Polarization gradient cooling of single atoms in optical dipole traps

We experimentally investigate ${\sigma }^{+}\text{−}{\sigma }^{-}$ polarization gradient cooling (PGC) of a single ${}^{87}\mathrm{Rb}$ atom in a tightly focused dipole trap and show that the cooling limit strongly depends on the polarization of the trapping field. For optimized cooling light power, the temperature of the atom reaches $10.4\left(6\right)\mu \mathrm{K}$ in a linearly polarized trap, approximately five times lower than in a circularly polarized trap. The inhibition of PGC is qualitatively explained by the fictitious magnetic fields induced by the trapping field. We further demonstrate that switching the trap polarization from linear to circular after PGC induces only minor heating.

Figure 1

(a) Energy-level scheme for the ${5S}_{1/2}$, $F=2$ to ${5P}_{3/2}$, $F=3$ transition near 780 nm of a ${}^{87}\mathrm{Rb}$ atom in a $\pi$-polarized (parallel to the $x$ axis) and a ${\sigma }^{+}$-polarized FORT. The inset illustrates the geometrical arrangement: The trapping beam propagates along the $z$ axis. (b)–(e) Calculated force on an atom of fixed velocity moving through a ${\sigma }^{+}\text{−}{\sigma }^{-}$ PGC field for different axes and FORT polarizations. Both beams of the PGC field have a Rabi frequency $\mathrm{\Omega }={\mathrm{\Gamma }}_0/2$ and are red-detuned from the natural transition frequency by $\mathrm{\Delta }=-3{\mathrm{\Gamma }}_0$, where ${\mathrm{\Gamma }}_0=2\pi \times 6.07\mathrm{MHz}$ is the natural linewidth. Black dashed and blue solid lines indicate the force for a free and a trapped atom, respectively. (b) $\pi$-polarized trap, PGC field along the $x$ axis. (c) ${\sigma }^{+}$-polarized trap, PGC field along the $x$ axis. (d) $\pi$-polarized trap, PGC field along the $z$ axis. (e) ${\sigma }^{+}$-polarized trap, PGC field along the $z$ axis.

Figure 2

Optical setup for trapping, polarization gradient cooling, and fluorescence detection of a single atom. APD: avalanche photodetector; DM: dichroic mirror; $\lambda /4$: quarter-wave plate; $\lambda /2$: half-wave plate; $B$: beam consisting of 780-nm cooling light and 795-nm repumping light with a waist of 1 mm. $B_3$ is perpendicular to $B_1$ and $B_2$.

Figure 3

Temperature of the atoms after PGC over the total cooling beam power in $B_1$, $B_2$, and $B_3$. Error bars represent statistical uncertainty (one standard deviation). Systematic uncertainties, caused by errors in the determination of trap frequencies and the beam waist, are smaller than the statistical uncertainties.

Figure 4

Temperature of the atoms after PGC for a varying cooling duration. Optimal cooling beam power is used respectively for both the $\pi$-polarized trap (red square) and the ${\sigma }^{+}$-polarized trap (blue circle). Solid lines are fits to exponentials. Error bars represent one standard deviation.

Figure 5

Temperature of the atoms after PGC in a $\pi$-polarized trap depending on the polarization extinction ratio. The cooling beam power is optimized for the highest value of $\epsilon$. Error bars represent one standard deviation.