Thermal broadening of the power spectra of laser-trapped particles in vacuum

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 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.