Measuring the Adiabatic Non-Hermitian Berry Phase in Feedback-Coupled Oscillators

TL;DR

This paper experimentally measures the adiabatic non-Hermitian Berry phase in a feedback-coupled oscillator system, revealing its geometric nature and effects like amplification, damping, and a non-Hermitian Aharonov-Bohm phenomenon.

Contribution

First experimental demonstration of the adiabatic non-Hermitian Berry phase using classical oscillators with feedback, highlighting its geometric effects in non-Hermitian systems.

Findings

Non-Hermitian Berry phase causes amplitude amplification and damping.

Observation of a non-Hermitian Aharonov-Bohm effect with imaginary flux.

Verification that the Berry phase is a purely geometric effect in this system.

Abstract

The geometrical Berry phase is key to understanding the behaviour of quantum states under cyclic adiabatic evolution. When generalised to non-Hermitian systems with gain and loss, the Berry phase can become complex, and should modify not only the phase but also the amplitude of the state. Here, we perform the first experimental measurements of the adiabatic non-Hermitian Berry phase, exploring a minimal two-site $\mathcal{PT}$-symmetric Hamiltonian that is inspired by the Hatano-Nelson model. We realise this non-Hermitian model experimentally by mapping its dynamics to that of a pair of classical oscillators coupled by real-time measurement-based feedback. As we verify experimentally, the adiabatic non-Hermitian Berry phase is a purely geometrical effect that leads to significant amplification and damping of the amplitude also for non-cyclical paths within the parameter space even when all eigenenergies are real. We further observe a non-Hermitian analog of the Aharonov--Bohm solenoid effect, observing amplification and attenuation when encircling a region of broken $\mathcal{PT}$ symmetry that serves as a source of imaginary flux. This experiment demonstrates the importance of geometrical effects that are unique to non-Hermitian systems and paves the way towards the further studies of non-Hermitian and topological physics in synthetic metamaterials.