Bose-Einstein Beam Condensation in Optical Multimode Fibers

Nonlinear optics in multimode fibers has recently attracted increased attention. One particularly intriguing phenomenon is beam self-cleaning [1]. Upon nonlinear propagation in the multimode fiber, an initially noisy speckled input beam [Fig. 1b] contracts into a much cleaner profile with significantly enhanced fundamental mode contents [Fig. 1e]. This process has often been discussed using a thermodynamic picture and explained by convergence to a Rayleigh-Jeans distribution [2], [3]. However, this explanation has been controversially received as it relies on the absence of dissipative mechanisms and therefore does not allow a decrease of entropy during nonlinear propagation. Here we now show that much stronger beam self-cleaning is possible in a dual-clad multimode fiber with dissipative core. Starting at an initial occupation of 34% for linear propagation, a total of 92% of the energy condenses in a Townes profile for nonlinear propagation at maximum available power, see Fig. 1c,d,f. Concomitantly, we observe a dramatic decrease of entropy from 78% to below 20% in the system. In order to evaluate the thermodynamic behavior of the system, we fit Bose-Einstein distributions to modal decompositions, cf. Fig. 1c,f. This analysis indicates an abrupt drop of the chemical potential of the system by two orders of magnitude at a threshold temperature of 43.5 nK, i.e., a clear indication for an underlying phase transition.