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Dr. Clara Wanjura

Group leader

  • Head of research group Topology and neuromorphic computing
  • Theory Division
  • Room A.2.110
  • Phone +49 9131 7133 420
  • Email

Since December 2024, Clara Wanjura is leading her own research group (more details can be found below or on the group website).

2021

Correspondence between Non-Hermitian Topology and Directional Amplification in the Presence of Disorder

Correspondence between Non-Hermitian Topology and Directional Amplification in the Presence of Disorder

Clara C. Wanjura, Matteo Brunelli, Andreas Nunnenkamp

Physical Review Letters 127 213601 (2021) | Journal

For non-Hermitian (NH) topological effects to be relevant for practical applications, it is necessary to study disordered systems. Without disorder, a class of driven-dissipative cavity arrays displays directional amplification when associated with a nontrivial winding number of the NH dynamic matrix. In this work, we show analytically that the correspondence between NH topology and directional amplification holds even in the presence of disorder. We first demonstrate that an NH topological phase is preserved as long as the size of the point gap—defined as the minimum distance of the disorderless complex spectrum from the origin—is larger than the maximum amount of disorder. The disorder is assumed to be bounded but otherwise general, meaning it can be complex and both local (on-site disorder) and nonlocal (disordered couplings). We then derive analytic bounds for the probability distribution of the scattering matrix elements, showing that the key features of nontrivial NH topology—specifically, that the end-to-end forward gain grows exponentially with system size while the reverse gain is suppressed—are preserved in disordered systems. Our results prove that NH topology in cavity arrays is robust against disorder.

A central theme of my research is the exploration of coupled mode systems such as optical, optomechanical and photonic systems, and how to harness them for science and quantum technologies. Specifically, I am working along two main lines of research: scattering phenomena associated with non-Hermitian topology enabling devices such as topological, directional amplifiers and sensors; and neuromorphic computing.

Academic Background:

  • 12/2025 – present:  Max Planck Research Group Leader, Max Planck Institute for the Science of Light
  • 12/2024 – 11/2025: Minerva Fast Track Research Group Leader, Max Planck Institute for the Science of Light
  • 11/2022 – 12/2024: Postdoctoral fellow, Max Planck Institute for the Science of Light
  • 10/2018 – 07/2022: PhD Student, Cavendish Laboratory, University of Cambridge
  • 10/2017 – 03/2018: Visiting Student, Cavendish Laboratory, University of Cambridge
  • 10/2016 – 07/2018: Master’s Studies in Physics, Ulm University
  • 10/2013 – 10/2016: Bachelor’s Studies in Physics, Ulm University

 

Selected Prizes and Awards:

Please find my detailed CV here.

 

About the Max Planck Research Group

Advances in engineering optical and hybrid systems allow us to realise more and more complex physical systems. It is therefore an exciting time for theoretical physicists to devise coupled multimode systems that can be harnessed for quantum science and technological applications. In this new Max Planck Research Group, we are exploring two directions fuelled by these advances.

 

Topology in driven-dissipative quantum systems

Topology is a powerful principle for understanding many physically very different complex systems and has been a major research theme in condensed matter physics. More recently, a notion of topology in systems experiencing gain and loss has been investigated, sparking the field of non-Hermitian topology. Non-Hermitian topology can lead to a variety of phenomena that have no Hermitian counterpart. In particular, we have previously shown that non-trivial non-Hermitian topology is in one-to-one correspondence with the phenomenon of directional amplification, i.e, signals are amplified in one direction but blocked or attenuated in reverse. Such unidirectionality is highly sought-after for quantum information processing applications. We recently collaborated with Ewold Verhagen's group at AMOLF, Amsterdam, and demonstrated topological amplification in an optomechanical experiment. Furthermore, non-Hermitian topology is a resource for sensing. In the group, we are continuing to explore how the unique properties of non-Hermitian, topological systems can be harnessed for technological applications such as signal routing, non-reciprocity and directional amplification, sensing, as well as multi-partite entanglement generation.

Non-trivial, non-Hermitian topology is in one-to-one correspondence with directional amplification

Further reading:

C. C. Wanjura, M. Brunelli, A. Nunnenkamp. Topological framework for directional amplification in driven-dissipative cavity arrays. Nature Communications 11, 3149 (2020).

C. C. Wanjura, M. Brunelli, A. Nunnenkamp. Correspondence between non-Hermitian topology and directional amplification in the presence of disorder. Phys. Rev. Lett. 127, 213601 (2021).

M. Brunelli, C. C. Wanjura, A. Nunnenkamp. Restoration of the non-Hermitian bulk-boundary correspondence via topological amplification. SciPost Phys. 15, 173 (2023). 

C. C. Wanjura, J. J. Slim, J. del Pino, M. Brunelli, E. Verhagen, A. Nunnenkamp. Quadrature nonreciprocity in bosonic networks without breaking time-reversal symmetry. Nature Physics 19, 1429–1436 (2023).

J. J. Slim, C. C. Wanjura, M. Brunelli, J. del Pino, A. Nunnenkamp, E. Verhagen. Optomechanical realization of the bosonic Kitaev chain. Nature 627, 767–771 (2024).

 

You can learn more on non-Hermitian physics in this online seminar series.

 

Neuromorphic Computing

With the exponentially growing trend in digital neural network sizes and the associated energy consumption of machine learning applications, there is a need for alternative hardware approaches. In response to this demand, neuromorphic computing aims to replace our digital neural networks with physical systems. Indeed, optical or photonic systems can be engineered to perform the desired machine learning tasks and are a promising platform for neuromorphic computing as they offer high computation speeds at a low energy consumption. However, realising the necessary non-linear computation had previously been challenging. We made an important step to solving this challenge by developing a new framework for performing non-linear computation with purely linear scattering (check out our video below). This approach can be implemented in essentially any linear system with access to a sufficient number of tunable parameters, in particular, in existing scalable state-of-the-art platforms such as optics, microwave and electrical circuits and integrated photonics. Another very important aspect is physical training, i.e., physical access to gradients. It has been shown that in-silico training, i.e. training in simulation, does generally not transfer well to the experiment since even small discrepancies between model and reality can lead to a disastrous accumulation of errors during training. Therefore, we are looking into new training approaches for neuromorphic systems.

Fully non-linear neuromorphic system based on linear wave propagation

Learn more on non-linear computation with linear wave scattering in this video:

Further reading:

C. C. Wanjura, F. Marquardt. Fully non-linear neuromorphic computing with linear wave scattering. Nature Physics (2024).

Q. Wang, C. C. Wanjura, F. Marquardt. Training coupled phase oscillators as a neuromorphic platform using equilibrium propagation. arXiv:2402.08579 (2024).

A. Momeni, B. Rahmani et al. Training of physical neural networks. arxiv:2406.03372 (2024).

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