Loading dynamics of optical trap and parametric excitation resonances of trapped atoms

We study the loading dynamics of an optical dipole trap and an optical lattice both experimentally and theoretically. A simple power dependence for the number of trapped atoms (N∝P^3/2) is revealed in both cases. We then study the parametric excitation of the trapped atoms. High order parametric resonance is observed close to but lower than 4ν in a CO₂ laser optical lattice. The existence of the high harmonic and its shift toward lower frequency are attributed to the anharmonicity of the optical trapping potential. We investigate the discrepancy between experimentally measured optical lattice frequencies and the theoretical calculation for several published experiments and present corrected formula for trap frequency calculations. Using this corrected formula and accounting for the off-center lattice sites, we present a modified formula for calculating the optical lattice frequency and obtain better agreement between experimental measurement and theoretical calculation.