Accumulation and thermalization of cold atoms in a finite-depth magnetic trap

We study the continuous accumulation of cold atoms from a magneto-optical trap (MOT) into a finite depth trap, consisting in a magnetic quadrupole trap dressed by a radiofrequency (rf) field. Chromium atoms $\left({}^{52}\mathrm{Cr}\right)$ in a MOT are continuously optically pumped by the MOT lasers to metastable dark states. In the presence of a rf field, the temperature of the metastable atoms that remain magnetically trapped can be as low as $25\mathrm{\mu }\mathrm{K}$, with a density of ${10}^{17}\mathrm{atoms}{\mathrm{m}}^{-3}$, resulting in an increase of the phase-space density, still limited to $7.0\times {10}^{-6}$ by inelastic collisions. To investigate the thermalization issues in the truncated trap, we measure the free evaporation rate in the rf-truncated magnetic trap, and deduce the average elastic cross section for atoms in the ${}^{5}D_4$ metastable states, ${\sigma }_{el}=7.0\times {10}^{-16}{\mathrm{m}}^2$.

Figure 1

(Color online) Relevant level structure for chromium. The cooling transition is ${}^{7}S_3\to {}^{7}P_4$. Atoms are depumped to the ${}^{5}D_4$ metastable state. For this state, we also present a sketch of the rf dressed magnetic Zeeman eigenenergies. Along the $x$ axis, the avoided crossing occurs at $R_{rf}$. The density profiles are also qualitatively represented (shaded area) for atoms in the MOT (a), and for metastable states depending on the sign of their magnetic quantum numbers (b) and (c).

Figure 2

Accumulation time $T_{\mathrm{load}}$ in the truncated MT, as a function of the rf frequency. The error bar is the typical statistical error in an exponential fit to the number of accumulated atoms as a function of $\tau$.

Figure 3

Atom number (triangles) and peak atomic density (squares) after $3\mathrm{s}$ of accumulation as a function of rf frequency. Solid and dotted lines: theory (see text). The error bars correspond to the uncertainty in determining the total number of atoms by absorption imaging (see text).

Figure 4

Temperature of the atoms (triangles) and phase-space density (squares) after $3\mathrm{s}$ of accumulation, as a function of the rf frequency. Solid and dotted lines: theory (see text). The error bars correspond to the estimated errors on temperature and density measurements (see text).

Figure 5

Number of elastic collisions before the steady state is reached when atoms are accumulated in the rf-truncated magnetic trap. When this number is smaller than approximately 4, thermal equilibrium is not reached, and our theoretical model does not apply.

Figure 6

$\eta$ as a function of the rf frequency. For $\eta \le 4$, the density distribution at thermal equilibrium is modified by the trap truncation, which is not taken into account in the theoretical model.

Figure 7

Decay of metastable atoms when no rf is applied (squares). Solid line: result of the fit (see text). The dotted line is a result of a purely exponential fit of the experimental data for $t>5\mathrm{s}$. The dashed line is a result of an exponential fit for $t<1\mathrm{s}$. The time constant of both fits are given.

Figure 8

Time evolution of the temperature without rf (squares) and with a $3\mathrm{MHz}$ rf field (triangles). Lines are guides for the eye. The error bar illustrates the typical combined statistical and systematic errors on temperature measurements.