  Active particles break out of thermodynamic equilibrium thanks to their
directed motion, which leads to complex and interesting behaviors in the
presence of confining potentials. When dealing with active nanoparticles,
however, the overwhelming presence of rotational diffusion hinders directed
motion, leading to an increase of their effective temperature, but otherwise
masking the effects of self-propulsion. Here, we demonstrate an experimental
system where an active nanoparticle immersed in a critical solution and held in
an optical harmonic potential features far-from-equilibrium behavior beyond an
increase of its effective temperature. When increasing the laser power, we
observe a cross-over from a Boltzmann distribution to a non-equilibrium state,
where the particle performs fast orbital rotations about the beam axis. These
findings are rationalized by solving the Fokker-Planck equation for the
particle's position and orientation in terms of a moment expansion. The
proposed self-propulsion mechanism results from the particle's non-sphericity
and the lower critical point of the solute.
