Understanding and engineering dissipation in nanoscale quantum devices
Lead Research Organisation:
University of St Andrews
Abstract
The march of technological progress has given us devices that are ever smaller and more complex: today's smart phones for example are almost unrecognizable in their size and their range of functions from the models of 25 years ago. This progress has taken us to the point where devices must now be understood in terms of the quantum behaviour of their constituent particles, a new frontier in technology that furthermore will lead to completely new applications.
However, building fully quantum mechanical models of devices is notoriously difficult: the amount of information needed to describe a quantum system scales exponentially with its size. The situation is even worse when one must consider how the environment interacts with the device, and yet this is a crucial consideration for real devices. However, we have recently developed a new quantum simulation technique with remarkable efficiency: by keeping just the most important information we are able to track the behaviour of a single particle even when it is interacting very strongly with all of the other particles in its environment.
In this project, we will exploit this new technique to design, simulate, and optimize four types of nanoscale devices with various technological applications. The functioning of all these devices relies on similar physics, namely how the device interacts with the environment. As such, our new method is ideally suited to all these areas.
First, we will model solid state single photon sources. These produce quanta of light - photons - one at a time, and underpin future ideas for secure communication and quantum computing. We will find how the coupling between the photons and the vibrations of the solid determines affects their performance. Understanding this will allow us to determine how devices, either machined as thin wires or membranes or drawn as nanometre patterns in a solid matrix, could create more effective photon sources.
Second, solar panels need to first absorb light energy from the sun, and then to transport it to electrodes. We will investigate the quantum mechanics of this energy transport problem, in particular for solar cells made of organic materials. Here, vibrations are very strongly coupled to the excited electrons that transport the energy, and our new technique is ideal for studying how this process works and how it might be improved by informed selection of component organic molecules.
Third, a new frontier in electronics will be enabled if we can build circuits using molecules. Electric current is then a consequence of how electrons can tunnel quantum mechanically from one molecule to the next; this depends both on electronic coupling between molecules and how the molecules vibrate. We will use our technique to build models of molecular junctions, and explore how strong electronic and vibrational coupling changes the quantum transport properties of these materials.
Fourth, diamonds have recently been at the forefront of a whole new kind of imaging technology. In particular, single electrons in diamond have a tiny magnetic moment, a 'spin', whose motion depends on how strong the magnetic field is at the position of the electron. Remarkably, the spin of a single electron can be measured in diamond, and so magnetic imaging with nanometre accuracy is a possibility. The limit of how well these 'nano-magnetometers' can work is set by how well they can be isolated from their environment. In this project, we will first use our novel approach to understand the dynamics of a spin coupled to its environment, and then show how to isolate spins more effectively.
The project will advance several different nanotechnologies, and at the same time we will develop a unique and freely available tool that can be applied to a huge variety of new systems in future.
However, building fully quantum mechanical models of devices is notoriously difficult: the amount of information needed to describe a quantum system scales exponentially with its size. The situation is even worse when one must consider how the environment interacts with the device, and yet this is a crucial consideration for real devices. However, we have recently developed a new quantum simulation technique with remarkable efficiency: by keeping just the most important information we are able to track the behaviour of a single particle even when it is interacting very strongly with all of the other particles in its environment.
In this project, we will exploit this new technique to design, simulate, and optimize four types of nanoscale devices with various technological applications. The functioning of all these devices relies on similar physics, namely how the device interacts with the environment. As such, our new method is ideally suited to all these areas.
First, we will model solid state single photon sources. These produce quanta of light - photons - one at a time, and underpin future ideas for secure communication and quantum computing. We will find how the coupling between the photons and the vibrations of the solid determines affects their performance. Understanding this will allow us to determine how devices, either machined as thin wires or membranes or drawn as nanometre patterns in a solid matrix, could create more effective photon sources.
Second, solar panels need to first absorb light energy from the sun, and then to transport it to electrodes. We will investigate the quantum mechanics of this energy transport problem, in particular for solar cells made of organic materials. Here, vibrations are very strongly coupled to the excited electrons that transport the energy, and our new technique is ideal for studying how this process works and how it might be improved by informed selection of component organic molecules.
