Sideband-Enhanced Cold Atomic Source for Optical Clocks

We demonstrate the enhancement and optimization of a cold strontium atomic beam from a two-dimensional magneto-optical trap (2D MOT) transversely loaded from a collimated atomic beam by adding a sideband frequency to the cooling laser. The parameters of the cooling and sideband beams are scanned to achieve the maximum atomic beam flux and are compared with Monte Carlo simulations. We obtain a 2.3 times larger total atomic flux and a brightness increase of a factor 4 compared with a conventional, single-frequency 2D MOT for a given total power of 200 mW. We show that the sideband-enhanced 2D MOT can reach the loading-rate performances of space-demanding Zeeman-slower-based systems, while it can overcome systematic effects due to thermal-beam collisions and hot-black-body-radiation shift, making it suitable for both transportable and accurate optical lattice clocks. Finally, we numerically study possible extensions of the sideband-enhanced 2D MOT to other alkaline-earth species.

Figure 1

One-dimensional simulation of the atomic trajectories of strontium atoms (light-blue line) for different capture processes in a 2D MOT. The color map plotted on the background depicts the acceleration value at each point of the phase space. (a) Single-frequency 2D MOT. The total saturation and the detuning of the MOT beams are $s=7$ and $\mathrm{\Delta }/\mathrm{\Gamma }=-1.6$, respectively. The estimated capture velocity is $72(1)\mathrm{m}/\mathrm{s}$. (b) Sideband-enhanced 2D MOT. The saturation parameter is $s=3.5$ for the 2D MOT beam with $\mathrm{\Delta }/\mathrm{\Gamma }=-1.6$ and $s_{\mathrm{SB}}=3.5$ for the sideband beam with ${\mathrm{\Delta }}_{\mathrm{SB}}/\mathrm{\Gamma }=-3.2$. The estimated capture velocity is $90(1)\mathrm{m}/\mathrm{s}$. The magnetic field gradient and beam width used in this calculation are $b=0.22\mathrm{T}/\mathrm{m}$ and $w=1\mathrm{cm}$, respectively. (c) Acceleration profile at $r=-w/2$ of the sideband trapping (red line) and standard 2D MOT trapping (blue line).

Figure 2

The vacuum system. It hosts a high-vacuum (HV) region for atomic beam production and an ultrahigh-vacuum (UHV) region for cooling and trapping the atomic sample. A DPC connects the two regions. The size of the entire vacuum apparatus is roughly $70\times 70\times 45{\mathrm{cm}}^3$.

Figure 3

Optical setup of the blue-laser system used for cooling, trapping, and probing ultracold strontium atoms. Each AOM is drawn with its driving frequency (in megahertz), and the sign corresponds to the diffraction order. Beam-shaping lenses are not shown. PBS, polarizing beam splitter. ${\mathrm{hor}}_1$ and ${\mathrm{hor}}_2$ are the two orthogonal MOT beams in the x-y plane, respectively.

Figure 4

Monte Carlo simulation of the velocity and position transverse coordinates of the 2D MOT-generated atomic beam at the end of the simulation time $t_{\mathrm{tot}}$. Density maps of the captured trajectories for (a) the single-frequency 2D MOT ($s_{\mathrm{2D}}=s_{\mathrm{tot}}=6.56$, ${\mathrm{\Delta }}_{\mathrm{2D}}=-1.6\mathrm{\Gamma }$) and (b) adding a sideband beam ($s_{\mathrm{SB}}=3.45$, $s_{\mathrm{2D}}=s_{\mathrm{tot}}-s_{\mathrm{SB}}$, ${\mathrm{\Delta }}_{\mathrm{SB}}=-3.1\mathrm{\Gamma }$).

Figure 5

Experimental characterization of the strontium atomic source in the single-frequency 2D MOT configuration. (a) Number of atoms loaded in the MOT as a function of the 2D MOT detuning ${\mathrm{\Delta }}_{\mathrm{2D}}$ at fixed saturation parameter $s_{\mathrm{2D}}=3.6$. The blue points are the experimental values of the number of atoms in the MOT. The turquoise regions are the MC simulations properly scaled with the experimental points. (b) Number of atoms in the MOT as function of the 2D MOT saturation $s_{\mathrm{2D}}$ at fixed detuning ${\mathrm{\Delta }}_{\mathrm{2D}}=-1.6\mathrm{\Gamma }$. (c) Number of atoms in the MOT as a function of the push detuning ${\mathrm{\Delta }}_{\mathrm{push}}$ at fixed saturation $s_{\mathrm{push}}=0.34$. All the data are taken at $T_{\mathrm{ov}}=460{}^{\circ }\mathrm{C}$.

Figure 6

Atomic flux generated from the atomic source as a function of the 2D MOT saturation parameter, without (blue circles) and with (red diamonds) the use of the sideband ($P_{\mathrm{SB}}=200\mathrm{mW}-P_{\mathrm{2D}}$). These data are taken at $s_{\mathrm{push}}=0.34$, ${\mathrm{\Delta }}_{\mathrm{2D}}/\mathrm{\Gamma }=-1.6$, ${\mathrm{\Delta }}_{\mathrm{SB}}/\mathrm{\Gamma }=-3.13$ and compared with MC estimates (shaded lines).

Figure 7

Number of atoms captured in the MOT region for different power distributions of $s_{\mathrm{tot}}=6.56$ between the sideband beam $s_{\mathrm{SB}}$ and the 2D MOT beam $s_{\mathrm{2D}}$. All the data are measured with 2D MOT detuning ${\mathrm{\Delta }}_{\mathrm{2D}}=-1.6\mathrm{\Gamma }$ and sideband detuning ${\mathrm{\Delta }}_{\mathrm{SB}}=-3.13\mathrm{\Gamma }$. The red diamonds are the number of atoms trapped in the MOT at increasing sideband-beam saturation parameter $s_{\mathrm{SB}}$. The pink shaded area represents the MC simulation in this experimental configuration. The blue circles describe the corresponding number of atoms trapped in the MOT with the sideband-beam AOM turned off.

Figure 8

Enhancement factor $\eta$ as a function of the sideband-parameter scan. (a) Experimental data compared with (b) MC numerical results at fixed total saturation parameter $s_{\mathrm{tot}}=6.56$ and ${\mathrm{\Delta }}_{\mathrm{2D}}=-1.6\mathrm{\Gamma }$. (c),(d) Same as (a),(b) but for $s_{\mathrm{tot}}=3.6$.

Figure 9

Doppler spectrum from transverse spectroscopy on the 2D MOT $\mathrm{Sr}$ atomic beam. The inset shows the corresponding Doppler temperatures compared with the MC simulation results and the corresponding Doppler limit.