## Rydberg Positronium-electron scattering

In our last experiment, we showed how a curved quadrupole guide can be used to transport Rydberg Positronium (Ps*) around a 45 degree bend (blue path in picture below) into a region away from the positron beam line (yellow path below), which can then be implemented into a scattering region (PRA 95 053409). In addition, this new off-axis setup eliminated detection difficulties that were encountered in our previous straight guide experiments.

The scattering chamber setup is shown in the right hand side picture below. Guided Ps* atoms emerging from the end of the quadrupole are introduced into a scattering region where they collide with electrons that are thermoinically ejected (orange path) from a Molybdenum filament . This region is surrounded by gamma-ray detectors coupled to photomultiplier tubes (PMT) which record annihilation events inside the chamber. However, these PMTs in themselves are not sufficient to conclude what kind of interaction has taken place, we can only conclude that a Ps atom annihilated if an event is detected, but not if there were intermediate steps (such as charge exchange between the free electrons and the valence electron) before annihilation. To overcome this, we used a micro-channel plate (MCP) which has the benefit of being able to detect only certain charged particles (i.e. differentiating between electrons and positrons) depending on the electric fields applied in the detection region.

When the Ps*collides with free electrons a few different things can happen; the electron could break up the Ps* into electron and positron (ionisation: $e^{-} + Ps^{*} \rightarrow e^{-} + e^{+} + e^{-}$ ) or, the positron from the Ps* will be stolen away by the incoming free electron, resulting in a new short lived Ps which annihilates before hitting the MCP, thus giving a diminished signal (charge exchange: $e^{-} + Ps^{*} \rightarrow Ps + e^{-}$). Additionally, Positronium and an electron can form a negative Ps ion (Ps¯ ), which is the bound state of a Ps atom and an orbiting electron, this ions have been shown to be quite unstable, having a lifetime of <1ns.

Above you can see some experimental Time of Flight (TOF) data showing the possibility of having detected a charge exchange process. The blue curve on the left panel is a TOF signal of guided Positronium atoms after hitting the MCP detector. The Ps* atoms have a mean flight time of around 10$\mu$s. When we let the electron beam into the scattering region  we observe a suppression of the TOF spectra (green curve), this is due to the electric fields in front of the MCP detector, which should only allow positrons to be detected. The PMT signal for both cases (shown in the right panel) are the same indicating that this drop in MCP signal is in fact electron related, not as a result of less Positronium being guided. All that remains to do now is to determine the nature of this signal but nonetheless, it’s intriguing how readily Ps* interacts with electrons (maybe other particles too), especially when considering that a direct method of producing anti-Hydrogen is via charge exchange collisions between Ps* and antiproton ( $Ps^{*} + \overline{p} \rightarrow \overline{H}+ e^{-}$ ).

## Optimizing Positronium Rydberg manipulation

In recent experiments we showed how we successfully manipulated the trajectories of Rydberg Positronium atoms using electric field inside a curved quadrupole guide, which allows us to perform velocity selection on the Positronium atoms that enter the quadrupole field.

These curved guide experiments were performed by exciting Positronium to n = 14, which is a state that has a relatively low mean lifetime of ~8 $\mu$s, which is comparable to the flight time of our experiment, meaning that many of the n = 14 atoms undergo radiative decay before they can be detected. However, when judging what the most efficient n for guiding is, we need to have into consideration a few other factors. The lifetime of different n states goes up as $n^3$, but the field-ionisation rate goes up as ~$n^{-4}$, and the dipole moment as $n^2$. Combining all of these factors and implementing them into trajectory-simulations based on the electric fields generated by the curved guide, we were able to determine that the most efficient n for curved guiding is n = 14, as it can be seen from the graph below.

These simulations agree with our data and were instrumental in determining the optimum parameters of the experiment.

We are currently working on implementing this off-axis curved guide into a scattering experiment using helium ions, below you can see at the bottom of the image the new scattering chamber that has been coupled to the Positronium Rydberg beam.

