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Journal of Applied Physics

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

Jinwei Wu, Raymond Newell, M. Hausmann, David J. Vieira, Xinxin Zhao

Published Sep 1, 2006• 20 citations

Abstract

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∝P3∕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.

DOI: 10.1063/1.2266164

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Parametric modulation is an effective tool to measure the trap frequency and investigate the atom dynamics in an optical dipole trap or lattices. Herein, we report on experimental research of parametric resonances in an optical dipole trap. By modulating the trapping potential, we have measured the atomic loss dependence on the frequency of the parametric modulations. The resonance loss spectra and the evolution of atom populations at the resonant frequency have been demonstrated and compared under three modulation waveforms (sine, triangle and square waves). A phenomenological theoretical simulation has been performed and shown good accordance with the observed resonance loss spectra and the evolution of atom populations. The theoretical analysis can be easily extended to a complex waveform modulation and reproduce enough of the experiments.

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We present a method to measure the trap frequency or the spring constant of a magneto-optical atom trap via the parametric resonance. When the intensity of the cooling laser is modulated at around twice its resonant trap frequency, the trapped atoms are parametrically excited and divided into two groups oscillating with the motional phase difference of $\ensuremath{\pi}$. We find that one can measure the natural trap frequency as the modulation amplitude is decreased down to its threshold value. The experimental results are in good agreement with the three-dimensional Doppler cooling theory based on the rate equation model.

We present a simple Fokker-Planck model for the evolution of the number of atoms and the spatial distribution in a

{\mathrm{CO}}_{2}

laser trap which is loaded from a magneto-optical trap (MOT). Deep

{\mathrm{CO}}_{2}

laser traps can achieve very high densities, but reach equilibrium slowly compared to shallow traps. Equilibrium times range from milliseconds for shallow traps to seconds in traps which are deep compared to the thermal energy. A universal function for the maximum number of trapped atoms is given, assuming that the optical dipole trap reaches thermal equilibrium with the MOT.