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.
