Techniques to control the quantum state of light play a crucial role in a wide range of fields, from quantum information science to precision measurements. While for electrons in solid state materials complex quantum states can be created by mere cooling, in the field of optics manipulation and control currently builds on non-thermodynamic methods. Using an optical dye microcavity, we have split photon wavepackets by thermalization within a potential with two minima subject to tunnel coupling. Even at room temperature, photons condense into a quantum-coherent bifurcated ground state. Fringe signals upon recombination show the relative coherence between the two wells, demonstrating a working interferometer with the non-unitary thermodynamic beamsplitter. This energetically driven optical state preparation opens up an avenue for exploring novel correlated and entangled optical manybody states.

The versatility of quantum gas experiments greatly benefits from the ability to apply variable potentials. Here we describe a method which allows the preparation of potential structures for microcavity photons via spatially selective deformation of optical resonator geometries with a heat-induced mirror surface microstructuring technique. We investigate the thermalization of a two-dimensional photon gas in a dye-filled microcavity composed of the custom surface-structured mirrors at wavelength-scale separation. Specifically, we describe measurements of the spatial redistribution of thermal photons in a coupled double-ridge structure, where photons form a Bose-Einstein condensate in a spatially split ground state, as a function of different pumping geometries.

The compressibility of a medium, quantifying its response to mechanical perturbations, is a fundamental property determined by the equation of state. For gases of material particles, studies of the mechanical response are well established, in fields from classical thermodynamics to cold atomic quantum gases. We demonstrate a measurement of the compressibility of a two-dimensional quantum gas of light in a box potential and obtain the equation of state for the optical medium. The experiment was carried out in a nanostructured dye-filled optical microcavity. We observed signatures of Bose-Einstein condensation at high phase-space densities in the finite-size system. Upon entering the quantum degenerate regime, the measured density response to an external force sharply increases, hinting at the peculiar prediction of an infinite compressibility of the deeply degenerate Bose gas.

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