Phase diagram of spatiotemporal instabilities in a large magneto-optical trap

Large clouds of cold atoms prepared in a magneto-optical trap are known to present spatiotemporal instabilities when the frequency of the trapping lasers is brought close to the atomic resonance. This system bears similarities with trapped plasmas where the role of the Coulomb interaction is played by the exchange of scattered photons, and astrophysical objects, such as stars whose size is dependent on radiative forces. We present in this paper a study of the phase space of such instabilities and reveal different dynamical regimes. Three-dimensional simulations of the highly nonlinear atomic dynamics permit a detailed analysis of the experimental observations.

Figure 1

($\delta ,\mathbf{\nabla }B$) instability phase diagram (experiment). The atom number is fixed at $N=1.5\times {10}^{10}$. Each image corresponds to the average of 50 single-shot fluorescence images with intensity displayed in logarithmic scale (the intensity range is 2 decades). The field of view is $6.5\times 6.5{\mathrm{cm}}^2$. The dashed line materializes the instability threshold. The three different instability regimes (see the text) are roughly delineated by the bold boxes.

Figure 2

Different instability regimes (experiment). We show single-shot images illustrating the cloud's dynamics in the three regimes identified in Fig. 1. (a) TR ($\mathbf{\nabla }B=1.2\mathrm{G}/\mathrm{cm},\delta =-\mathrm{\Gamma }$). (b) SIR ($\mathbf{\nabla }B=12\mathrm{G}/\mathrm{cm},\delta =-\mathrm{\Gamma }$). (c) AR ($\mathbf{\nabla }B=7.2\mathrm{G}/\mathrm{cm}, \delta =-1.8\mathrm{\Gamma }$). The dotted lines in the bottom right image show the directions of two pairs of MOT beams.

Figure 3

Characterization of the three instability regimes using the eight angular sectors method (experiment). We use the same examples for the three regimes of instability as in Fig. 2. (a) TR ($\mathbf{\nabla }B=1.2\mathrm{G}/\mathrm{cm},\delta =-\mathrm{\Gamma }$), (b) SIR ($\mathbf{\nabla }B=12\mathrm{G}/\mathrm{cm},\delta =-\mathrm{\Gamma }$) and (c) AR ($\mathbf{\nabla }B=7.2\mathrm{G}/\mathrm{cm}$ and $\delta =-1.8\mathrm{\Gamma }$). We show for each set of parameters the average image (intensity in logarithmic scale) and the histograms of the intensities in each sectors. In (d), we show color maps of the mean histogram width (left) and histogram width dispersion (right). The bold lines delineate the instability threshold (dashed line) and various regimes (solid lines) as in Fig. 1.

Figure 4

Different instability regimes (simulations). We illustrate three of the instability regimes obtained in the simulations that are similar to those observed in the experiment (see Fig. 2). The images in each line correspond to different times in the simulation. (a) $\mathbf{\nabla }B=1.2\mathrm{G}/\mathrm{cm},\delta =-1.3\mathrm{\Gamma }$. (b) $\mathbf{\nabla }B=12\mathrm{G}/\mathrm{cm},\delta =-2.6\mathrm{\Gamma }$. (c) $\mathbf{\nabla }B=4.8\mathrm{G}/\mathrm{cm},\delta =-1.9\mathrm{\Gamma }$.

Figure 5

Other instability regimes (simulations). These instability regimes are not observed in the experiment. (a) $\mathbf{\nabla }B=7.2\mathrm{G}/\mathrm{cm},\delta =-1.1\mathrm{\Gamma }$. (b) $\mathbf{\nabla }B=9.6\mathrm{G}/\mathrm{cm},\delta =-2.9\mathrm{\Gamma }$. (c) $\mathbf{\nabla }B=6\mathrm{G}/\mathrm{cm},\delta =-3.3\mathrm{\Gamma }$.