## Periodic Reporting for period 1 - ESPCSS (Efficient Spin-Photon Coupling in the Solid-State)

Reporting period: 2016-04-01 to 2018-03-31

"The central problem addressed in this research is how to efficiently couple single electrons and single photons in a controllable and repeatable manner. Free-space approaches to this problem typically suffer from two obstacles; the difficulty in isolating single electrons hinders efficient photon absorption, while the isotropic nature of photon emission leads to photon loss and low efficiencies. In order to overcome these problems, this research aims to take a solid-state approach, in which electrons are confined and localised in semiconductor nanostructures known as ""Quantum Dots"", which can in principle allow for efficient and coherent electron-photon coupling. Using these solid-state nanostructures, however, introduces additional problems, such as coupling to lattice vibrations and nuclear spins in the solid. The purpose of this research was to understand and design ways in which these effects could be minimised, necessitating the development of new theoretical techniques to model such systems.

The efficient coupling of single electrons and single spins would represent significant milestone in our ability to control the microscopic realm, and by extension would be of huge importance to a number of technologies which promise to impact society. In particular, nearly all quantum technologies rely on coupling two or more quantum systems and in an efficient and controlled manner. This is especially true in photonic quantum computing architectures, as well as quantum communication protocols using quantum repeaters. At the heart of these schemes lie photon-photon and photon-electron interactions, and a major challenge in these cases is achieving these interactions with sufficient efficiency that the advantage of exploiting quantum mechanical interactions is not lost. A successful quantum communication network would allow for completely secure communication channels, while an operational quantum computer has the potential to transform how we approach computation problems, and could lead to methods of, for example, drug discovery, which are completely beyond the reach of conventional computers.

With this in mind, the objectives of this research are to:

1) Develop and new theoretical framework of solid-state electron-photon coupling, which would allow for an accurate description of light-matter coupling quantum dots, and

2) Use this framework to develop ways in which the solid-state environment in quantum dots can be controlled and modified to increase the efficiency and controllability of electron-photon coupling.

This research concluded with the establishment of such a theoretical framework, with which it has been possible to place quantitative bounds on the impact of lattice vibrations on electron-photon coupling in quantum dots in a number of settings, and the design of protocols which act to minimise the impact of coupling to nuclear spins."

The efficient coupling of single electrons and single spins would represent significant milestone in our ability to control the microscopic realm, and by extension would be of huge importance to a number of technologies which promise to impact society. In particular, nearly all quantum technologies rely on coupling two or more quantum systems and in an efficient and controlled manner. This is especially true in photonic quantum computing architectures, as well as quantum communication protocols using quantum repeaters. At the heart of these schemes lie photon-photon and photon-electron interactions, and a major challenge in these cases is achieving these interactions with sufficient efficiency that the advantage of exploiting quantum mechanical interactions is not lost. A successful quantum communication network would allow for completely secure communication channels, while an operational quantum computer has the potential to transform how we approach computation problems, and could lead to methods of, for example, drug discovery, which are completely beyond the reach of conventional computers.

With this in mind, the objectives of this research are to:

1) Develop and new theoretical framework of solid-state electron-photon coupling, which would allow for an accurate description of light-matter coupling quantum dots, and

2) Use this framework to develop ways in which the solid-state environment in quantum dots can be controlled and modified to increase the efficiency and controllability of electron-photon coupling.

This research concluded with the establishment of such a theoretical framework, with which it has been possible to place quantitative bounds on the impact of lattice vibrations on electron-photon coupling in quantum dots in a number of settings, and the design of protocols which act to minimise the impact of coupling to nuclear spins."

The main results resulting from this project are:

1) The establishment of a unified theory allowing for the accurate theoretical description of the impact of lattice vibrations on electron-photon coupling in quantum dots embedded in photonic cavities at low temperatures. Using this theory, it has been possible to accurately model leading designs for quantum dot based single photon sources, which are essential components in quantum computing and communication protocols. The results demonstrate that even in photonic cavities, lattice vibrations in quantum dots lead to fundamental limits on the efficiency and indistinguishability of single photons. This result has a wide and substantial impact on quantum dot research, and motivates alternative approaches to combating the effects of thermal excitations in these solid-state systems.

2) The identification of a new mechanism by which lattice vibrations can affect electron-photon coupling in quantum dots at elevated temperatures. Building upon the previous theory, this research found that beyond very low temperatures (10K), lattice vibrations are able to couple to electrons in quantum dots via a new non-linear mechanism, which affects interactions with photons in a quite distinct manner. Importantly, these effects cannot be combated using filtering or optical cavities, and highlights the necessity to work at low temperatures, something that was not previously fully appreciated.