## Rydberg Ps electrostatically guided in curved quadrupole

The latest efforts of our research at UCL have been focused on manipulating Positronium (Ps) atoms in highly-excited principal quantum number n states (Rydberg states) [PRL. 114, 173001]. In one of our latest works we showed how we can exploit the large electric dipole moment of low-field-seeking Rydberg states (those states which have positive Stark shift) to confine them in a quadrupole “guide” [PRL 117, 073202].

As a direct follow-up to that study, we devised a modified version of a quadrupole guide with a 45° bend that would allow us to perform velocity selection on the atoms being guided by tuning the efficiency with which the Rydberg Ps atoms are transmitted through the bend, in addition, in our previous set-up we experienced technical difficulties since the detection scheme was in-line with our positron beam, so having a curved guide would also be beneficial for that reason.

The schematic figure above depicts our current experimental setup, which we have used to guide Rydber Ps atoms around a 45° bend into a region off-axis with our positron beam. We have not yet implemented velocity selection, but we have clear evidence that we can efficiently guide Ps atoms in this configuration.

The left panel in the figure above shows the time of flight (TOF) distribution of n = 14 atoms excited to high-field seeking states (as measured by the detectors at the end of the curved guide, i.e. “LYSO C” and “NaI”), and a background wavelength with is off-resonant with any transition, essentially acting like a “laser on” and “laser off” measurement. The right panel shows the background-subtracted trigger rate for this measurement (“laser on” – “laser off”), which shows clear evidence of atoms with a TOF arrival time of ~8 $\mu \mathrm{s}$.

In addition to this being a stepping stone to demonstrate velocity selection due to the acceptance of the curved section of the guide, we may also improve this set-up into eventually developing a ring-like stark decelerator, and other Ps atom optics.

## Production and time-of-flight measurements of high Rydberg states of Positronium

One of our recent studies focused on measuring the lifetimes of Rydberg states of Positronium (Ps) [PRA. 93, 062513]. However, some of the limitations that prevented us from measuring lifetimes of states with higher principal quantum number (n), is the fact that such states can be easily ionised by the electric fields generated by the electrodes in our laser-excitation region (these electrodes are normally required to achieve an excitation electric field of nominally ~ 0 V/cm).

We have recently implemented a simple scheme to overcome this complication, whereby we make use of a high-voltage switch to turn discharge the electrodes in the interaction region after the laser excitation has taken place.

The figure shown above show the Background-subtracted spectra (the SSPALS detector trace is recorded with a background and resonant wavelength, they are then normalised and subtracted from each other) for n = 18 and n = 19. It is clear from the “Switch Off” that when the high voltage switched is not utilised (and the voltages to all electrodes are always on), that most of the annihilations happen at early times, especially around ~100ns, this is the time it takes for the atoms to travel out of the low-field region, and become field-ionised by the DC voltage on the electrodes.

On the other hand, the “Switch On” curves show that both n = 18 and 19 have many more delayed events (after ~ 400 ns) due to Rydberg Ps being able to travel for much longer distances before annihilating when the switch is used to discharge the electrode biases.

The figure above shows  data taken by a detector set up for single-gamma-ray detection, approximately 12 cm away from the Ps production target, on the same experiment as described for the previous figure. It is clear from this data that the time-of-flight (TOF) to this detector is ~2 $\mu \mathrm{s}$ However, in this case it is clear that only the n = 19 state benefited from having the “switch on”, indicating that is the smallest-n state that this scheme is necessary for our current electric-field configuration.

Comparing the SSPALS and TOF figures it can be seen that even though the n = 18 SSPALS signal was changed drastically, the n = 18 TOF distribution remained the same, this is a clear example of how changes in the SSPALS spectrum discussed in the first figure are indicative of changes in atom distributions close to the Ps production region, but are not necessarily correlated to TOF distributions measured at different positions across the Ps flight paths

These methods will eventually lead to more accurate measurement of the lifetimes of higher n-states of Ps, and the possibility of using those states with higher electric dipole moments for future atom-optics experiments, such as Ps electrostatic lenses and Stark decelerators.

## Efficient production of n = 2 Positronium in S states

We routinely excite Positronium (Ps) into its first excited state (n = 2) via 1-photon resonant excitation [NJP. 17 043059], and even though most of the time this is an intermediate step for subsequent excitation to Rydberg (high n) states [PRL. 114, 173001], there is plenty of interesting physics to be explored in n = 2 alone, as we discussed in one of our recent studies [PRL. 115, 183401 and  PRA. 93, 012506].

