Scaling behavior of a very large magneto-optical trap

We investigate the scaling behavior of a very large magneto-optical trap (VLMOT) containing up to $1.4\times {10}^{11}{\mathrm{Rb}}^{87}$ atoms, loaded from a background vapor. By varying the diameter of the trapping beams, we are able to change the number of trapped atoms by more than 5 orders of magnitude. We then study the scaling laws of the loading and size of the VLMOT, and analyze the shape of the density profile in this regime where the Coulomb-like, light-mediated repulsive interaction between atoms is expected to play an important role.

Figure 1

Experimental scheme. We show the MOT trapping scheme along one of the three spatial dimensions, corresponding to the axis of the coils generating the magnetic field gradient ($x$). The arrangement is identical for the other two dimensions (except for the magnetic coils). A CCD is used to image the fluorescence of the cold cloud in the ($x,y$) plane (see text for details).

Figure 2

Loading the VLMOT (experiment). We plot the number of trapped atoms $N$ as a function of the diameter $D$ of the trapping beams (see text), for three different MOT detunings: ${\delta }_{\mathrm{MOT}}=-3\Gamma$ (stars); ${\delta }_{\mathrm{MOT}}=-4\Gamma$ (dots); ${\delta }_{\mathrm{MOT}}=-5\Gamma$ (squares). We observe a fast increase, followed by a progressive saturation. The line is a fit $N\propto D^{5.82}$ of the data for ${\delta }_{\mathrm{MOT}}=-4\Gamma$. The error bars are smaller than the symbol size.

Figure 3

Capture velocity vs MOT beam diameter (numerics). Using a simple Doppler model, we compute the MOT's capture velocity versus $D$, for the detunings of Fig. 2. The lines emphasize the two observed regimes: $v_c\propto D^{1.11}$ (dotted line) and $v_c\propto D^{0.356}$ (solid line).

Figure 4

Variation of VLMOT size with $N$. We show two examples of fluorescence images (see text for details), respectively, at low [$N=4.2\times {10}^6$ (a)] and large [$N=1.3\times {10}^{11}$ (b)] number of trapped atoms. The MOT detuning is ${\delta }_{\mathrm{MOT}}=-4\Gamma$. The field of view is 23 mm. The axis of the magnetic gradient coils is along $x$.

Figure 5

VLMOT size scaling. We measure the FWHM size of the cloud along the magnetic coils axis $L_x$ as a function of the number of atoms. The three sets of data correspond to different MOT detunings: ${\delta }_{\mathrm{MOT}}=-3\Gamma$ (stars); ${\delta }_{\mathrm{MOT}}=-4\Gamma$ (dots); ${\delta }_{\mathrm{MOT}}=-5\Gamma$ (squares). A fit of the ${\delta }_{\mathrm{MOT}}=-4\Gamma$ data for $N>2\times {10}^7$ yields $L_x\propto N^{0.394\pm 0.004}$ (solid line). The dashed line corresponds to the prediction of the standard model [2] $L\propto N^{1/3}$.

Figure 6

VLMOT peak density and optical density. We plot in (a) the peak spatial density and in (b) the on-resonance optical density of the cloud obtained from the data of Fig. 5 (see text). The error bars are computed from the statistical errors on the measured atom number and MOT size.

Figure 7

Impact of multiple scattering during imaging. We compare the fluorescence profiles obtained for the same cloud ($N=2\times {10}^{10}$) but with different detuning values used for the imaging: ${\delta }_{\mathrm{im}}=-2\Gamma$ (1), ${\delta }_{\mathrm{im}}=-4\Gamma$ (2), ${\delta }_{\mathrm{im}}=-6\Gamma$ (3), ${\delta }_{\mathrm{im}}=-8\Gamma$ (4), and ${\delta }_{\mathrm{im}}=-10\Gamma$ (5). The inset shows the evolution of the measured FWHM with ${\delta }_{\mathrm{im}}$.

Figure 8

Fluorescence profiles of the cloud. We plot the fluorescence profiles along $x$ (dots) and $y$ (circles) for four different atom numbers: (a) $N=3.2\times {10}^7$; (b) $N=1.2\times {10}^9$; (c) $N=2\times {10}^{10}$; (d) $N=1.3\times {10}^{11}$. The lines correspond to a Gaussian shape. (a)–(d) Data are all scaled in the same way: All profiles are vertically normalized to a maximum value = 1 (note the log scale), while the horizontal scaling is different for all four plots such that the profile's FWHM is equal to 1. (e) Shows the data of (d) along $x$, in linear scale.

Figure 9

Ellipticity of the cloud. We plot the ellipticity $\epsilon$ of the MOT measured versus the number of atoms $N$. $\epsilon$ is measured at $90\%$ (half-filled circles), $50\%$ (dots), and $10\%$ (circles) of the peak value of the fluorescence images. The shaded area corresponds to the limits obtained from the model of Ref. [21], while the dashed line $\epsilon =\sqrt{2}$ is the expected ellipticity for a MOT in the temperature-limited regime.

Figure 10

Ellipticity of the cloud versus MOT detuning. We plot here the ellipticity measured at $50\%$ of the peak value of the fluorescence images, for different values of ${\delta }_{\mathrm{MOT}}$: ${\delta }_{\mathrm{MOT}}=-3\Gamma$ (stars); ${\delta }_{\mathrm{MOT}}=-4\Gamma$ (dots); ${\delta }_{\mathrm{MOT}}=-5\Gamma$ (squares). The shaded area corresponds to the limits obtained from the model of Ref. [21], while the dashed line $\epsilon =\sqrt{2}$ is the expected ellipticity for a MOT in the temperature-limited regime.