3) The design of a protocol is minimise the impact of coupling to nuclear spins in the generation of electron-photon entanglement. This part of the research designed and analysed a way in which single photons can successively interact with an electron in a quantum dot in such a way as to bypass the effect of coupling to nuclear spins, which would otherwise lead to efficiency and coherence losses. The protocol exploits a mathematical symmetry in the quantum state produced, which effectively decouples the relevant photonic degrees of freedom from the solid-state environment of the quantum dot. This is a significant result, as it indicates that the effects of nuclear spins can be combated without the need to physically manipulate them, leading to a significant reduction in the experimental complexity in producing electron-photon entanglement.

In order to disseminate this research, several publications have been written (see publications tab), while the work has been presented at a number of conferences and workshops, including OECS (Bath, Sept 2017), CLEO Europe (Munich, June 2017), the Quantum Innovators Workshop (Waterloo, October 2016) and Single Photon Single Spin (Oxford, Sept 2016). Furthermore, outreach activities were completed, which were participation in the School of Physics Open Days, the presentation of a display detailing MSCA fellowships at Bristol, and participation in the forthcoming Physics Summer School.

1) The establishment of a unified theory allowing for the accurate theoretical description of the impact of lattice vibrations on electron-photon coupling in quantum dots embedded in photonic cavities at low temperatures. Using this theory, it has been possible to accurately model leading designs for quantum dot based single photon sources, which are essential components in quantum computing and communication protocols. The results demonstrate that even in photonic cavities, lattice vibrations in quantum dots lead to fundamental limits on the efficiency and indistinguishability of single photons. This result has a wide and substantial impact on quantum dot research, and motivates alternative approaches to combating the effects of thermal excitations in these solid-state systems.

2) The identification of a new mechanism by which lattice vibrations can affect electron-photon coupling in quantum dots at elevated temperatures. Building upon the previous theory, this research found that beyond very low temperatures (10K), lattice vibrations are able to couple to electrons in quantum dots via a new non-linear mechanism, which affects interactions with photons in a quite distinct manner. Importantly, these effects cannot be combated using filtering or optical cavities, and highlights the necessity to work at low temperatures, something that was not previously fully appreciated.

3) The design of a protocol is minimise the impact of coupling to nuclear spins in the generation of electron-photon entanglement. This part of the research designed and analysed a way in which single photons can successively interact with an electron in a quantum dot in such a way as to bypass the effect of coupling to nuclear spins, which would otherwise lead to efficiency and coherence losses. The protocol exploits a mathematical symmetry in the quantum state produced, which effectively decouples the relevant photonic degrees of freedom from the solid-state environment of the quantum dot. This is a significant result, as it indicates that the effects of nuclear spins can be combated without the need to physically manipulate them, leading to a significant reduction in the experimental complexity in producing electron-photon entanglement.

In order to disseminate this research, several publications have been written (see publications tab), while the work has been presented at a number of conferences and workshops, including OECS (Bath, Sept 2017), CLEO Europe (Munich, June 2017), the Quantum Innovators Workshop (Waterloo, October 2016) and Single Photon Single Spin (Oxford, Sept 2016). Furthermore, outreach activities were completed, which were participation in the School of Physics Open Days, the presentation of a display detailing MSCA fellowships at Bristol, and participation in the forthcoming Physics Summer School.

Progress beyond the state of the art is most explicit in the development of a unified treatment of electron-photon coupling, lattice vibrations, and photonic cavities mentioned above. This theoretical framework allows for an accurate description of electron-photon coupling in quantum dot-cavity structures, and does so in a way that avoids commonplace approximations that are typically employed. This extends the parameter regime over which we have an accurate theory significantly, and in particular now allows to us to model experimentally relevant systems currently being measured in many laboratories, as well as future more sophisticated experiments.

Aside from its fundamental relevance, this theory allows for the quantitative scrutiny of various quantum dot based single photon source and electron-photon coupling designs. The theory puts bounds on important figures of merit which characterise these devices, and points towards ways in which new methods of improvement may be achieved. This provides a concrete contribution to the quest to develop quantum computation and communication technologies, which will fuel a new quantum tech industry, and which will in turn enhance society with new ways in which to communicate and to tackle scientific and mathematical problems with a wide range of applications.

Aside from its fundamental relevance, this theory allows for the quantitative scrutiny of various quantum dot based single photon source and electron-photon coupling designs. The theory puts bounds on important figures of merit which characterise these devices, and points towards ways in which new methods of improvement may be achieved. This provides a concrete contribution to the quest to develop quantum computation and communication technologies, which will fuel a new quantum tech industry, and which will in turn enhance society with new ways in which to communicate and to tackle scientific and mathematical problems with a wide range of applications.