[Paper Review] Direct Measurement of a Non-Hermitian Topological Invariant in a Hybrid Light-Matter System

Rui Su, Eliezer Estrecho+8 more|arXiv (Cornell University)|Dec 11, 2020

Quantum Mechanics and Non-Hermitian Physics75 references106 citations

TL;DR

This study presents the first direct experimental measurement of a non-Hermitian topological invariant—fractional spectral winding—in a hybrid light-matter system using room-temperature exciton-polaritons in a lead halide perovskite microcavity. By mapping the complex energy spectrum and resolving exceptional points, the authors demonstrate topological stability of bulk Fermi arcs and confirm the emergence of non-Hermitian topology through momentum-space winding of complex eigenenergies, validated via polarisation-resolved spectroscopy and a tailored non-Hermitian Hamiltonian model.

ABSTRACT

Topology is central to understanding and engineering materials that display robust physical phenomena immune to imperfections. Different topological phases of matter are characterised by topological invariants. In energy-conserving (Hermitian) systems, these invariants are determined by the winding of eigenstates in momentum space. In non-Hermitian systems, a novel topological invariant is predicted to emerge from the winding of the complex eigenenergies. Here, we directly measure the non-Hermitian topological invariant arising from exceptional points in the momentum-resolved spectrum of exciton polaritons. These are hybrid light-matter quasiparticles formed by photons strongly coupled to electron-hole pairs (excitons) in a halide perovskite semiconductor at room temperature. We experimentally map out both the real (energy) and imaginary (linewidth) parts of the spectrum near the exceptional points and extract the novel topological invariant - fractional spectral winding. Our work represents an essential step towards realisation of non-Hermitian topological phases in a condensed matter system.

Motivation & Objective

• To experimentally measure the non-Hermitian topological invariant—spectral winding—arising from exceptional points in a condensed matter system.
• To demonstrate the existence of topologically protected bulk Fermi arcs connecting paired exceptional points in momentum space.
• To establish a direct link between non-Hermitian topology and observable spectral features such as linewidth and circular polarisation.
• To validate the theoretical prediction that spectral winding and eigenstate winding are distinct topological invariants in non-Hermitian systems.
• To provide a solid-state platform for exploring non-Hermitian topology in the presence of strong interactions and many-body effects at room temperature.

Proposed method

• Development of a 4×4 non-Hermitian Hamiltonian model to describe the complex energy dispersion of exciton-polaritons, incorporating both real (energy) and imaginary (linewidth) parts of the eigenenergies.
• Use of angle-resolved photoluminescence (PL) spectroscopy with polarisation control (H/V and D/A states) to map the momentum-resolved spectrum across the 2D momentum space.
• Employment of Lorentzian fitting to extract mode energies and linewidths from PL spectra at each momentum point, with orthogonal polarisation pairs used to resolve degenerate modes near exceptional points.
• Implementation of a transfer matrix method with a Lorentz oscillator model to simulate the reflectance and predict linewidth and energy behaviour, accounting for anisotropic coupling and losses.
• Theoretical analysis showing that spectral winding (from complex eigenenergies) and pseudospin winding (from eigenstate phases) are topologically inequivalent, with spectral winding being robust under perturbations.
• Use of circular polarisation as a signature of the imaginary part of the artificial gauge field, linking non-Hermitian effects to observable spin textures near exceptional points.

Experimental results

Research questions

• RQ1 Can the non-Hermitian topological invariant—spectral winding—be directly measured in a real, spatially homogeneous condensed matter system?
• RQ2 Do exceptional points in the momentum-resolved spectrum of exciton-polaritons host topologically protected Fermi arcs, and can they be experimentally resolved?
• RQ3 How does the imaginary part of the effective gauge field influence the pseudospin texture and circular polarisation of the emitted light near exceptional points?
• RQ4 Is the spectral winding invariant robust against perturbations that open the energy gap, and how does it differ from the winding of eigenstate phases?
• RQ5 Can a hybrid light-matter system like exciton-polaritons at room temperature serve as a viable platform for studying non-Hermitian topology with strong interactions?

Key findings

• The authors directly measured the fractional spectral winding invariant—half-integer winding number—by mapping the complex energy spectrum of exciton-polaritons in momentum space.
• Paired exceptional points were experimentally observed, connected by topologically protected bulk Fermi arcs, confirmed through momentum-resolved PL mapping.
• The linewidth of the exciton-polariton modes increases linearly with momentum, consistent with the model's prediction of momentum-dependent losses.
• Circular polarisation was maximised near the exceptional points, providing a direct experimental signature of the imaginary part of the effective gauge field acting on the pseudospin.
• The spectral winding invariant remained stable under gap-opening perturbations, confirming its topological robustness, while the eigenstate winding was found to be topologically distinct.
• The experimental data revealed jumps in extracted energy and linewidth values due to switching between orthogonal polarisation bases, indicating the need for full polarisation tomography to eliminate phase discontinuities.