Non-Hermitian topology and directional amplification*

A remarkable phenomenon associated with Hermitian topology is the quantum Hall effect – the quantisation of the Hall resistance in terms of a topological invariant. So far, such a clear observable signature of non-Hermitian topology had been lacking. In this talk, I will show that non-trivial, non-Hermitian topology is in one-to-one correspondence with the phenomenon of directional amplification [1-2] in one-dimensional bosonic systems, e.g., cavity arrays. Directional amplification allows to selectively amplify signals depending on their propagation direction and has attracted much attention as key resource for applications, such as quantum information processing. Remarkably, in non-trivial topological phases, the end-to-end gain grows exponentially with the number of sites [1]. Furthermore, we show this effect to be robust against disorder [2] with the amount of tolerated disorder given by the separation between the complex spectrum and the origin. Beyond that, it is possible to restore the bulk-boundary correspondence with the help of the singular value decomposition which has a clear link to directional amplification [3].

In collaboration with the group of Ewold Verhagen at AMOLF, Amsterdam, we experimentally demonstrate the connection between non-Hermitian topology and directional amplification in a cavity optomechanical system [4] by realising a bosonic version of the Kitaev-Majorana chain proposed in [5]. Furthermore, we show in the experiment that a similar system proposed in [6] can be utilised as a sensor with a sensitivity that grows exponentially with system size [4].

Our work opens up new routes for the design of both phase-preserving and phase-sensitive multimode robust directional amplifiers and sensors based on non-Hermitian topology that can be integrated in scalable platforms such as superconducting circuits, optomechanical systems and nanocavity arrays.

[1] Wanjura, Brunelli, Nunnenkamp. Nat Commun 11, 3149 (2020).

[2] Wanjura, Slim, del Pino, Brunelli, Verhagen, Nunnenkamp. arXiv:2207.08523 (2022).

[3] Brunelli, Wanjura, Nunnenkamp. SciPost Phys 15, 173 (2023).

[4] Slim, Wanjura, Brunelli, del Pino, Nunnenkamp, Verhagen. arXiv:2309.05825 (2023).

[5] McDonald, Pereg-Barnea, Clerk. Phys Rev X 8, 041031 (2018).

[6] McDonald, Clerk. Nat Commun 11, 5382 (2020).