Cavity-enhanced photoionization of an ultracold rubidium beam for application in focused ion beams

A two-step photoionization strategy of an ultracold rubidium beam for application in a focused ion beam instrument is analyzed and implemented. In this strategy the atomic beam is partly selected with an aperture after which the transmitted atoms are ionized in the overlap of a tightly cylindrically focused excitation laser beam and an ionization laser beam whose power is enhanced in a build-up cavity. The advantage of this strategy, as compared to without the use of a build-up cavity, is that higher ionization degrees can be reached at higher currents. Optical Bloch equations including the photoionization process are used to calculate what ionization degree and ionization position distribution can be reached. Furthermore, the ionization strategy is tested on an ultracold beam of ${}^{85}\mathrm{Rb}$ atoms. The beam current is measured as a function of the excitation and ionization laser beam intensity and the selection aperture size. Although details are different, the global trends of the measurements agree well with the calculation. With a selection aperture diameter of $52\mu \mathrm{m}$, a current of $\left(170\pm 4\right)$ pA is measured, which according to calculations is 63% of the current equivalent of the transmitted atomic flux. Taking into account the ionization degree the ion beam peak reduced brightness is estimated at $1\times {10}^7$ A/(${\mathrm{m}}^2\mathrm{sr}\mathrm{eV}$).

Figure 1

The strategy to ionize a beam ultracold ${}^{85}\mathrm{Rb}$ atoms. On the left a schematic energy level scheme is shown with the excitation and ionization transition indicated. On the right a schematic side view of the ionization of atomic beam is shown. The ultracold rubidium atoms are selected with an aperture to set the ion beam current, excited by a tightly cylindrically focused excitation laser beam that travels in the $y$ direction and ionized by the overlapping ionization laser beam that travels in the $x$ direction, whose power is enhanced in a build-up cavity and which is focused less tightly than the excitation beam.

Figure 2

Analytical solutions to the OBE including ionization [Eq. (7)] in the case that $\gamma =\frac{\mathrm{\Omega }}{10}$ and ${\gamma }_{\text{i}}=\frac{{\gamma }_{\text{i,cr}}}{10},{\gamma }_{\text{i,cr}}\text{and}10{\gamma }_{\text{i,cr}}$, where ${\gamma }_{\text{i,cr}}$ is the critical value for the ionization rate given by Eq. (10). The solutions are given by Eqs. (A12) and (A13). For the case that ${\gamma }_i=10{\gamma }_{\text{i,cr}}$, a plot is also shown of the predicted ionized population by looking at the ionization as a continuous measurement of the excited state population which suppresses the excitation from happening by the quantum Zeno effect.

Figure 3

The ground-state population (${\rho }_{\text{gg}}$), excited-state population (${\rho }_{\text{ee}}$), and ionized-state population (${\rho }_{\text{ii}}$) as a function of position for four different situations: for a single atom traveling at 91 m/s and without ionization, for a single atom traveling at 91 m/s and with ionization, for all atoms averaged over the longitudinal velocity distribution, and for all atoms averaged over the longitudinal velocity distribution and averaged over a standing wave of ionization light intensity.

Figure 4

Simulation results, which show the dependence of the ionization process on the ionization laser intensity: (a) The ionized population and the ionization position distribution as a function of the longitudinal position at several different ionization laser intensities, indicated in the plots. (b) The ionization degree (corresponding to the left axis) and the FWHM and FW90 width of the ionization position distribution (corresponding to the right axis) as a function of the ionization laser intensity. Shown on the top axis is also the corresponding ionization rate. All simulations in this figure are done with $s=3000$ and ${\sigma }_e=3\mu \mathrm{m}$.

Figure 5

Simulation results, which show the dependence of the ionization process on the excitation laser intensity: (a) Ionized population and the ionization distribution as a function of the longitudinal position at several different maximum excitation laser saturation parameters, indicated in the plots. (b) The ionization degree (corresponding to the left axis) and the FWHM and FW90 width of the ionization position distribution (corresponding to the right axis) as a function of the excitation laser saturation parameter. Shown on the top axis is also the corresponding Rabi frequency. All simulations in this figure are done with $I_{\text{i}}={10}^{10}{\mathrm{W}/\mathrm{m}}^2$ and ${\sigma }_e=3\mu \mathrm{m}$.

Figure 6

Experimental data (markers) of the beam current plotted against the excitation laser beam maximum saturation parameter for several different maximum ionization laser beam intensities. The atomic beam is selected with an aperture with a diameter of $52\mu \mathrm{m}$. The lines represent simulation data under the same conditions as the measurement, which were fitted to the measurement. The fit resulted in a maximum incoming flux equivalent to 81 pA and a saturation intensity of $52{\mathrm{W}/\mathrm{m}}^2$. The ${\chi }^2$ value of the fit is 11.

Figure 7

Experimental data (markers) of the beam current plotted against the ionization laser beam maximum intensity for several different maximum excitation laser beam saturation parameters. The atomic beam is selected with an aperture with a diameter of $52\mu \mathrm{m}$. The lines represent simulation data under the same conditions as the measurement, which were performed using the saturation intensity found from the data plotted in Fig. 6 and is also scaled with the same maximum incoming flux equivalent is found from that data.

Figure 8

Transverse atom distribution just before ionization (solid curves) and transverse ion distribution just after ionization (dashed curves) as a function of $y$ (for orientation see Fig. 1) for two different aperture diameters (see legend) and in the situation that the aperture is positioned at $z=-30$ mm (top) and $z=-5$ mm (bottom). The distributions are normalized such that the integral results in the fraction of incoming atoms that is transmitted by the aperture or ionized.

Figure 9

Experimental data (markers) of the beam current plotted against the area of the aperture used to select the atomic beam. The data is taken at a Knudsen source temperature of 433 K, with $I_{\text{i}}=6\times {10}^9{\mathrm{W}/\mathrm{m}}^2$ and $s=6000$. The lines show simulation data under the same conditions as the measurement. The solid line shows the current equivalent of the atomic flux that is transmitted through the selection aperture. The dashed line shows the current that is actually created. A fit is performed to find the current equivalent of the (unselected) incoming flux that matches the calculation data best with the experimental data, which resulted in 1.4 nA.