Measurements of trap parameters of a magneto-optical trap by parametric resonance

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 π. 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