Lifetime spectra were produced from microwave quenching data similar to those shown in Fig. 4. For each spectrum the amplitudes of the smoothed peaks were evaluated at 100 ns intervals corresponding to the times at which the microwave radiation pulses were applied, taking into account a 70 ns delay between the application of the microwave pulse and the peak amplitude of the subsequent annihilation pulse. This delay is due to the ground state decay rate and the LYSO detector response. The amplitude data plotted for each time step are shown in Fig. 7 for each of the three detectors D1-3, along with a simple with an exponential fit, which yielded lifetimes on the order of 200 ns. It should be pointed out that there is no reason to expect the collision (and hence decay) rate to be exponential, and thus the quoted lifetimes, which are derived from exponential fits, should be considered estimates at best. Nevertheless, it is clear that the \(2\,^{3}\mathrm {S}_{1}\) lifetimes are considerably shorter than the expected 1070 ns.
In principle the Ps atoms could travel the entire length of the waveguide before being quenched. Ps atoms emitted from SiO2 targets are expected to mean longitudinal speeds of order 107 cm/s [38], meaning that it would take around 1.6 μs to leave the guide (not taking into account the effects of scattering from random nanocrystal surface orientations, which can only increase the transit times). As atoms travel further from the source, the detection efficiency for detectors D1 and D2 would decrease, owing to the decreasing solid angle subtended; this would make the apparent lifetime shorter. However, D3 was located in a position that would be less sensitive to this effect. Moreover, the D3 geometrical detection efficiency would initially increase until atoms reached half way along the waveguide. Although the lifetimes obtained from the data shown in Fig. 7 are not expected to be very accurate, the fact that they are all essentially the same indicates that Ps atoms do not annihilate over a large volume, so that while D1 and D2 may have a different effective solid angle coverage to that of D3, there does not appear to be a strong time dependence, which is consistent with a short Ps lifetime.
Ps atoms in pure \(2\,^{3}\mathrm {S}_{1}\) states entered the microwave guide as shown in Fig. 1. The laser excitation process means that Ps atoms have a relatively narrow velocity spread in the x direction as a result of the 100 GHz laser bandwidth. However the velocity distribution in the y direction is much broader (FWHM ≈ 500 GHz) [39], meaning that a large fraction of Ps atoms can be expected to collide with the internal waveguide surfaces. After such collisions the Ps atoms may reflect from the nano crystals with randomized trajectories, in accordance with the random cube orientations (see Fig. 6). This means that Ps atoms may be reflected back into the wavegude immediately, or after multiple scattering events in the inner structure of the MgO layer.
The short observed lifetime of \(2\,^{3}\mathrm {S}_{1}\) atoms indicates that Ps atoms do not survive collisions with MgO nanocrystals. Excited state Ps atoms created in MgO samples have been studied in previous experiments [40]. In that work Ps atoms were generated and excited inside MgO powder samples and were then able to travel into vacuum after scattering from the internal MgO crystal surfaces. However, \(2\,^{3}\mathrm {S}_{1}\) states were not measured as the single-photon production method used here [33] is not compatible with the formation of atoms in the MgO powder. Atoms excited to \(2\,^{3}\mathrm {P}_{J}\) states and to Rydberg states with principal quantum numbers n ranging from 10–17 were studied; It was found that the \(1\,^{3}\mathrm {S}_{1}\) ground state and the \(2\,^{3}\mathrm {P}_{J}\) energy levels were shifted, but that Rydberg levels were not [40]. Since Rydberg atoms are extremely sensitive to electric fields [41] we can conclude from this that MgO does not support electric fields strong enough to quench \(2\,^{3}\mathrm {S}_{1}\) atoms. Even if the field were localized to the surface region, Rydberg atoms excited with low positron beam implantation energy would sample the near surface region, and would therefore be sensitive to these fields. No such level shifts were observed for Rydberg states, however, and it does not appear that the short lifetime observed in this work was caused by electric fields.
