Bose-Einstein condensation of an optical thermodynamic system into a solitonic state

Recent years have seen a resurgence of interest in multimode fibers due to their intriguing physics and applications, with spatial beam self-cleaning (BSC) having received special attention. In BSC light condenses into the fundamental fiber mode at elevated intensities. Despite extensive efforts utilizing optical thermodynamics to explain such counterintuitive beam reshaping process, several challenges still remain in fully understanding underlying physics. Here we provide compelling experimental evidence that BSC in a dissipative dual-core fiber can be understood in full analogy to Bose-Einstein condensation (BEC) in dilute gases. Being ruled by the identical Gross-Pitaevskii Equation, both systems feature a Townes soliton solution, for which we find further evidence by modal decomposition of our experimental data. Specifically, we observe that efficient BSC only sets in after an initial thermalization phase, causing converge towards a Townes beam profile once a threshold intensity has been surpassed. This process is akin to a transition from classical to quantum-mechanical thermodynamics in BEC. Furthermore, our analysis also identifies dissipative processes as a crucial, yet previously unidentified component for efficient BSC in multimode fiber. This discovery paves the way for unprecedented applications of multimode-fiber based systems in ultrafast lasers, communications, and fiber-based delivery of high-power laser beams.