Third, a new frontier in electronics will be enabled if we can build circuits using molecules. Electric current is then a consequence of how electrons can tunnel quantum mechanically from one molecule to the next; this depends both on electronic coupling between molecules and how the molecules vibrate. We will use our technique to build models of molecular junctions, and explore how strong electronic and vibrational coupling changes the quantum transport properties of these materials.
Fourth, diamonds have recently been at the forefront of a whole new kind of imaging technology. In particular, single electrons in diamond have a tiny magnetic moment, a 'spin', whose motion depends on how strong the magnetic field is at the position of the electron. Remarkably, the spin of a single electron can be measured in diamond, and so magnetic imaging with nanometre accuracy is a possibility. The limit of how well these 'nano-magnetometers' can work is set by how well they can be isolated from their environment. In this project, we will first use our novel approach to understand the dynamics of a spin coupled to its environment, and then show how to isolate spins more effectively.
The project will advance several different nanotechnologies, and at the same time we will develop a unique and freely available tool that can be applied to a huge variety of new systems in future.
Planned Impact
Our work will first have an impact on researchers in academia and industry working on the four specific technologies we have highlighted, but in the longer term the tools we will develop have the potential for even more wide-ranging impact.
Single photon sources are a fundamental resource for many proposed quantum technologies. For example, they are important for secure quantum communication, and our work will be of benefit for developers and users of this technology. There is a large effort in this area through the UK Quantum Technology Hub for Quantum Communication. Many companies have interest in this technology, including HP, NEC, and ID Quantique. Other photonic quantum technologies, such as photonic quantum computers, also rely on good single photon sources and are being pursued internationally (e.g. in the CQC2T ARC Centre of Excellence, Australia and the Psi Quantum spin-out).
Solar energy is the most readily available and plentiful potential energy source, yet its take up has been somewhat inhibited by high embedded cost and complex fabrication techniques. Efficient exciton transport underpins organic molecular architectures for photovoltaic cells, a technology that promises to develop a cheap and flexible solution to power generation and which can also be used to make mobile local power sources, required for the 'internet of things'. Our work promises a new approach to designing appropriate materials for this. Academia and industry are heavily invested in the area (e.g. companies G24Power, Ossila, Merck, Cambridge Display Technology).
The use of molecular electronics promises to deliver smaller scale circuits that has the potential to extend Moore's Law. However, at this scale fully quantum mechanical models of (strongly coupled) molecular junctions are vital: the lack of accurate models is one reason why progress in this area has perhaps been slower than initially hoped. This kind of model is what we will deliver. The reliance of modern society on devices of ever decreasing size means that our work could potentially be felt across a very wide user base: Current interest from companies in molecular electronics includes labs at IBM.
Magnetic imaging with NV centres, has great potential for example in medical imaging, where it can be used to detect the weak magnetic signals coming from brain or heart (see e.g. Budker and Romalis, Nat. Phys. 3 227). Our full account of environmental effects and how this might lead to more sensitive devices will benefit developers of such devices, and ultimately the patients who might be treated. As well as interest in academia, there is also industry work here from Lockheed Martin and Element Six.
Beyond these four specific areas of application, the tools we will develop as part of this proposal will be coded in a very general way and so enable fully quantum mechanical simulations of any Hilbert space of small (~10) dimension, strongly coupled to most kinds of environment. Our publicly-available code could then be applied to many other kinds of system underpinning further applications. For example, understanding decoherence in solid state quantum computers based on silicon or superconducting qubits, atom-photon bound states for controlled quantum gates, heat transport in nanojunctions, or fundamental studies of spatio-temporal correlations. To ensure these benefits are maximised, we will continue to release up-to-date code with all our latest functionality, so that other groups might benefit directly from it (see doi.org/10.5281/zenodo.1322407).
An obvious way in which our work will impact society is through training of individuals in a range of skills. Well-trained quantum theorists are important for a plethora of emerging industries, and are increasingly required in UK academia through the Hubs initiatives. Our track record of producing excellent graduates and post-doctoral scientists means that we are well placed to make such impact.
Single photon sources are a fundamental resource for many proposed quantum technologies. For example, they are important for secure quantum communication, and our work will be of benefit for developers and users of this technology. There is a large effort in this area through the UK Quantum Technology Hub for Quantum Communication. Many companies have interest in this technology, including HP, NEC, and ID Quantique. Other photonic quantum technologies, such as photonic quantum computers, also rely on good single photon sources and are being pursued internationally (e.g. in the CQC2T ARC Centre of Excellence, Australia and the Psi Quantum spin-out).
