Periodic Reporting for period 1 - SSFI (Spin-resolved strong field ionisation)
Periodo di rendicontazione: 2021-09-01 al 2023-08-31
Problem being addressed:
Molecular movies depicting chemical reactions via attosecond (10^-18 s) snapshots, which vastly improve our understanding of molecular dynamics, is within our grasp. Strong-field imaging techniques under development, such as photoelectron holography, promise just this. However, up until very recently, all strong-field theoretical models have neglected spin, spin-orbit coupling and orbital angular momentum (OAM). Initial work including spin in the initial state, along with recent experiments, has shown that spin in strong-field processes is vitally important, leading to different ionization probabilities which in turn may alter the all important electron dynamics. Furthermore, recent work has demonstrated that the OAM of the photoelectron may be measured, providing yet another degree of freedom for exploration that is intimately connected to spin.
Impact for society:
This will enable the role of spin to be fully understood in SFP and thus fully fledged imaging protocols can be explored where the additional observable, spin, is fully accounted for and exploited.
In NSDI the combination of quantum interference, high momentum and spin correlation (possibly even entanglement) will lead to a wealth of applications in imaging and beyond, if these properties can be understood.
Overall objectives:
I will utilise and develop cutting edge theoretical frameworks to fully include electron spin, orbital angular momentum and spin-orbit coupling for strong-field processes in atoms and molecules. I will develop a semi-analytic model, which fully includes spin and spin-orbit coupling. This is motivated by the long history of semi-analytic methods that have been developed in this field, which have enabled unprecedented access into the electron dynamics for strong-field processes. As such, developing a model for spin will reveal deep new physical insight. A proper treatment allows more advanced and robust imaging techniques. I will explore the use of spin to enhance existing imaging processes, such as photoelectron holography. Furthermore, I will develop the semi-analytic model for two electrons and explore spin entanglement and correlation with momentum in two-electron ionisation processes, to design entirely new imaging procedures. This analysis will also open up the possibility of exploiting this system for quantum information purposes.
Molecular movies depicting chemical reactions via attosecond (10^-18 s) snapshots, which vastly improve our understanding of molecular dynamics, is within our grasp. Strong-field imaging techniques under development, such as photoelectron holography, promise just this. However, up until very recently, all strong-field theoretical models have neglected spin, spin-orbit coupling and orbital angular momentum (OAM). Initial work including spin in the initial state, along with recent experiments, has shown that spin in strong-field processes is vitally important, leading to different ionization probabilities which in turn may alter the all important electron dynamics. Furthermore, recent work has demonstrated that the OAM of the photoelectron may be measured, providing yet another degree of freedom for exploration that is intimately connected to spin.
Impact for society:
This will enable the role of spin to be fully understood in SFP and thus fully fledged imaging protocols can be explored where the additional observable, spin, is fully accounted for and exploited.
In NSDI the combination of quantum interference, high momentum and spin correlation (possibly even entanglement) will lead to a wealth of applications in imaging and beyond, if these properties can be understood.
Overall objectives:
I will utilise and develop cutting edge theoretical frameworks to fully include electron spin, orbital angular momentum and spin-orbit coupling for strong-field processes in atoms and molecules. I will develop a semi-analytic model, which fully includes spin and spin-orbit coupling. This is motivated by the long history of semi-analytic methods that have been developed in this field, which have enabled unprecedented access into the electron dynamics for strong-field processes. As such, developing a model for spin will reveal deep new physical insight. A proper treatment allows more advanced and robust imaging techniques. I will explore the use of spin to enhance existing imaging processes, such as photoelectron holography. Furthermore, I will develop the semi-analytic model for two electrons and explore spin entanglement and correlation with momentum in two-electron ionisation processes, to design entirely new imaging procedures. This analysis will also open up the possibility of exploiting this system for quantum information purposes.
Phases of the project:
A—Initial model development:
Here the semi-analytical CQSFA model received considerable developments in-order to hugely increase accuracy and to later allow for the addition of spin and spin-orbit coupling. This included basic model developments: generalized solutions to the saddle-point equations, generalizing the model to 3D, allowing the modelling of short laser pulses, including pivotal Maslov phases, and improving the interface with quantum chemistry codes to enable a better description of the bound state. The Maslov phases were used for a project for two MSc students, which I supervised. The paper is in preparation. I was also involved in a collaboration exploring alternative ways to develop the CQSFA, that had an important impact on the project, which resulted in two publications in PRA.
B—Development and applications of orbital angular momentum:
A crucial part to understand is the behaviour of orbital angular momentum (OAM) before spin-orbit coupling. The behaviour of OAM is relatively simple, which allowed for rapid development of existing models with adaptions. Here, we explored two projects (i) The development of an ultrafast chiral molecule detection method, which uses laser assisted transfer of chirality from an initial state to final electron vortices. This work is published in PRL. Further work adapting the CQSFA to model this effect in molecules and including the molecular chiral potential was done as part of a BSc project for two students, and a manuscript is in preparation. Another development is the inclusion of short elliptical pulses to make direct comparison with methods such as PECD. A manuscript is also in preparation (ii) The second project adapted an SFA model for non-sequential double ionization to include the OAM. In this work, we found under certain conditions, protected entangled state in OAM between the photoelectron could be found that are robust to various incoherent effects. These were used to explore entanglement assisted ultrafast imaging. This work was published in Nature Communications.
