All atomic systems, including positronium (Ps) can be excited to states with high principal quantum number n using lasers, these are called Rydberg states. Atoms in such states exhibit interesting features that can be exploited in a variety of ways. For example, Rydberg states have very long radiative lifetimes (on the order of 10 µs for our experiments). This is a particularly useful feature in Ps because when it is excited to large-n states, the overlap between the electron and positron wavefunction is suppressed. Therefore the self-annihilation lifetime becomes so large in comparison to the fluorescence lifetime, that the effective lifetime of Ps in a Rydberg state becomes the radiative lifetime of the Rydberg state. Most Rydberg Ps atom will decay back to the ground state first, before self-annihilating [Phys. Rev. A 93, 062513 (2016)]. The large distance between the positron and electron centers of charge in certain Rydberg states also means that they exhibit large static electric dipole moments, and thus their motion can be manipulated by applying forces with inhomogeneous electric fields [Phys. Rev. Lett. 117, 073202 (2016), Phys. Rev. A 95, 053409 (2017)]
In addition to these properties, Rydberg atoms have high tunnel ionization rates at relatively low electric fields. This property forms the basis for state-selective detection by electric field ionization. In a recent series of experiments, we have demonstrated state-selective field ionization of positronium atoms in Rydberg states (n = 18- 25) in both static and time-varying (pulsed) electric fields.
The set-up for this experiment is shown below where the target (T) holds a SiO2 film that produces Ps when positrons are implanted onto it. The first grid (G1) allows us to control the electric field in the laser excitation region, and a second Grid (G2) with a varying voltage provides a well defined ionization region. An electric field is applied by either applying a constant voltage to Grid 2 as in the case of the static field configuration, or by ramping a potential on Grid 2 as in the case of the pulsed field configuration.
Figure 1: Experimental arrangement showing separated laser excitation and field ionization regions.
In this experiment we detect the annihilation gamma rays from:
the direct annihilation of positronium
annihilations that occur when positronium crashes into the grids and chamber walls
annihilations that occur after the positron, released via the tunnel ionization process, crashes into the grids or chamber walls
We subtract the time-dependent gamma ray signal when ground state Ps traverses the apparatus from the signal detected from Rydberg atoms when an electric field is applied in the ionizing region. This forms a background subtracted signal that tells us where in time there is an excess or lack of annihilation radiation occurring when compared to background (this SSPALS method is described further in NIM. A 828, 163 (2016) and and here).
Static Electric Field Configuration
In this version of the experiment, we let the excited positronium atoms fly into the ionization region where they experience a constant electric field. In the case where a small electric field (~ 0 kV/cm) is applied in the ionizing region, the excited atoms fly unimpeded through the chamber as shown in the animation below. Consequently, the background subtracted spectrum is identical to what we expect for a typical Rydberg signal (see the Figure below for n=20). There is a lack of ionization events early on (between 0 and 160 ns) compared to the background (ground state) signal that manifests itself as a sharp negative peak. This is because the lifetime of Rydberg Ps is orders of magnitude larger than the ground state lifetime.
Later on at ~ 200 ns, we observe a bump that arises from an excess of Rydberg atoms crashing into Grid 2. Finally, we see a long positive tail due to long-lived Rydberg atoms crashing into the chamber walls.
Figure 2: Trajectory simulation of Rydberg Ps atoms travelling through the ~0 V/cm electric field region (left panel) and measured background-subtracted gamma-ray flux , the shaded region indicates the average time during which Ps atoms travel from he Target to Grid 2 (right panel).
On the other hand, when the applied electric field is large enough, all atoms are quickly ionized as they enter the ionizing region. Correspondingly, the ionization signal in this case is large and positive early on (again between 0 and 160 ns). Furthermore, instead of a long positive tail, we now have a long negative tail due to the lack of annihilations later in the experiment (since most, if not all, atoms have already been ionized). Importantly, since in this case field ionization occurs almost instantaneously as the atoms enter the ionization region, the shape of the initial ionization peak is a function of the velocity distribution of the atoms in the direction of propagation of the beam.
Figure 3: Trajectory simulation of Rydberg Ps atoms travelling through the ~2.6 kV/cm electric field region (left panel) and measured background-subtracted gamma-ray flux , the shaded region indicates the average time during which Ps atoms travel from he Target to Grid 2 (right panel).
We measure these annihilation signal profiles over a range of fields and calculate the signal parameter Sᵧ. A positive value of Sᵧ implies that there is an excess of ionization occurring within the ionization region; whereas, a negative Sᵧ means that there is a lack of ionization within the region with respect to background. Therefore, if Sᵧ is approximately equal to 0%, only half of the Ps atoms re being ionized. A plot of the experimental Sᵧ parameter for different applied fields and for different n’s is shown in the plot below.Figure 4: Electric field scans for a range of n states ranging from 18 to 25 showing that at low electric fields none of the states ionize (thus the negative values of Sᵧ) and as the electric field is increased, different n states can be observed to have varying ionizing electric field thresholds.
It is clear that different n-states can be distinguished using these characteristic Sᵧ curves. However, the main drawback in this method is that both the background subtracted profiles and the Sᵧ curves are convoluted with the velocity profile of the beam of Rydberg Ps atoms. This drawback can be eliminated by performing pulsed field ionization.
Pulsed Electric Field Configuration
We have also demonstrated the possibility of distinguishing different Rydberg states of positronium by ionization in a ramped electric field. The set-up is the same as in the static field scenario but now instead of fixing a potential on Grid 2, the potential on this grid is decreased from 3 kV to 0 kV hence increasing the field from 0 kV/cm to ~ 1800 kV/cm (the initial 3kV is necessary to help cool down Ps [New J. Phys. 17,043059 (2015)]).
The advantage of performing state selective field ionization this way is that we can allow most of the atoms to enter the ionization region before pulsing the field. This eliminates the dependence of the signal on the velocity distribution of the atoms and thus the signal is only dependent on the ionization rates of that Rydberg state in the increasing electric field.
Below is a plot of our results with a comparison to simulations (dashed lines). We see broad agreement between simulation and experiment and, we are able to distinguish between different Rydberg states depending on where in time the ionization peak occurs. This means that we should be able to detect a change in an initially prepared Rydberg population due to some process such as microwave induced transitions.
Figure 5: Pulsed-field ionization signal as a function of electric field for a range of n states.
The development of state selective ionization techniques for Rydberg Ps opens the door to measuring the effect of blackbody transitions on an initially prepared Rydberg population and a methodology for detecting transitions between nearby Rydberg-levels in Ps. Which could also be used for electric field cancellation methods to generate circular Rydberg states of Ps.