Direct measurement of loading and loss rates in a magneto-optical trap with atom-number feedback

We have measured the loading and loss rates in a magneto-optical trap only with a few atoms by directly counting atom-number changing events. Unambiguous formulas are presented for the calculation of those rates from a step-wise time sequence of the fluorescence of the trapped atoms. With a recently developed atom-number feedback technique we could efficiently measure the loading rate as a function of the magnetic field gradient for the initial number of trapped atoms of zero. We could also measure the one- and two-atom loss rates as functions of the trap laser intensity for a precisely prepared initial number of trapped atoms. Each of these rates has been measured independently by directly counting the corresponding atom-number-changing events, without any influence from or inference to the other rates.

Figure 1

Typical time trace of fluorescence from our MOT in which a small number of atoms are trapped. Sudden jumps of signal means the atom number is changed by loading and loss processes.

Figure 2

Loading and loss rates obtained by counting individual atom-number-changing events. Solid curves are the fits given by Eq. (1). (a) Loading rate $R=0.08\pm 0.003{\mathrm{s}}^{-1}$, (b) one-atom loss coefficient ${\Gamma }_1=0.043\pm 0.002{\mathrm{s}}^{-1}$, and (c) two-atom loss coefficient, ${\Gamma }_2=0.0056\pm 0.0007{\mathrm{s}}^{-1}$.

Figure 3

Histograms of time intervals $T_i\left(N\right)$ with exactly $N$ atoms: (a) $N=0$, (b) $N=1$, (c) $N=2$, (d) $N=3$, and (e) $N=4$. The histograms show the decay of $N$-atom traps. By fitting the decay, the lifetime $\tau \left(N\right)$ of $N$-atom trap can be obtained. The results are $\tau \left(0\right)=(13\pm 1)\mathrm{s}$, $\tau \left(1\right)=(7.9\pm 0.5)\mathrm{s}$, $\tau \left(2\right)=(5.9\pm 0.7)\mathrm{s}$, $\tau \left(3\right)=(4.6\pm 0.3)\mathrm{s}$, and $\tau \left(4\right)=(3.4\pm 0.3)\mathrm{s}$.

Figure 4

Observed loading rate as a function of the magnetic field gradient for three different background rubidium pressures. The current on Rb dispenser was 0A (triangle), 1.9A (square), 2.1A (circle), respectively.

Figure 5

One-atom loss rate $L_1\left(5\right)$ for $N=5$ as a function of the trap laser intensity, obtained from the atom number changing events from 5 to 4. Solid line is a fit based on a model described in the text.

Figure 6

Two-atom-loss event rate for $N=5$ as a function of the trap laser intensity, obtained from the atom number changing events from 5 to 3. Solid line is a fit based on a model described in the text.

Figure 7

Calculated $\beta$ from the data of Fig. 6. The dashed line is the contribution from ground-ground-pair HFC collisions whereas the dotted line is the contribution from ground-excited-pair FSC collisions.