  Although the temperature of a thermodynamic system is usually believed to be
a positive quantity, under particular conditions, negative temperature
equilibrium states are also possible. Negative temperature equilibriums have
been observed with spin systems, cold atoms in optical lattices and
two-dimensional quantum superfluids. Here we report the observation of
Rayleigh-Jeans thermalization of light waves to negative temperature
equilibrium states. The optical wave relaxes to the equilibrium state through
its propagation in a multimode optical fiber, i.e., in a conservative
Hamiltonian system. The bounded energy spectrum of the optical fiber enables
negative temperature equilibriums with high energy levels (high order fiber
modes) more populated than low energy levels (low order modes). Our experiments
show that negative temperature speckle beams are featured, in average, by a
non-monotonous radial intensity profile. The experimental results are in
quantitative agreement with the Rayleigh-Jeans theory without free parameters.
Bringing negative temperatures to the field of optics opens the door to the
investigation of fundamental issues of negative temperature states in a
flexible experimental environment.
