Non-Hermitian Topological Physics in Grand Canonical Photon Lattices

Project Information

TOPOGRAND

Grant agreement ID: 101040409

DOI

10.3030/101040409

EC signature date 26 September 2022

Start date 1 January 2023

End date 31 December 2027

Funded under

• European Research Council (ERC)

Total cost

€ 1 498 750,00

EU contribution

€ 1 498 750,00

Coordinated by

RUPRECHT-KARLS-UNIVERSITAET HEIDELBERG
Germany

Periodic Reporting for period 1 - TOPOGRAND (Non-Hermitian Topological Physics in Grand Canonical Photon Lattices)

Reporting period: 2023-01-01 to 2025-06-30

Summary of the context and overall objectives of the project

Topology is a powerful paradigm for the classification of phases of matter. One of its direct manifestations in the widely studied Hermitian systems, which are isolated from the environment, are robust states that emerge at the interfaces between matter with distinct topological order. Real systems, however, are never truly isolated from their surroundings and the influence of the environment on the topologically protected states remains to a large extent unknown. Even more importantly, understanding and controlling the openness of non-Hermitian systems can provide fundamentally new ways to create novel topological states of matter.

TopoGrand will realise a new experimental platform to synthesise non-Hermitian topological materials. It will employ a room-temperature photonic platform combining nanostructured optical microcavities with a molecular medium, to achieve non-Hermitian topological lattices of photon condensates. The system will feature tuneable openness that is unique among other presently available experimental platforms: a controlled flux of excitations via spatially selective pumping and loss, energy dissipation at variable rates, and coherence modified by grand canonical reservoirs.

New physics will be accessed in the course of this work: TopoGrand will demonstrate genuine non-Hermitian topological phases and edge states without a Hermitian counterpart. Specifically, we will test the emergence of interface states at a topological phase boundary and their robustness against lattice disorder, as well as reservoir-induced fluctuations.

The project presents a completely new approach to topology, which will allow us to create reconfigurable photonic materials with topological protection simply by controlling the environment. With the novel toolbox, I will explore the emerging links between photonics, condensed matter systems and quantum computing, and emulate finite-temperature topological systems, which are at the forefront of research in quantum physics.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

During the first reporting period, the project work has focused on the development of the experimental apparatuses for the study of topological states in arrays of photon Bose-Einstein condensates within structured dye-filled microcavities and grand canonical fluctuation dynamics. For this, three experimental setups have been built addressing the project aims. The progress towards these goals, along with achievements, is discussed in the following.

Aim 1: Implementation of coupled differentially pumped photon condensates in 1D lattices
The first step of the project focused on the experimental realization of 1D lattice potentials for photon condensates, which now can be created within optical cavities formed by mirrors with variable surface profiles. For this, a direct laser writing setup for high-reflectivity mirrors was developed. In the experiment, a laser beam is directed over the silicon layer embedded in a dielectric mirror, which serves as the writing sample. Through the absorption of laser light, locally deposited heat induces a static mirror surface elevation. By scanning the mirror sample through the laser beam focus, we have achieved position-resolved surface topographies of up to 25nm height. Using this structuring method, we have demonstrated photon Bose-Einstein condensation in a four-site ring lattice, where residual variations of the potential energy at the lattice sites arising from surface imperfections of 1Å could be well corrected by the cavity alignment. In larger lattices, those imperfections pose a significant limitation. To address this issue, we developed an all-optical technique to adjust the potential energy after the mirror structuring process in a site-resolved way. This marks an important advance in the control of the lattice potentials and a corresponding publication is currently in preparation.

Aim 2: Identification of Topological Edge States in Non-Hermitian Systems
This project aims to demonstrate topological states of light within a lattice of coupled photon Bose-Einstein condensates. The goal is to implement a non-Hermitian topological lattice model with a four-site unit cell with tuneable gain and loss. An experimental apparatus has been developed for this purpose, facilitating spatially-resolved pumping of photon condensates at individual lattice sites and enabling the extraction of band structures and density distributions. At the beginning of the project, both theoretical and experimental investigations of the non-Hermitian topological system were conducted in a proof-of-concept study using waveguide arrays. The study allowed for the first demonstration of topological states solely induced by tailored losses in the waveguides starting from a topologically trivial lattice. The next step is to investigate this topological system in arrays of photon condensates, which, unlike purely dissipative waveguides, allow for the implementation of gain. In this system, we want to measure topological band structures and steady-state characteristics of non-Hermitian topological edge states.

Aim 3: Probing Topological States with Reservoir-Induced Grand Canonical Fluctuations
This project task explores the interplay between topological states and decoherence processes resulting from number and phase fluctuations. Within the dye-microcavity platform, such condensate fluctuations can be introduced by a grand canonical particle exchange with reservoirs of excited dye molecules. In the beginning of the project, a series of studies were conducted to further explore grand canonical condensates. The fluctuation-dissipation theorem was demonstrated, verifying that measurements of susceptibility and number fluctuations are related by thermal energy. The findings of the study which began prior to the start of the project are directly relevant to Topogrand’s objectives. Furthermore, studies of the time-resolved second-order correlation dynamics, the photon condensate response, as well as the time-periodic driving of the photon condensate were published. The results provide valuable tools to analyse the fluctuation dynamics of topological states in photon condensate arrays, setting the stage for future work on finite-temperature topological states within the project.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

The experimental demonstration of non-Hermitian topological states in 1D waveguide arrays constitutes an important breakthrough, because the study demonstrates for the first time the feasibility to induce and control topological edge states only by tailored contact to the environment. In this way, the study opens a conceptually new approach to synthesising topological materials by open-system control. This establishes a new paradigm in topological physics, which does not any more rely on the formation of topological bands by spatio-temporal control of the intrinsic structure of the systems, but rather on the tailored contact of the systems to the environment, which can be externally controlled.

The demonstration of polymer-based nanostructured optical cavities imprinted using a direct laser writing method significantly advances the field beyond state of the art. This new approach allowed for the study of the thermodynamics in 1D photon gases and was in part envisaged within the project work. Preliminary follow-up work has demonstrated that the method is well applicable to periodic arrays of photon condensates, highlighting the breakthrough character of the study.