Laser cooling of ${}^{85}\mathrm{Rb}$ atoms to the recoil-temperature limit

We demonstrate the laser cooling of ${}^{85}\mathrm{Rb}$ atoms in a two-dimensional optical lattice. We follow the two-step degenerate Raman sideband cooling scheme [Kerman et al., Phys. Rev. Lett. 84, 439 (2000)], where a fast cooling of atoms to an auxiliary state is followed by a slow cooling to a dark state. This method has the advantage of independent control of the heating rate and cooling rate from the optical pumping beam. We operate the lattice at a Lamb-Dicke parameter $\eta =0.45$ and show the cooling of spin-polarized ${}^{85}\mathrm{Rb}$ atoms to the recoil temperature in both dimensions within 2.4 ms with the aid of adiabatic cooling.

Figure 1

Two-step degenerate Raman sideband cooling energy scheme. The figure only shows the most relevant energy levels. The blue double arrows indicate the degenerate two-photon Raman transition for the interchange of vibrational energy and Zeeman energy. The dashed arrow indicates the relevant spontaneous emission in the cooling process. Due to the small separation between the excited hyperfine states of the $D_2$ line manifold, we employ a $D_1$ line for optical pumping to avoid coupling to other excited states. The ${\sigma }^{+}$-polarized optical pumping beam (thick red arrow) represents the fast cooling to the $|F=3,m_{\mathrm{F}}=2,n=0\rangle$ state, and the $\pi$-polarized optical pumping beam (thin red arrow) represents the slow cooling to the $|F=3,m_{\mathrm{F}}=3,n=0\rangle$ state. Both frequencies are detuned by $\mathrm{\Delta }$ from the excited state. The light shift and power broadening from the optical pumping beam and the lattice beams are omitted in the figure.

Figure 2

Optical arrangement for the experiment. The thick blue arrows on the horizontal $x-y$ plane are the lattice beams, and the red arrow from the top is the optical pumping beam. The imaging beams are from the cooling and repumping beams of the MOT and the fluorescence images are collected from the CCD camera. NPBS is a nonpolarizing beam splitter for separating the optical pumping beam and fluorescence.

Figure 3

Timing sequence. The sub-Doppler cooling process ends at $t=0$ s and the $t=1$ s, where MOT cooling, repumping beams, and anti-Helmholtz are off. Each experimental trial lasts for 2 s. Each second differs in the imaging time for the time-of-flight measurement. The optical pumping beam is on for 2.4 ms. The optical lattice power is ramped up and down in $800\mu \mathrm{s}$. The sideband cooling duration in the diagram includes only the time where the optical pumping beam is on.

Figure 4

The final temperature in the $y$ axis as a function of optical pumping beam total power with different detunings $\mathrm{\Delta }$. The blue circles and red triangles correspond to $-4$ and $-20$ MHz detuning from the $D_1$ line $F=3$ to $F^{\prime }=2$ transition, respectively. The lattice beams have a waist of 7 mm and 47 mW on each beam and the cooling process is held for 2.4 ms. The dashed line indicates the recoil temperature of ${}^{85}\mathrm{Rb}$. The curves are the theoretical fitting discussed in the text.

Figure 5

The final temperature after sideband cooling as a function of the cooling duration. The total optical pumping beam power is 1 mW and the detuning $\mathrm{\Delta }=+20$ MHz from $|5S_{1/2},F=3\rangle$ to $|5P_{1/2},F^{\prime }=2\rangle$ transition. Each lattice beam power is 47 mW. The measurements are done in the $y$ axis.

Figure 6

The final temperature with varying optical potential in the $x$ and $y$ directions. The horizontal axis is the corresponding Lamb-Dicke parameter. The blue triangles are the calculated temperature of the ground-state energy of the harmonic potential for reference. The fitting curve is for the $x$ axis only.