An optical bottle method is developed to determine the potential-energy profile of colloidal Rayleigh nanoparticles in an optical trap. The three-dimensional distribution of fluorescent particles in the trap is measured by laser scanning confocal fluorescence microscopy. At sufficiently low concentrations at which interactions between the particles are negligible, the single-particle trapping potential-energy profile is determined from the equilibrium number-density profile by use of the Boltzmann distribution. Fluorescence imaging as well as calculations based on a discrete dipole approximation show that effects due to scattering forces are negligible for polystyrene particles of size less than 10% of the wavelength of the trapping laser, thus justifying the assumption of conservative forces in the equilibrium potential-energy determinations. The new optical bottle method measures the entire two-dimensional trapping-potential profile for an individual nanoparticle without the restriction that only one particle be contained in the trap, thus obviating the need for high laser power.
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