It is possible that interactions with surfaces lead to decay via pick-off annnihilation, which is the process wherein the positron in a Ps atom annihilates with an external electron in the surrounding medium rather than by self-annihilation [42]. Gidley and co-workers have previously used MgO lined cavities to contain ground state Ps atoms for precision decay rate measurements [43]. The rationale for this approach was that Ps-MgO interactions would lead to only a small increase in the annihilation rate, based on earlier measurements of long-lived Ps in several insulating materials [44]. It was found, however, that high-precision measurements were still sensitive to Ps-MgO interactions, which therefore had to be taken into account before agreement with QED theory was obtained [8, 9]. Nevertheless, the effect of MgO interactions was shown to be relatively small, and was only noticed because of the high precision of the measurements (of order ppm).
If the pick-off process is responsible for the present observed lifetimes, it would imply that \(2\,^{3}\mathrm {S}_{1}\) atoms are orders of magnitude more sensitive to interactions with MgO surfaces than \(1\,^{3}\mathrm {S}_{1}\) atoms. However, it is not clear why Rydberg atoms would not also be susceptible to the same decay mechanisms, and in fact one would expect them to be even more sensitive than \(2\,^{3}\mathrm {S}_{1}\) atoms, given that the electron and positron are less strongly bound. However, Rydberg atoms generated in MgO powder were able to leave without significant losses [40], and it therefore does not seem likely that an enhanced pick-off rate is responsible for the present observations.
It is known from Ps beam experiments [45] that when Ps atoms scatter from atoms and molecules they become polarized during the collision [46, 47]. This means that the pure \(2\,^{3}\mathrm {S}_{1}\) states may acquire some P character, facilitating faster (radiative) decay [31]. However, for a direct scattering process one would expect the interaction time to be much less than the 3.2 ns \(2\,^{3}\mathrm {P}_{J}\) lifetime, and so for adiabatic interactions this mechanism would not significantly change the decay rate unless the scattering rates were correspondingly high. The MgO structure (see Fig. 6) contains large open volumes, which is why the ground state Ps lifetime in bulk MgO samples is close to the vacuum lifetime [44]. In previous measurements ground state Ps atoms were observed to travel through ≈ 30 μm thick layers of MgO [36] without measurable time delays or losses compared to passing through a few hundred nm of the same sample. These data suggest that the large open areas in MgO samples allow Ps atoms to pass through with only a small number of collisions. Thus, we would not expect a small increase in the decay rate due to impulse polarization to be enhanced by a large number of collisions, and thence lead to the short observed \(2\,^{3}\mathrm {S}_{1}\) lifetimes.
The previously observed energy shifts indicated that resonant interactions between Ps atoms and MgO surfaces can be mediated via photo-luminescent MgO absorption bands [40]. The associated energy shifts were observed for atoms that were mostly not in a near surface region, which was taken to be evidence for a strong coupling with multiple MgO absorbers, giving rise to a much stronger interaction. It is therefore possible that when \(2\,^{3}\mathrm {S}_{1}\) atoms scatter from MgO nanocrystal surfaces they become polarized, and are then able to interact via this same mechanism. The increased strength of this interaction compared to a simple scattering process could then lead to a non-adiabatic process that transfers population to the \(2\,^{3}\mathrm {P}_{J}\) levels, with a concomitant reduction in the observed lifetime. Further studies are required to determine if this is in fact the mechanism responsible for our observations, including testing other insulating surface materials.
An insulating cavity has been used to physically confine excited state atoms in recent measurements of \(1\,^{3}\mathrm {S}_{1}\rightarrow 2\,^{3}\mathrm {S}_{1}\) transitions [48]. In this case a relatively small (≈ 3 mm path length) silica lined cavity was used to confine Ps atoms, and allow them to make multiple passes through a narrow laser beam (0.37 mm waist) so as to increase the total interaction time. The production of \(2\,^{3}\mathrm {S}_{1}\) atoms was observed using a lifetime method sensitive to decay events in a time window of 2-4 μs after the positron implantation, which implies that the \(2\,^{3}\mathrm {S}_{1}\) lifetime was not as short as in the present measurement, although it was not possible to determine the actual lifetime from the data presented in [48]. Nevertheless, these data could mean that interactions of \(2\,^{3}\mathrm {S}_{1}\) Ps atoms with MgO and silica are different. This could be the case if the energy shifting interaction observed for MgO [40] is not present in amorphous silica. We note also that spatial confinement of muonium atoms using silica cavities has been demonstrated [49].