Solar energy is the most readily available and plentiful potential energy source, yet its take up has been somewhat inhibited by high embedded cost and complex fabrication techniques. Efficient exciton transport underpins organic molecular architectures for photovoltaic cells, a technology that promises to develop a cheap and flexible solution to power generation and which can also be used to make mobile local power sources, required for the 'internet of things'. Our work promises a new approach to designing appropriate materials for this. Academia and industry are heavily invested in the area (e.g. companies G24Power, Ossila, Merck, Cambridge Display Technology).
The use of molecular electronics promises to deliver smaller scale circuits that has the potential to extend Moore's Law. However, at this scale fully quantum mechanical models of (strongly coupled) molecular junctions are vital: the lack of accurate models is one reason why progress in this area has perhaps been slower than initially hoped. This kind of model is what we will deliver. The reliance of modern society on devices of ever decreasing size means that our work could potentially be felt across a very wide user base: Current interest from companies in molecular electronics includes labs at IBM.
Magnetic imaging with NV centres, has great potential for example in medical imaging, where it can be used to detect the weak magnetic signals coming from brain or heart (see e.g. Budker and Romalis, Nat. Phys. 3 227). Our full account of environmental effects and how this might lead to more sensitive devices will benefit developers of such devices, and ultimately the patients who might be treated. As well as interest in academia, there is also industry work here from Lockheed Martin and Element Six.
Beyond these four specific areas of application, the tools we will develop as part of this proposal will be coded in a very general way and so enable fully quantum mechanical simulations of any Hilbert space of small (~10) dimension, strongly coupled to most kinds of environment. Our publicly-available code could then be applied to many other kinds of system underpinning further applications. For example, understanding decoherence in solid state quantum computers based on silicon or superconducting qubits, atom-photon bound states for controlled quantum gates, heat transport in nanojunctions, or fundamental studies of spatio-temporal correlations. To ensure these benefits are maximised, we will continue to release up-to-date code with all our latest functionality, so that other groups might benefit directly from it (see doi.org/10.5281/zenodo.1322407).
An obvious way in which our work will impact society is through training of individuals in a range of skills. Well-trained quantum theorists are important for a plethora of emerging industries, and are increasingly required in UK academia through the Hubs initiatives. Our track record of producing excellent graduates and post-doctoral scientists means that we are well placed to make such impact.
Organisations
- University of St Andrews (Lead Research Organisation)
- Sorbonne University (Collaboration, Project Partner)
- University of Warwick (Collaboration)
- UNIVERSITY OF EXETER (Collaboration)
- University of Cambridge (Collaboration, Project Partner)
- Max Planck Society (Collaboration)
- University of Sheffield (Collaboration)
- Heriot-Watt University (Collaboration)
- University of Oxford (Collaboration, Project Partner)
- University of Sheffield (Project Partner)
- University of Exeter (Project Partner)
- Max Planck Institutes (Project Partner)
- University of Warwick (Project Partner)
Publications

Chiu Y
(2022)
Numerical evaluation and robustness of the quantum mean-force Gibbs state
in Physical Review A

Cygorek M
(2022)
Simulation of open quantum systems by automated compression of arbitrary environments
in Nature Physics

Fowler-Wright P
(2022)
Efficient Many-Body Non-Markovian Dynamics of Organic Polaritons.
in Physical review letters

Fux G
(2023)
Tensor network simulation of chains of non-Markovian open quantum systems
in Physical Review Research

Fux GE
(2021)
Efficient Exploration of Hamiltonian Parameter Space for Optimal Control of Non-Markovian Open Quantum Systems.
