Type-II Zeeman slowing: Characterization and comparison to conventional radiative beam-slowing schemes

We describe a Zeeman slowing method reported in [New J. Phys. 20, 042001 (2018)] and compare it to conventional radiative beam-slowing schemes. The scheme is designed to work on a type-II level structure, making it particularly attractive for radiative beam slowing of molecules. Working on the $D_1$ line of atomic ${}^{39}\mathrm{K}$, we demonstrate efficient slowing of an atomic beam from $400\mathrm{m}{\mathrm{s}}^{-1}$ down to $35\mathrm{m}{\mathrm{s}}^{-1}$ with a final flux of $3.3\times {10}^9{\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}$. We give experimental details and compare our results to other established radiative slowing schemes in atomic and molecular physics. We find type-II Zeeman slowing to outperform white-light slowing commonly used in molecular beam slowing and to be comparably as efficient as traditional type-I Zeeman slowing being the standard beam-slowing technique in atomic physics.

Figure 1

(a) Application of the deceleration force when $a_{\max }={10}^5\text{m}{\text{s}}^{-2}$ of different radiation pressure slowing methods while decelerating particles from $160\mathrm{m}{\mathrm{s}}^{-1}$ down to $10\mathrm{m}{\mathrm{s}}^{-1}$. (b) One-dimensional velocity trajectory simulations over time $t$ during the slowing process with initial velocities ranging from 160 to $80\mathrm{m}{\mathrm{s}}^{-1}$. (c) One-dimensional velocity trajectory simulations over slowing distance $z$ during the slowing process. Note that Zeeman slowing is the only method where all particles reach the target velocity at the same point in space. Also note that, for chirped slowing and Zeeman slowing, the deceleration stops at the target velocity, whereas for white-light slowing the remaining finite deceleration force leads to further deceleration.

Figure 2

(a) Type-II Zeeman slower scheme for ${}^{39}\mathrm{K}$. The effective detuning ${\delta }_{\mathrm{eff}}$ of ${\mathcal{L}}_{\mathrm{sl}}$ together with the applied magnetic field $B$ dictates which velocity class is addressed [see relation (2)]. (b) Sideband spectrum of the slowing laser (black) to address the transition frequencies for the different hyperfine levels in high magnetic fields. (c) Spectrum of the frequency-broadened repumping laser realized with a current modulated distributed feedback diode. Sinusoidal modulation with $f_{\mathrm{mod}}=12\mathrm{MHz}$ modulated to a width of approximately $900\mathrm{MHz}$.

Figure 3

(a) Half section view of the vacuum chamber showing the overall geometry of the apparatus. (b) Quarter section view of the magnetic-field coil. Between the inner and the outer tube of the brass holder, cooling water is flushed, which holds the coil at a temperature of $T<70{}^{\circ }\text{C}$. (c) Detection chamber showing the slowing and detection lasers. For the fluorescence measurement the lens and curved mirror are additionally installed in this chamber (not shown here).

Figure 4

(a) Differential absorption signals for type-II Zeeman slowing for several final velocities. The inset shows the corresponding configurations of the applied magnetic field. (b) Corresponding three dimensional Monte Carlo simulations. The dotted black curve shows the initial velocity distribution. When only the offset field is applied (dashed orange curve) the slowing results in a final peak velocity of $v_{\mathrm{p}}\approx 350\mathrm{m}{\mathrm{s}}^{-1}$. By adding a Zeeman field (dot-dashed green and solid blue curves) the slowing laser is kept in resonance with the slowed ${}^{39}\mathrm{K}$ resulting in a shift of $v_{\mathrm{p}}$ to lower velocity classes. The simulations are in good agreement with the measured results but typically predict slightly narrower velocity peaks.

Figure 5

Type-II Zeeman slowing with different capture velocities. By addressing higher-velocity classes while keeping the final velocity constant, the slowing performance can be optimized. For the dotted orange curve $\mathrm{\Delta }B\approx 147\mathrm{G}$ corresponds to a velocity change of $\mathrm{\Delta }v\approx 211\mathrm{m}{\mathrm{s}}^{-1}$. The solid blue curve shows the optimized result with $\mathrm{\Delta }B\approx 234\mathrm{G}$ corresponding to $\mathrm{\Delta }v\approx 335\mathrm{m}{\mathrm{s}}^{-1}$ such that significantly more velocity classes are being slowed and compressed into the final velocity peak.

Figure 6

In solid blue the optimized signal is shown alongside with the corresponding magnetic field for our Type-II Zeeman slower. The dashed green and dotted orange lines show the results when the capture velocity is increased even further with capture velocities too high to be slowed over the finite slowing path. The atoms fall out of resonance with ${\mathcal{L}}_{\mathrm{sl}}$ before reaching their final velocity. For the dashed green curve, atoms traveling at the centerline of the slowing lasers are still slowed to the desired final velocity, atoms traveling off center fall out of resonance with the slowing beam. This is due to the Gaussian beam profile of the slowing laser having a significantly lower intensity in the wings. For the dotted orange curve the magnetic-field gradient is so steep that all atoms fall out of resonance with the slowing laser at higher velocity classes.

Figure 7

(a) Differential absorption signal of type-I Zeeman slowing in a ${\sigma }^{-}$ configuration (see inset). The dotted blue curve shows the initial velocity distribution, whereas the solid orange curve shows the slowed distribution. (b) Corresponding Monte Carlo simulation. The inset shows the applied magnetic field. We do not use an offset field for the type-I slower.

Figure 8

(a) Achieved white-light slowing signals for different $v_{\mathrm{fin}}$. The dotted black line shows the initial velocity distribution. The dashed blue and solid orange curves show the slowed velocity distributions and the inset shows the corresponding force profiles calculated by multilevel rate equations spanning over a velocity range of $\mathrm{\Delta }v\approx 400\mathrm{m}{\mathrm{s}}^{-1}$. The density at low velocity classes increases when the slowing force is applied, but the efficiency is rapidly decreasing when slowing to low velocities. (b) The corresponding Monte Carlo simulations show a similar behavior but in the simulations there are nearly no atoms lost at higher velocity classes, as can be seen for the solid orange curve in panel (b). This is most probably due to a lower deceleration force in the experiment in comparison to the predicted force.