  Laser trapped nanoparticles have been recently used as model systems to study
fundamental relations holding far from equilibrium. Here we study, both
experimentally and theoretically, a nanoscale silica sphere levitated by a
laser in a low density gas. The center of mass motion of the particle is
subjected, at the same time, to feedback cooling and a parametric modulation
driving the system into a non-equilibrium steady state. Based on the Langevin
equation of motion of the particle, we derive an analytical expression for the
energy distribution of this steady state showing that the average and variance
of the energy distribution can be controlled separately by appropriate choice
of the friction, cooling and modulation parameters. Energy distributions
determined in computer simulations and measured in a laboratory experiment
agree well with the analytical predictions. We analyse the particle motion also
in terms of the quadratures and find thermal squeezing depending on the degree
of detuning.