In this study we showed that the polarisation of the excitation laser, as well as the electric field that the atoms are subjected to, have a drastic effect on the effective lifetime of the excited states and when Ps annihilates.

Above you can see the data for two laser polarisations, showing the Signal parameter S(%) as a function of electric field, this is essentially a measure of how likely Ps is to annihilate compared to ground-state (n = 1) Ps, that is to say, if S(%) is positive then n = 2 Ps in such configuration annihilates with shorter lifetimes than n = 1 Ps (142 ns), whereas if S(%) is negative then n = 2 Ps will annihilate with longer lifetimes than 142 ns, These longer lifetimes are present in the parallel polarisation (pannel a).

Using this polarisation, and applying a large negative or positive electric field (around 3 kV/cm), provides such long lifetimes due to the excited state containing a significant amount of triplet S character (2S), a substate of = 2 with spin = 1 and $\ell$= 0. If the Ps atoms are then allowed to travel (adiabatically) to a region of zero nominal electric field (our experimental set-up [RSI. 86, 103101] guarantees such transport), then they will be made up almost entirely of this long-lived triplet S character, and will thus annihilate at much later times than the background n = 1 atoms. These delayed annihilations can be easily detected by simply looking at the gamma-ray spectrum recorded by our LYSO detectors [NIMA. 828, 163] when the laser is on resonance (“Signal”), and subtracting it from the spectrum when the laser is off resonance (“Background”).

The figure above shows such spectra taken with the parallel laser polarisation, at a field where there should be minimal 2S Production (a), and a field where triplet S character is maximised (b).   It is obvious that on the second case, there are far more annihilations at later times, indicated by the positive values of the data on times up to 800 ns. This is clear evidence that we have efficiently produced = 2 triplet S states of Ps using single-photon excitation. Previous studies of 2S Ps produced such states either by collisional methods [PRL34, 1541], which is much more inefficient than single-photon excitation,  or by two-photon excitation, which is also more inefficient, requires much more laser power and is limited by photo-ionisation [PRL. 52, 1689].

This observation is the initial step before we begin a new set of experiments where we  will attempt to measure the = 2 hyperfine structure of Ps using microwaves!

## P.A.M. Dirac

Yesterday marked the 114th anniversary of the birth of Paul Adrien Maurice Dirac, one of the world’s greatest ever theoretical physicists. Born on the 8th of August 1902 in Bristol (UK), Dirac studied for his PhD at St. John’s college Cambridge University, where he would subsequently discover the equation that now bears his name,

iγ·∂ψ =  mψ .

The Dirac equation is a solution to the problem of describing an electron in a way that is consistent with both quantum mechanics and Einstein’s theory of relativity. His solution was unique in its natural inclusion of the electron “spin”, which had to otherwise be invoked to account for fine structure in atomic spectra. His brilliant contemporary, Wolfgang Pauli, described Dirac’s thinking as acrobatic. And several of Dirac’s theories are regarded as among the most beautiful and elegant of modern physics.

An important prediction of the Dirac equation is the existence of the anti-electron (also known as the  positron). This particle is equal in mass to the more familiar electron, but has the opposite electric charge. Dirac published his theory of the anti-electron in 1931 – two years before “the positive electron” was discovered by Carl Anderson. Dirac accurately mused that the anti-proton might also exist, and most physicists now believe that all particles posses an antimatter counterpart. But antimatter is apparently – and as yet inexplicably – much scarcer than matter.

In 1933 Dirac shared the Nobel prize in physics with Erwin Schrödinger “for the discovery of new productive forms of atomic theory”. Dirac died aged 82 in 1984. He’s commemorated in Westminster Abbey by an inscription in the Nave, not far from Newton’s monument. Separated in life by more than two centuries, Paul Dirac and Sir Isaac Newton are arguably the fathers of antimatter and gravity.

The Strangest Man by Graham Farmelo is a fascinating account of Dirac’s life and work.