in Physical review letters

Gribben D
(2022)
Exact Dynamics of Nonadditive Environments in Non-Markovian Open Quantum Systems
in PRX Quantum

Gribben D
(2022)
Using the Environment to Understand non-Markovian Open Quantum Systems
in Quantum

Lacroix T
(2021)
Unveiling non-Markovian spacetime signaling in open quantum systems with long-range tensor network dynamics
in Physical Review A

Popovic M
(2021)
Quantum Heat Statistics with Time-Evolving Matrix Product Operators
in PRX Quantum

Rouse D
(2022)
Analytic expression for the optical exciton transition rates in the polaron frame
in Physical Review B
Description | * developed a method for simulating 'open' quantum systems efficiently. Quantum systems that can be measured in the laboratory are not isolated: they interact continuously with their environment. When the interaction with the environment is relatively strong, it is very difficult to predict what the dynamics of the quantum system will be. This is because the environment consists of an enourmous number of particles, and it is impossible to track all of them in a computer simulation. However, we have developed a method that allows for efficient simulation for many kinds of envinronment. Moreover we are able to simulate different ways of controlling such systems in the lab, without recalutating the effect of the environment. |
Exploitation Route | We have released an open source software package that can be used by others to simulate the open quantum system of their choice. See https://oqupy.readthedocs.io/en/latest/index.html |
Sectors | Digital/Communication/Information Technologies (including Software),Electronics,Energy |
URL | https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.126.200401 |
Description | Modelling Room Temperature Bose-Einstein Condensation |
Amount | £3,000 (GBP) |
Organisation | Laidlaw Foundation |
Sector | Charity/Non Profit |
Country | United Kingdom |
Start | 05/2022 |
End | 07/2022 |
Title | OQuPy software package |
Description | A suite of software tools in python, for simulating non-Markovian dynamics. These use the process tensor matrix product operator formalism, a development from the TEMPO method on which this EPSRC project is based. |
Type Of Material | Improvements to research infrastructure |
Year Produced | 2022 |
Provided To Others? | Yes |
Impact | Only just released, we hope that this tool will enable researchers worldwide to expliot the powerful numerical tools we are developing as part of this project. |
URL | https://oqupy.readthedocs.io/en/latest/index.html |
Title | PT-TEMPO |
Description | We have provided an open source software package that allows users to perform simulations of non-Markovian open systems. In particular, this tool enables the efficient calculation of the "process tensor", an object that captures the effect of an envinroment on an open quantum system. This process tensor can then be used to simulate system dynamics using a user-defined choice of system Hamiltonain. |
Type Of Material | Improvements to research infrastructure |
Year Produced | 2021 |
Provided To Others? | Yes |
Impact | None yet (other than users beginning to use the tool). |
URL | https://doi.org/10.5281/zenodo.4428317 |
Title | Data Underpinning: Numerical evaluation and robustness of the quantum mean-force Gibbs state |
Description | |
Type Of Material | Database/Collection of data |
Year Produced | 2022 |
Provided To Others? | Yes |
URL | https://risweb.st-andrews.ac.uk/portal/en/datasets/data-underpinning-numerical-evaluation-and-robust... |
Title | Data underpinning: Efficient Many-Body Non-Markovian Dynamics of Organic Polaritons |
Description | Data for each plot of the figures appearing in the article. |
Type Of Material | Database/Collection of data |
Year Produced | 2022 |
Provided To Others? | Yes |
URL | https://risweb.st-andrews.ac.uk/portal/en/datasets/data-underpinning-efficient-manybody-nonmarkovian... |
Title | Dataset and Mathematica notebook for: Analytic expression for the optical exciton transition rates in the polaron frame |
Description | Contained here: (1) A Mathematica notebook to calculate the truncated excitation and decay rates (2) A dataset containing the numerical calculations used in Figure 5 to benchmark the truncated mode approximation |
Type Of Material | Database/Collection of data |
Year Produced | 2021 |
Provided To Others? | Yes |
URL | https://risweb.st-andrews.ac.uk/portal/en/datasets/dataset-and-mathematica-notebook-for-analytic-exp... |
Title | Exact dynamics of non-additive environments in non-Markovian open quantum systems (dataset) |
Description | |
Type Of Material | Database/Collection of data |
Year Produced | 2022 |
Provided To Others? | Yes |
