EPSRC Reference: 
EP/X032256/1 
Title: 
Controlling light with nonHermitian Schrödinger dynamics 
Principal Investigator: 
Graefe, Dr E 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

Department: 
Mathematics 
Organisation: 
Imperial College London 
Scheme: 
Standard Research  NR1 
Starts: 
01 April 2023 
Ends: 
31 January 2024 
Value (£): 
79,947

EPSRC Research Topic Classifications: 

EPSRC Industrial Sector Classifications: 
No relevance to Underpinning Sectors 


Related Grants: 

Panel History: 

Summary on Grant Application Form 
Much of modern technology, ranging from medical applications over data transmission to novel technologies for quantum computing, rely on the control of light in optical waveguides. Thus, any improvement in the control mechanisms has a large ripple on effect. Intuitively, to maximise efficiency of any optical device, one would seek to minimise absorption and losses, and for decades (if not centuries) this has been a guiding principle in the design of control schemes. Only fairly recently has the idea of using engineered losses to actively control dynamics been explored, and has led to a spectacular amount of new applications. The mathematics underpinning these ideas is borrowed from fundamental quantum physics from a field known as nonHermitian and PTsymmetric quantum theory. While the implementation of quantum dynamics generated by nonHermitian Hamiltonians in waveguides has been a major success story over the last decade, many important aspects remain unexplored. In particular the application of explicitly timedependent schemes that are of great importance in the absence of losses, has been little investigated, due to its nontrivial underlying mathematics. To propel the applications to the next level, it is imperative that the mathematical foundations of timedependent nonHermitian quantum systems are understood and made accessible to practitioners in physical applications.
The main goal of this grant is to categorise and then exploit the rich mathematical nature of systems described by nonHermitian Hamiltonians with explicitly timedependent parameters. This is a challenging task, since the quantum adiabatic theorem, that provides the foundations of most Hermitian systems, breaks down in the nonHermitian case. Recently we were able to make substantial progress for specific model systems, using the language of dynamical systems and tools from geometry and group theory. We will build on this to realise the vision of providing the mathematical foundations for next generation nonHermitian waveguide applications.

Key Findings 
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Summary 

Date Materialised 


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Organisation Website: 
http://www.imperial.ac.uk 