## A guide to positronium

Positronium (Ps) is a hybrid of matter and antimatter. Made of just two particles – an electron and a positron – the atomic structure of Ps is similar to hydrogen. The ultimate aim of our experiments at UCL is to observe deflection of a Ps beam due to gravity, as nobody knows if antimatter falls up or down.

In this post, we outline how we recently managed to guide positronium using a quadrupole. Because the Ps atom doesn’t have a heavy nucleus, it’s extremely light and will typically move very, very quickly (~100 km/s). A refinement of the guiding techniques we used can, in principle, be applied to decelerate Ps atoms to speeds that are more suitable for studying gravity.

Before guiding positronium we have to create some. Positrons emitted from a radioisotope of sodium are trapped in a combination of electric and magnetic fields. They are ejected from the trap and implanted into a thin-film of mesoporous silica, where they bind to electrons to form Ps atoms; the network of tiny pores provides a way for these to get out and into vacuum.

The entire Ps distribution is emitted from the film in a time-window of just a few billionths of a second.  This is well matched to our pulsed lasers, which we use to optically excite the atoms to Rydberg levels (high principal quantum number, n). If we didn’t excite the Ps then the electron-positron pairs would annihilate into gamma-ray photons in much less than a millionth of a second, and each would be unlikely to travel more than a few cm. However, in the excited states self-annihilation is almost completely suppressed and they can, therefore, travel much further.

Each Rydberg level contains many sublevels that have almost the same internal energy. This means that for a given n its sublevels can all be populated using a narrow range of laser wavelengths. But if an electric field is applied the sublevels are shifted. This so-called “Stark shift” comes from the electric dipole moment, i.e., the distribution of electric charge within the atom. The dipole is different for each sublevel and it can either be aligned or anti-aligned to the electric field. This results in a range of both positive and negative energy shifts, broadening the overall spectral line. Tuning the laser wavelength can now be used to select a particular sublevel. Or rather, to select a Rydberg-Stark state with a particular electric dipole moment. Stark broadening is demonstrated in the plot below. [For higher electric fields the individual Stark states can be resolved.]

The Stark effect provides a way to manipulate the motion of neutral atoms using electric fields. As an atom moves between regions of different electric field strength its internal energy will shift according to its electric dipole moment. However, because the total energy must be conserved the kinetic energy will also change. Depending on whether the atom experiences a positive or negative Stark shift, increasing fields will either slow it down or speed it up. The Rydberg-Stark states can ,therefore, be broadly grouped as either low-field-seeking (LFS) or high-field-seeking (HFS). The force exerted by the electric field is much smaller than would be experienced by a charged particle. Nevertheless, this effect has been demonstrated as a useful tool for deflecting, guiding, decelerating, and trapping Rydberg atoms and polar molecules.

A quadrupole is a device made from a square array of parallel rods.  Positive voltage is applied to one diagonal pair and negative to the other. This creates an electric field that is zero along the centre but which is very large directly between neighbouring rods. The effect this has on atoms in LFS states is that when they drift away from the middle into the high fields they slow down, and eventually turn around and head back towards the centre, i.e., they are guided. On the other hand, atoms in HFS states are steered away from the low-field region and out to the side of the quadrupole.

Using gamma-ray detectors at either end of a 40 cm long quadrupole we measured how many Rydberg Ps atoms entered and how many were transported through it. With the guide switched off some atoms from all states were transmitted. However, with the voltages switched on there was a five-fold increase in the number of low-field-seeking atoms getting through, whereas the high-field-seeking atoms could no longer pass at all.

A large part of why we chose to use positronium for our gravity studies is that it’s electrically neutral. As the electromagnetic force is so much stronger than gravity we, therefore, avoid otherwise overwhelming effects from stray electric fields. However, by exciting Ps to Rydberg-Stark states with large electric dipole moments we reintroduce the same problem. Nonetheless, it should be possible to exploit the LFS states to decelerate the atoms to low speeds, and then we can use microwaves to drive them to states with zero dipole moment. This will give us a cold Rydberg Ps distribution that is insensitive to electric fields and which can be used for gravitational deflection measurements.

Our article “Electrostatically guided Rydberg positronium” has been published in Physical Review Letters.