URL | https://risweb.st-andrews.ac.uk/portal/en/datasets/exact-dynamics-of-nonadditive-environments-in-non... |
Title | Using the Environment to Understand non-Markovian Open Quantum Systems (dataset) |
Description | |
Type Of Material | Database/Collection of data |
Year Produced | 2022 |
Provided To Others? | Yes |
URL | https://risweb.st-andrews.ac.uk/portal/en/datasets/using-the-environment-to-understand-nonmarkovian-... |
Description | Cambridge - Cavendish |
Organisation | University of Cambridge |
Department | Cavendish Laboratory |
Country | United Kingdom |
Sector | Academic/University |
PI Contribution | Theory of small laser devices ("nanoparticle on mirror"). |
Collaborator Contribution | Experimental measurements on the devices. |
Impact | No publushed paper yet, but we do have a preprint. |
Start Year | 2020 |
Description | Erlangen |
Organisation | Max Planck Society |
Department | Max Planck Institute for the Science of Light |
Country | Germany |
Sector | Academic/University |
PI Contribution | Theory expertise on the photonic systems studied by partner. |
Collaborator Contribution | Experimental data, expertise. |
Impact | No concrete outputs yet. |
Start Year | 2020 |
Description | Exeter |
Organisation | University of Exeter |
Department | School of Physics |
Country | United Kingdom |
Sector | Academic/University |
PI Contribution | We are developing the theory of single photon sources in low dimensional materials. This is a system being worked on experimentally by the group in Exeter. |
Collaborator Contribution | Experimental expertise and data. |
Impact | None yet. |
Start Year | 2020 |
Description | Heriot Watt |
Organisation | Heriot-Watt University |
Department | School of Engineering & Physical Sciences |
Country | United Kingdom |
Sector | Academic/University |
PI Contribution | This is a formal collaboration - this EPSRC award is joint between the St Andrews and Heriot Watt groups. We are developing the theory of open quantum systems and applying this to four different applications: spin sensors, energy transfer systems, single photon sources and molecular devices. The St Andrews team are focussed mainly on the second and third of these, though both teams are contributing to all aspects of the project. |
Collaborator Contribution | This is a formal collaboration - this EPSRC award is joint between the St Andrews and Heriot Watt groups. We are developing the theory of open quantum systems and applying this to four different applications: spin sensors, energy transfer systems, single photon sources and molecular devices. The Heriot Watt team are focussed mainly on the first and last of these, though both teams are contributing to all aspects of the project. |
Impact | None yet for this award. |
Start Year | 2020 |
Description | Hitachi Cambridge |
Organisation | Hitachi Cambridge Laboratory |
Country | United Kingdom |
Sector | Private |
PI Contribution | We provide theory expertise about the photonic systems being studied by the experimental partner here in Cambridge. |
Collaborator Contribution | Providing experimental data and expertise on photonic devices. |
Impact | No concrete outputs so far - the project is at an early stage. |
Start Year | 2020 |
Description | Oxford |
Organisation | University of Oxford |
Department | Department of Materials |
Country | United Kingdom |
Sector | Academic/University |
PI Contribution | A listed project partner on this project, we are working with Prof Andrew Briggs in Oxford on molecular devices, in particular looking at tunnel coupling to leads. We are using a new theoretical tool, TEMPO, to model such devices which are being measured in Prof Briggs' lab. |
Collaborator Contribution | Exchange of expertise and results. |
Impact | No direct outputs yet. |
Start Year | 2020 |
Description | Sheffield |
Organisation | University of Sheffield |
Department | Department of Physics and Astronomy |
Country | United Kingdom |
Sector | Academic/University |
PI Contribution | Development of theory of single photon source in semiconductor quantum dots. |
Collaborator Contribution | Experimental data and expertise. |
Impact | None yet. |
Start Year | 2020 |
Description | Sorbonne |
Organisation | Sorbonne University |
Country | France |
Sector | Academic/University |
PI Contribution | Two two partners offer different theoretical approaches to non-Markovian quantum simulations that we compare. |
Collaborator Contribution | Two two partners offer different theoretical approaches to non-Markovian quantum simulations that we compare. |
Impact | No outputs yet. |
Start Year | 2020 |
Description | Warwick |
Organisation | University of Warwick |
Department | Department of Physics |
