Evaporative cooling of a small number of atoms in a single-beam microscopic dipole trap

We demonstrate experimentally the evaporative cooling of a few hundred rubidium-87 atoms in a single-beam microscopic dipole trap. Starting with 800 atoms at a temperature of 125 $\mu$K, we produce an unpolarized sample of 40 atoms at 110 nK, within 3 s. The phase-space density at the end of the evaporation reaches unity, close to quantum degeneracy. The gain in phase-space density after evaporation is ${10}^3$. We find that the scaling laws used for much larger numbers of atoms are still valid despite the small number of atoms involved in the evaporative cooling process. We also compare our results to a simple kinetic model describing the evaporation process and find good agreement with the data.

Figure 1

Trapping and detection scheme showing the two super-imposed single-beam dipole traps (see text) with comparable depths ($\sim 1$ mK) but different sizes (waists $4\mu$m and $1.6\mu$m). The large-numerical-aperture lens collects light-induced fluorescence. Imaging with an intensified camera (I-CCD) enables atom counting and temperature measurements, from which we extract the phase-space density. $\vec{g}$ indicates the direction of gravity.

Figure 2

Evolution of the trap depth as a function of time during evaporation. Solid line: experimental ramp with linear pieces after optimization. The trap depth is measured with a $10\%$ uncertainty. Dotted line: theoretical prediction by O'Hara et al. [23].

Figure 3

(a) Evolution of the ratio $\eta =U/k_{\mathrm{B}}T$ versus the number of atoms $N$ during evaporation (filled circles). Dashed line: average value of $\eta$ for $70\le N\le 400$. (b) Evolution of the measured temperature $T$ (filled circles; right axis) and the phase-space density $D=N{(\hslash \omega /k_{\mathrm{B}}T)}^3$ (triangles; left axis) versus the number of atoms. Solid lines are fits by power laws performed for data corresponding to $70\le N\le 400$. Error bars correspond to $10\%$ uncertainties on the measured temperature, number of atoms, trap depth $U$, and oscillation frequency $\omega$. In (b), the horizontal dashed line at value $D=\zeta \left(3\right)\simeq 1.202$ indicates the transition between a thermal and a degenerate polarized sample.

Figure 4

Evolution of (a) the spatial density $n_0$ and (b) the elastic collision rate ${\gamma }_{\mathrm{el}}=n_0\sigma \overline{v}\sqrt{2}$ at the center of the trap, versus the number of atoms. Triangles: values extracted from the measurements of $T$, $N$, and the trap depth $U$. Error bars correspond to $10\%$ uncertainties on $T$, $N$, and the oscillation frequency $\omega$. Solid lines: kinetic model using $\sigma =\epsilon 4\pi a^2$ with $\epsilon =4/3$ (i.e., atoms are equally distributed among the Zeeman sublevels of $F=1$).

Figure 5

Comparison between the data and the model of Eqs. (4). Evolution of (a) the temperature $T$, (b) the number of atoms $N$, and (c) the phase-space density $D=N{(\hslash \omega /k_{\mathrm{B}}T)}^3$, as a function of the evaporation time. The dots and triangles are the data. Error bars correspond to $10\%$ uncertainties on $T$, $N$ and the oscillation frequency $\omega$. The solid and dotted lines are respectively the predictions of the model for $\sigma =(4/3)\times 4\pi a^2$ (i.e. the atoms are equally distributed among the Zeeman sub-levels of $F=1$) and $\sigma =2\times 4\pi a^2$ (i.e. the atoms are all in the same Zeeman sub-level). Here, we have taken $\{K_1;K_2;K_3\}=\{0.1$ s${}^{-1};1.5\times {10}^{-14}$ cm${}^3$ s${}^{-1};4\times {10}^{-29}$ ${\mathrm{cm}}^6$ s${}^{-1}\}$. In (c), the dashed line corresponds to $D=\zeta \left(3\right)\simeq 1.202$. Inset in (a) : evolution of $\eta =U/k_{\mathrm{B}}T$.