Photon-scattering-rate measurement of atoms in a magneto-optical trap

We present a technique for empirically determining the photon scattering rate of atoms in a magneto-optical trap (MOT). An accurate measurement of the scattering rate provides a way to accurately determine the number of atoms in the MOT, the excited-state fraction, and the in situ light intensity experienced by the atoms in the trap. We validate this technique for determining the scattering rate by comparing the atom number determined by the fluorescence emitted by atoms in a MOT with an independent and unrelated measure of the number determined by an absorption measurement of an optical pumping beam. We also observe minor deviations from the two-level model for the single-photon scattering rate and extend our analysis to a four-level model. The main advantage of the method described here is that it provides a simple way of determining the photon scattering rate of the MOT empirically and, thus, of evaluating the atom number from fluorescence measurements more accurately.

Figure 1

A schematic of the fluorescence detector, vapor cell, quadrupole magnets, MOT laser beams, and probe beam used in these experiments. The MOT was configured as a retroreflection MOT and in addition to the cooling and repump beams (the six laser beams shown intersecting in the center of the magnetic field coils), the probe laser is shown (drawn as the narrow laser entering the side face of the vacuum cell). See the text for details.

Figure 2

A plot of the scattered light from the MOT versus time. Section is the fluorescence of the full MOT at the standard settings, and B shows the change in fluorescence when the pump laser detuning and power are rapidly switched to the test settings. Between B and C, the trapping lasers and the magnetic field were turned off to empty the atoms out of the trapping region. The trapping lasers were then turned back on to obtain a measurement of the scattered light signal at the test (C) and at the standard (D) settings, respectively.

Figure 3

A plot of the scattered light parameter $G$ as a function of the pump laser test powers $P$. The different lines are linear fits to the data corresponding to detunings of $\Delta /2\pi =-6.0(•)$, $-8.0(\circ )$, $-10.0\left(\blacksquare \right)$, $-12.0(\square )$, $-13.5\left(▴\right),$ and $-15.0\left(▵\right)$ MHz.

Figure 4

A plot of the slopes of the scattered light parameter $G$ as a function of the pump laser test powers $P$. The two-level-atom model predicts that these slopes should be constant as per Eq. (12). The increase in slope with increasing detuning is evidence for the breakdown of the two-level model as discussed below.

Figure 5

A plot of the intercepts from Fig. 3 as a function of $1+{\left(2\Delta /\gamma \right)}^2$. As expected from Eq. (12), these two quantities are linearly related but we also observe an additional, small, nonlinearity.

Figure 6

The optical pumping beam intensity as a function of time. (a) shows the probe beam intensity when the MOT contains atoms, while (b) indicates the absorption when no atoms are present. The atoms being optically pumped into the $5{}^2{S}_{1/2}$ $F=2$ state scatter photons out of the probe beam, producing the initial dip seen in (a).

Figure 7

The difference between the two probe beam absorption traces was fitted to a an exponential decay (solid line). The area under the difference plot is a measure of the number of photons scattered out of the probe beam.

Figure 8

A plot of the MOT fluorescence signal normalized by the single-atom scattering rate $V/{\gamma }_{\mathrm{sc}}$ as a function of the atom number in the MOT determined from the optical pumping beam absorption. For these data the pump laser detuning was held fixed at $\Delta /2\pi =-12$ MHz while the MOT fluorescence was recorded using four different pump powers, 5.0 mW $\left(\blacksquare \right)$, 11.4 mW $\left(▵\right)$, 18.0 mW $(\circ )$, and 25.5 mW $(•)$. Sample error bars are shown on the plot for several data points. The solid line is a linear fit to all the data points, constrained to pass through the origin.

Figure 9

A plot of the observed slopes $m^{\left(4\right)}$ as functions of $A/B=[1+{(2\Delta /\gamma )}^2]/\{1+{[2({\Delta }_{\mathrm{hf}}-\Delta )/\gamma ]}^2\}$. In agreement with the model Eq. (28), there should be a linear relationship between these two quantities.

Figure 10

A plot of the observed intercepts $b^{\left(4\right)}$ as functions of $A=[1+{(2\Delta /\gamma )}^2]$. The solid curve is a quadratic fit to the data.