Blue-Detuned Magneto-Optical Trap

We present the properties and advantages of a new magneto-optical trap (MOT) where blue-detuned light drives “type-II” transitions that have dark ground states. Using ${}^{87}\mathrm{Rb}$, we reach a radiation-pressure-limited density exceeding $10^{11}{\mathrm{cm}}^{-3}$ and a temperature below $30\mu \mathrm{K}$. The phase-space density is higher than in normal atomic MOTs and a million times higher than comparable red-detuned type-II MOTs, making the blue-detuned MOT particularly attractive for molecular MOTs, which rely on type-II transitions. The loss of atoms from the trap is dominated by ultracold collisions between Rb atoms. For typical trapping conditions, we measure a loss rate of $1.8(4)\times {10}^{-10}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$.

Figure 1

(a) Relevant energy levels and the transitions we drive. Relative decay rates are indicated by the thickness of the green wavy lines. The Zeeman structure of the $1\to 1$ transition is shown. Trapping is obtained when the light is red detuned and polarized to drive $\mathrm{\Delta }{m}_F=-1$ transitions or blue detuned and polarized to drive $\mathrm{\Delta }{m}_F=+1$. (b) Position-dependent acceleration curves for these two cases, showing that, near the trap center, the force is unchanged when the polarization and detuning are reversed. For large Zeeman splittings, the symmetry is broken by the other hyperfine components. (c) Velocity-dependent acceleration curves for the two cases. For positive detuning (blue curve) there is polarization-gradient cooling but Doppler heating, while for negative detuning (red curve), the opposite is true. (b) and (c) are calculated for a six-beam MOT using optical Bloch equations [13] that take into account the ${}^{87}\mathrm{Rb}$ level structure and Zeeman shifts, as well as the two laser frequency components of light. The parameters used were $\delta f_{11}=\pm 11.5\mathrm{MHz}$, $\delta f_{22}=\pm 26\mathrm{MHz}$, $I_t=113\mathrm{mW}/{\mathrm{cm}}^2$, and $B^{\prime }=87\mathrm{G}/\mathrm{cm}$.

Figure 2

Peak number density ($n_0$) versus the number of atoms in the MOT ($N$) for a range of magnetic field gradients. Dashed lines are fits to $n_0=N/(V_0+N/n_{\max })$.

Figure 3

Ballistic expansion of atoms released from the blue-detuned MOT. The parameters are $\delta f_{11}=35\mathrm{MHz}$, $\delta f_{22}=11.5\mathrm{MHz}$, and $B^{\prime }=87\mathrm{G}/\mathrm{cm}$. The MOT is loaded at $I_t=130\mathrm{mW}/{\mathrm{cm}}^2$ and $I_t$ is then reduced to $22\mathrm{mW}/{\mathrm{cm}}^2$ for 5 ms before the atoms are released. Images are $5\times 5\mathrm{mm}$ and correspond to the times indicated by the dotted lines in the lower panel. The lower panel shows the rms widths in the radial (circles) and axial (triangles) directions. The fitted temperatures are $T_{\rho }=30(1)$ and $T_z=29(1)\mu \mathrm{K}$.

Figure 4

(a) Temperature versus $\delta f_{22}$ when $\delta f_{11}=35\mathrm{MHz}$, $I_t=21\mathrm{mW}/{\mathrm{cm}}^2$, and $B^{\prime }=40\mathrm{G}/\mathrm{cm}$. (b) Temperature versus $\delta f_{11}$ when $\delta f_{22}=11.5\mathrm{MHz}$, $I_t=19\mathrm{mW}/{\mathrm{cm}}^2$, and $B^{\prime }=40\mathrm{G}/\mathrm{cm}$. (c) Temperature versus $I_t$ when $\delta f_{11}=35\mathrm{MHz}$, $\delta f_{22}=11.5\mathrm{MHz}$, and $B^{\prime }=88\mathrm{G}/\mathrm{cm}$. After loading the MOT at full intensity, $I_t$ is held at the reduced value for 5 ms before measuring the temperature. (d) Temperature versus $B^{\prime }$ when $\delta f_{11}=35\mathrm{MHz}$, $\delta f_{22}=11.5\mathrm{MHz}$, and $I_t=28\mathrm{mW}/{\mathrm{cm}}^2$.

Figure 5

(a) Number of atoms in the MOT as a function of time. The blue-detuned light is turned on at $t=0$. Parameters are $I_t=240\mathrm{mW}/{\mathrm{cm}}^2$, $\delta f_{11}=26\mathrm{MHz}$, $\delta f_{22}=12\mathrm{MHz}$, $B^{\prime }=48\mathrm{G}/\mathrm{cm}$. (Line) Fit to the model described in the text. (b) Lifetime $\tau$, measured for small $N$, as a function of $I_t$. Parameters are $\delta f_{11}=26\mathrm{MHz}$, $\delta f_{22}=12\mathrm{MHz}$, $B^{\prime }=39\mathrm{G}/\mathrm{cm}$.