Near-equilibrium thermalised quantum light

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Almost 60 years have passed since the first laser, one of the most important inventions of the 20th century, yet new mechanisms enabling highly coherent, directional light sources are still being discovered. Very recently, Bose-Einstein Condensation (BEC) of light has enabled exploration of the links between quantum statistics, phase transitions and lasers, not only expanding our understanding, but inspiring light sources with new capabilities. Such sources will enable simulation of quantum processes, otherwise intractable using modern computers, and imaging and sensing beyond the quantum limit by exploiting their unique quantum coherence properties.It's not a trivial statement that photons can be made to thermalise and undergo Bose-Einstein condensation (BEC) at room temperature. A fluorescent medium in an optical resonator is optically excited. The resonator has many optical modes, but one has a well-defined ground state. Photons emitted into the resonator modes undergo thermalisation by absorption and re-emission with the fluorescent medium. This is facilitated by the vibrational states of the medium, which relax rapidly, to maintain thermal equilibrium. Quantum statistics ensure that, with enough photons, BEC will occur, even at room temperature, resulting in a macroscopic population of the ground-state resonator mode. BEC is a universal process, so photon BEC can be compared to condensation in atomic systems, or exciton-polariton microcavities.This project uses four ingredients to shift the science of photon-based BEC from fundamental to applied research: quantum correlations, semiconductor photon BEC, planar waveguide resonators, and theoretical underpinning. Those ingredients of this project are: (A) Measurement and control of the quantum correlations among photons.- While lasers have well-defined Poissonian number statistics, the number of statistics of BEC are greatly influenced by the the fluorescent medium. We will measure both intra- and inter-mode correlations. In contrast to lasers, we expect that media made of finite numbers of emitters will generate sub-Poissonian correlations, e.g. relative-number squeezing. Using pulsed pumping and time-resolved measurements of non-stationary statistics we will uncover how to characterise and exploit these highly non-classical states of light.(B) Photon thermalisation and condensation in an inorganic semiconductor device.- The media used for photon BEC so far have been liquid dyes. By using a very standard inorganic semiconductor (GaAs) in a very non-standard way as the thermalisation medium, we will make devices whose properties (emission spectrum, threshold pump power, correlations) can be tuned through well-established fabrication techniques, suitable for robust and commercially viable technology.(C) New planar resonators for photon BEC control.- Open microcavity resonators have proven suitable for photon BEC and are flexible in terms of the potential-energy landscape for photons. We will explore condensation of propagating photons using an in-plane distributed-resonator geometry, where time can be mapped to propagation dimension. Effectively, we will achieve sub-picosecond temporal control over BECs by spatially varying resonator designs. (D) Theory of photon correlations.- The whole project will include a strong theoretical analysis and modelling programme. The basic model to be used is based on quantum master equations, applicable to both dyes and semiconductors. It will be solved with powerful numerical techniques to predict quantum correlations for conditions that well describe the experiments. Devices will be fabricated using existing collaborations by our project supporters with established methods. While this research is primarily curiosity-driven, it will uncover new quantum states of light, methods for characterising them, and routes to exploiting them, which will be useful for quantum sensing and simulation.