product operator methods. Much of this is now available through an open-source library, OQuPy [2].

These methods have enabled the exact modelling of open systems that was previously thought not possible, owing to the exponential growth of computational resources required as the simulation time increases.

We seek students who are interested in either technical developments of these methods, or applying these methods to new classes of physical systems.

Among technical extensions, there are challenges in making methods work for high temperature simulations, applying methods to problems with large Hilbert spaces, on modelling baths with slowly (algebraically) decaying correlations, and on exploiting time-translation invariance for generic environments (beyond the case of non-interacting harmonic oscillators).

Among applications, we are keen to apply these methods to open problems in modelling chemical reaction rates, modelling molecular magnets, modelling coherent processes in complex (e.g. biological) systems, and to explore how these methods might be applied in many-body systems.

We would be happy to discuss with potential students which of these, or other related directions, you would be most keen to explore.

[1] J. Keeling, E. M. Stoudenmire, M.-C. Banuls, D. R. Reichman. Process Tensor Approaches to Non-Markovian Quantum Dynamics. arXiv:2509.07661
[2] G. E. Fux, P. Fowler-Wright, J. Beckles, E. P. Butler, P. R. Eastham, D. Gribben, J. Keeling, D. Kilda, P. Kirton, E. D. C. Lawrence, B. W. Lovett, E. O'Neill, A. Strathearn, and R. de Wit. OQuPy: A Python package to efficiently simulate non-Markovian open quantum systems with process tensors. J. Chem. Phys. 161 124108 (2024)

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 - our papers discussing 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. PRX Quantum 3 010321 (2022)
[4] Numerically-exact simulations of arbitrary open quantum systems using automated compression of environments, Cygorek et al. Nature Physics 18 662 (2022)

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 Comms. 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 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. PRX Quantum 3 010321 (2022)
[5] Numerically-exact simulations of arbitrary open quantum systems using automated compression of environments, Cygorek et al. Nature Physics 18 662 (2022)
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)