Velocity selection of Rydberg positronium using a curved electrostatic guide

We report experiments in which a slow Rydberg positronium (Ps) beam was produced by velocity selection using a curved electrostatic quadrupole guide. Ps atoms in Rydberg-Stark states with principal quantum number $n=14$ were prepared by a two-color optical excitation process in a uniform electric field. Low-field-seeking Stark states were produced at the entrance of a 0.6-m-long quadrupole guide that includes a ${45}^{\circ }$ bend, and were detected at the end of the guide via their annihilation $\gamma$ radiation. The mean speed (kinetic energy) of atoms entering the guide was estimated to be $\approx 180$ km ${\mathrm{s}}^{-1}$ (185 meV), whereas the mean longitudinal speed of guided atoms was measured via time of flight and found to be $\approx 90$ km ${\mathrm{s}}^{-1}$, equivalent to a kinetic energy of 45 meV. The measured transport data are in broad agreement with Monte Carlo simulations, which are also used to establish the efficacy with which the arrangement we describe could be used to perform Ps-atom scattering measurements.

Figure 1

Stark structure at $n=14$ in Ps. Each Stark state, labeled with the index $k$ (see text for details), is displayed for fields in which the ionization rate is $<{10}^{10}{\mathrm{s}}^{-1}$. The thicker sections of each curve indicate the fields for which the ionization rate ranges from $\ge {10}^8$ to $\le {10}^{10}{\mathrm{s}}^{-1}$.

Figure 2

(a) Schematic representation of the experimental apparatus containing the curved guide. The positions of the five $\gamma$-ray detectors used in the experiment are indicated (see text for details). D1 and D2 are used to monitor Ps atoms in or near the excitation region via lifetime spectroscopy, whereas D3, D4, and D5 are used to generate single-event TOF spectra. (b) Close-up of the excitation region indicating the Ps formation target and excitation region and the position of the quadrupole guide rods relative to the grid electrode and (c) electric-field map within the guide with 5.5 kV applied to one pair of rods.

Figure 3

(a) Line shapes for the $2{}^{3}P_J\to 14{}^{3}S/14{}^{3}D$ transitions measured by D2 with and without a 333 V/cm electric field applied in the excitation region. The asymmetric line shape measured with the electric field applied is due to deflection of atoms towards or away from D2. The data have been normalized to the peak amplitude. (b) Total count rates for guided atoms as a function of the IR laser wavelength in the corresponding electric fields, measured by D4/5. The dashed vertical line represents the expected zero-field resonant wavelength, and the voltage applied to the guide was 5.5 kV.

Figure 4

TOF data measured using D3 and D4/5 for guide voltages of 0.5, 3.5, 4.5, and 5.5 kV, as indicated in the legend. Additional spectra (not shown) were recorded for guide voltages of 1.5, 2.5, and 5.0 kV and lfs Ps atoms with $n=14$. Each curve was acquired in 4 h.

Figure 5

Longitudinal velocity distributions as derived from TOF measurements obtained with no guide (triangles) [28], with a straight guide (squares) [52], and with the curved guide (circles). The electric potential applied to the guide rods is indicated in the legend. The curved-guide data are derived from the data shown in Fig. 4. TOF spectra were rebinned into 10 km ${\mathrm{s}}^{-1}$ steps to generate the velocity distributions.

Figure 6

Simulated trajectories for guide biases of (a) 0.5, (b) 2.5, (c) 4.5, and (d) 5.5 kV. The black lines represent atoms in the low-field-seeking state with $k=+12$, whereas the lighter red lines represent atoms in the high-field-seeking state with $k=12$. Also shown in each panel is an inset of the electric-field strength for each configuration and an outline of the chamber walls representing the ground plane of the electric field.

Figure 7

(a) Measured count rate and simulated guiding efficiency and (b) mean Ps velocities derived from the TOF data and simulations for different voltages applied to the quadrupole rods.

Figure 8

(a) Calculated cross section $\sigma$ for positron-atom bound-state formation in collisions of $n=14$ Ps atoms with Zn atoms and (b) simulated data indicating how the observed velocity distribution would be attenuated by Ps charge-exchange reactions with Zn at the indicated pressures. The measured TOF distribution has been rebinned into 5 km ${\mathrm{s}}^{-1}$ steps to generate the velocity distribution.