  We show that at low pressures the spectral widths of the power spectra of
laser-trapped particles are nearly independent from pressures and, due to the
nonlinearities of the trap, reflect the thermal distribution of particles. In
the experiments with nanoparticles trapped in an optical lattice, we identify
two distinct features of the widths. First, the widths along an optical lattice
are much broader than those in the other directions. Second, the spectral
widths are narrower for larger nanoparticles. We develop a theory of thermal
broadening and show that the spectral widths normalized by the frequencies of
the center-of-mass motion directly reveal the ratio of the thermal energy to
the trap depth. The presented model provides a good understanding of the
observed features. Our model holds also for smaller particles such as atoms and
molecules and can be readily extended to the general case with a single-beam
optical trap.