Country | United Kingdom |
Sector | Academic/University |
PI Contribution | We are developing the theory of a spin sensor in solid state materials. |
Collaborator Contribution | Experimental data and expertise on NV centre sensor system. |
Impact | None so far. |
Start Year | 2020 |
Title | Quantum heat statistics with time-evolving matrix product operators (associated code) |
Description | Code associated with the paper "Quantum heat statistics with time-evolving matrix product operators" (Popovic et al. PRX Quantum 2 020338). It is based on the original TEMPO code https://zenodo.org/record/1322407 described in the paper "Efficient non-Markovian quantum dynamics using time-evolving matrix product operators" (Strathearn et al. Nat. Comm. 9 3322). The changes allow the calculation of heat statistics for an open quantum system coupled to a bath. |
Type Of Technology | Software |
Year Produced | 2021 |
Open Source License? | Yes |
URL | https://zenodo.org/record/4884728 |
Title | mcygorek/ACE: ACE code (stage: resubmission of ACE article) |
Description | ACE code for numerically exact simulations of open quantum systems coupled to arbitrary environments. Restructured code with several new features. Parameter files are more consistent. Includes arbitrary 1d Potentials and time-dependent environment Hamiltonians plus environment loss terms. |
Type Of Technology | Software |
Year Produced | 2021 |
URL | https://zenodo.org/record/5214128 |
Title | tempoCollaboration/OQuPy: Version 0.3.1 |
Description | This open source project aims to facilitate versatile numerical tools to efficiently compute the dynamics of quantum systems that are possibly strongly coupled to structured environments. It allows to conveniently apply several numerical methods related to the time evolving matrix product operator (TEMPO) [1-2] and the process tensor (PT) approach to open quantum systems [3-5]. This includes methods to compute ... the dynamics of a quantum system strongly coupled to a bosonic environment [1-2]. the process tensor of a quantum system strongly coupled to a bosonic environment [3-4]. optimal control procedures for non-Markovian open quantum systems [5]. the dynamics of a strongly coupled bosonic environment [6]. the dynamics of a quantum system coupled to multiple non-Markovian environments [7]. the dynamics of a chain of non-Markovian open quantum systems [8]. the dynamics of an open many-body system with one-to-all light-matter coupling [9]. (new functionality in OQuPy 0.3.0 is listed in bold) Major code contributions Lead development by Gerald E. Fux Version 0.3.0 Piper Fowler-Wright: Open quantum systems with mean-field evolution [9] Version 0.2.0 Gerald E. Fux: Chains of open quantum systems [8]. Dainius Kilda: Precursor code for chains of open quantum systems [8]. Dominic Gribben: Bath dynamics extension [6]. Dominic Gribben: Multiple environments extension [7]. Version 0.1.2 (TimeEvolvingMPO) Gerald E. Fux: Improved memory cut-off [1]. Version 0.1.1 (TimeEvolvingMPO) No major code contributions in this version. Version 0.1.0 (TimeEvolvingMPO) Gerald E. Fux: Implement process tensor TEMPO (API and backend) [3-5]. Gerald E. Fux: Implement core TEMPO functionality (API and backend) [2]. Gerald E. Fux: Setup Project (CI, API design, project planning, etc.). Bibliography [1] Strathearn et al., New J. Phys. 19(9), p.093009 (2017). [2] Strathearn et al., Nat. Commun. 9, 3322 (2018). [3] Pollock et al., Phys. Rev. A 97, 012127 (2018). [4] Jørgensen and Pollock, Phys. Rev. Lett. 123, 240602 (2019). [5] Fux et al., Phys. Rev. Lett. 126, 200401 (2021). [6] Gribben et al., arXiv:20106.0412 (2021). [7] Gribben et al., PRX Quantum 3, 10321 (2022). [8] Fux et al., arXiv:2201.05529 (2022). [9] Fowler-Wright at al., arXiv:2112.09003 (2021). |
Type Of Technology | Software |
Year Produced | 2022 |
URL | https://zenodo.org/record/6599106 |
Description | Video contribution to Science Discovery Day 2021 |
Form Of Engagement Activity | Engagement focused website, blog or social media channel |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Media (as a channel to the public) |
Results and Impact | A short video was made for a general audience, which was then shared on Facebook and Twitter by the public engagement team at the University of St Andrews. This was done as part of Science Discovery Day 2021, which was an online event where multiple videos from staff and students of the University of St Andrews were shared on social media. The video in question was about A day in the life of a theoretical physicist and has gotten over 600 views and a few questions. |
Year(s) Of Engagement Activity | 2021 |
URL | https://www.youtube.com/watch?v=Fj2RhfXQs6s |