Degenerate Raman sideband cooling of ${}^{39}\mathrm{K}$

We report on a realization of sub-Doppler laser cooling of ${}^{39}\mathrm{K}$ atoms using degenerate three-dimensional Raman sideband cooling. We take advantage of the well-resolved excited hyperfine states on the $D_1$ optical transition to produce spin-polarized samples with $1.4\times {10}^8$ atoms at temperatures of 1.8 $\mu \mathrm{K}$. The phase-space densities are $\ge {10}^{-4}$, which significantly improves the initial conditions for a subsequent evaporative cooling step. The presented cooling technique using the $D_1$ line can be adapted to other atomic species and is applicable to high-resolution imaging schemes in far off-resonant optical lattices.

Figure 1

(a) Schematic of dRSC on the $D_1$ line on ${}^{39}\mathrm{K}$. One cycle consists of two 2-photon Raman transitions (double-sided arrows) between vibrational and magnetic states that are brought to degeneracy by an external magnetic field ($\mathrm{\Delta }{E}_{\mathrm{Z}}$) and optical pumping (single-sided blue arrow) via the $|F^{\prime }=1,m_{F^{\prime }}=-1\rangle$ state. The strong ${\sigma }^{-}$ component of the pumping beam broadens and shifts ($\mathrm{\Delta }{E}_{\mathrm{S}}$) the energy levels. The inset shows all the states and transitions involved in the cooling scheme. The arrows represent the repumper (brown), the spontaneous decay into states with $F=2$ (gray, wiggled), the spontaneous transitions to the lower ground state with $F=1$ (gray, dashed), and the decay into the dark state (black, wiggled). (b) Simplified optical setup. The lattice (red inward pointing arrows) is generated by one retroreflected standing wave with ${45}^{\circ }$ polarization with respect to the magnetic field axis ${\vec{B}}_z$ and two running waves with polarizations that all lie in one plane. The repumper and polarizer beams (blue-brown arrow) propagate parallel to ${\vec{B}}_z$ to allow for a dominantly circular polarization.

Figure 2

Level scheme of the two lowest energy levels of ${}^{39}\mathrm{K}$ and transitions used for dRSC and GMC. The lattice laser is detuned from the $D_2$ line and the remaining beams for GMC and dRSC are derived from one laser locked on the $D_1$ line. The arrows show the transitions used and the numbers give the experimentally found optimum detunings.

Figure 3

(a) and (b) Optical setups to generate the light for dRSC. (c) Timing diagram for the ${}^{39}\mathrm{K}$ laser cooling sequence. The continuous (blue, green, brown) lines correspond to either total powers or magnetic field gradient strength and the dashed (red, dark blue) lines to frequency detunings (3D MOT: $|F=2\rangle \to |F^{\prime }=3\rangle -D_2$ transition for cooling and $|F=1\rangle \to |F^{\prime }=2\rangle$ transition for repumping).

Figure 4

(a) Temperature after dRSC as a function of the lattice detuning ${\mathrm{\Delta }}_{\mathrm{L}}$ from the $D_2$ line at $P_{\mathrm{L}}=80$ mW. The vertical bar indicates the optimum detuning, which we find to be limited by lattice power. Error bars are smaller than the symbol size. (b) Number of atoms (solid symbols) and cloud radius ${\sigma }_x$ (open symbols) after dRSC as a function of the total lattice power $P_{\mathrm{L}}$ for $1.2\times {10}^8$ atoms (blue diamonds) and $2.8\times {10}^8$ atoms (red circles) after GMC at ${\mathrm{\Delta }}_{\mathrm{L}}=-10.8$ GHz. The solid and dashed lines are fits by a saturated growth function and an exponential decay function to guide the eye. The lowest temperatures are already reached at around 30 mW, whereas the capture efficiency still grows with increasing lattice power.

Figure 5

(a) Number of atoms after dRSC as a function of the polarizer detuning ${\mathrm{\Delta }}_{\mathrm{P}}$ at $P_{\mathrm{P}}=120\mu \mathrm{W}$. One can clearly see a minimum around zero detuning. (b) Number of atoms (solid circles) and cloud radius ${\sigma }_x$ (open circles) after dRSC as a function of the polarizer power $P_{\mathrm{P}}$ at ${\mathrm{\Delta }}_{\mathrm{P}}=8$ MHz. The solid and dashed lines are fits by a saturated growth function and an exponential decay function to guide the eye. Already very small powers make dRSC work, but higher ones are needed to reach the lowest temperatures.

Figure 6

Number of atoms (solid circles) and cloud radius ${\sigma }_x$ (open circles) after dRSC as a function of the cooling duration $t_{\mathrm{R}}$. The dashed line is a fit by an exponential decay function with a linearly rising offset to guide the eye. Cooling competes with atom loss, which results in an optimum cooling time of about 5 ms. At this point in time, the temperature is $1.6\mu \mathrm{K}$.