C—Development of spin and relativistic effects
Important theoretical work was done to include spin and spin-orbit coupling in the path-integral formalism of the CQSFA. This is a highly novel theory in this semi-classical treatment of spin, that allows interrogation of dynamical spin effect beyond any existing work from strong-field physics. However, implementation of this theory made it clear that any part of the wave function affected by spin-orbit coupling, also required a relativistic treatment. Thus, a theoretical framework was for relativistic corrections was also developed. Thus, the model now goes far beyond any semi-analytical/ semi-classical model used for this parameter range. The theoretical framework was added to the code base and thoroughly tested. Results were produced for hydrogen that clearly show deviations for high-energy rescattered photoelectron vs no relativistic or spin-orbit coupling. A preprint for this work is on arXiv.
A—Initial model development:
Here the semi-analytical CQSFA model received considerable developments in-order to hugely increase accuracy and to later allow for the addition of spin and spin-orbit coupling. This included basic model developments: generalized solutions to the saddle-point equations, generalizing the model to 3D, allowing the modelling of short laser pulses, including pivotal Maslov phases, and improving the interface with quantum chemistry codes to enable a better description of the bound state. The Maslov phases were used for a project for two MSc students, which I supervised. The paper is in preparation. I was also involved in a collaboration exploring alternative ways to develop the CQSFA, that had an important impact on the project, which resulted in two publications in PRA.
B—Development and applications of orbital angular momentum:
A crucial part to understand is the behaviour of orbital angular momentum (OAM) before spin-orbit coupling. The behaviour of OAM is relatively simple, which allowed for rapid development of existing models with adaptions. Here, we explored two projects (i) The development of an ultrafast chiral molecule detection method, which uses laser assisted transfer of chirality from an initial state to final electron vortices. This work is published in PRL. Further work adapting the CQSFA to model this effect in molecules and including the molecular chiral potential was done as part of a BSc project for two students, and a manuscript is in preparation. Another development is the inclusion of short elliptical pulses to make direct comparison with methods such as PECD. A manuscript is also in preparation (ii) The second project adapted an SFA model for non-sequential double ionization to include the OAM. In this work, we found under certain conditions, protected entangled state in OAM between the photoelectron could be found that are robust to various incoherent effects. These were used to explore entanglement assisted ultrafast imaging. This work was published in Nature Communications.
C—Development of spin and relativistic effects
Important theoretical work was done to include spin and spin-orbit coupling in the path-integral formalism of the CQSFA. This is a highly novel theory in this semi-classical treatment of spin, that allows interrogation of dynamical spin effect beyond any existing work from strong-field physics. However, implementation of this theory made it clear that any part of the wave function affected by spin-orbit coupling, also required a relativistic treatment. Thus, a theoretical framework was for relativistic corrections was also developed. Thus, the model now goes far beyond any semi-analytical/ semi-classical model used for this parameter range. The theoretical framework was added to the code base and thoroughly tested. Results were produced for hydrogen that clearly show deviations for high-energy rescattered photoelectron vs no relativistic or spin-orbit coupling. A preprint for this work is on arXiv.
The impacts are broken down into each work package below.
WP1: Develop single-electron semi-analytic model for SF ionization, including spin-orbit coupling
We developed a semi-analytical model that went well beyond anything previous regarding spin-orbit coupling, and found an unexpected relevance for relativistic effects. A new condition for where relativistic effects play a role for rescattered trajectories was derived, this will help the community in understanding and modelling. These result may have strong implications for imaging procedures such a LIED, where these rescattered electron play a crucial role. The model used also has a lot of flexibility.
Considerable progress was made in semiclassical modelling, in features such as the Maslov phase that will be very useful to the community.
WP2: Verify against ab-initio models and exploit for photoelectron holography in experiment.
We made extensive comparisons with the single-active electron TDSE model Qprop yielding unprecedented agreement. A novel imaging process for chiral molecules was formulated, with some similarities to photoelectric holography, which used the orbital angular momentum in place of the spin angular momentum. This enables a new time-resolved way to detect chirality that exploits OAM. Much work was done to model the same process using the CQSFA, GAMESS wave function were included in the code, an important step forwards. Began discussion with experimental collaborator who is interested in doing the experiments.
WP3: Extend model to two electrons, NSDI and understand spin entanglement.
We used an SFA model to explore entanglement of the orbital angular momentum in place of the spin angular momentum. We explored entanglement metrics and witnesses to quantify and suggest measurement of this entanglement. Suggestions for how to use this for attosecond metrology were developed. This has significant implications for ultrafast entanglement and using quantum metrology for attoscience.
WP1: Develop single-electron semi-analytic model for SF ionization, including spin-orbit coupling
We developed a semi-analytical model that went well beyond anything previous regarding spin-orbit coupling, and found an unexpected relevance for relativistic effects. A new condition for where relativistic effects play a role for rescattered trajectories was derived, this will help the community in understanding and modelling. These result may have strong implications for imaging procedures such a LIED, where these rescattered electron play a crucial role. The model used also has a lot of flexibility.
Considerable progress was made in semiclassical modelling, in features such as the Maslov phase that will be very useful to the community.
WP2: Verify against ab-initio models and exploit for photoelectron holography in experiment.
We made extensive comparisons with the single-active electron TDSE model Qprop yielding unprecedented agreement. A novel imaging process for chiral molecules was formulated, with some similarities to photoelectric holography, which used the orbital angular momentum in place of the spin angular momentum. This enables a new time-resolved way to detect chirality that exploits OAM. Much work was done to model the same process using the CQSFA, GAMESS wave function were included in the code, an important step forwards. Began discussion with experimental collaborator who is interested in doing the experiments.
WP3: Extend model to two electrons, NSDI and understand spin entanglement.
We used an SFA model to explore entanglement of the orbital angular momentum in place of the spin angular momentum. We explored entanglement metrics and witnesses to quantify and suggest measurement of this entanglement. Suggestions for how to use this for attosecond metrology were developed. This has significant implications for ultrafast entanglement and using quantum metrology for attoscience.