## Controlling Positronium Annihilation with Electric Fields

To produce Rydberg (highly-excited) states of positronium we use a multi-photon $1 ^3S \rightarrow 2 ^3P \rightarrow nS/nD$ excitation scheme [1].  These high-$n$ Ps atoms are long-lived and could potentially be used for (anti)-gravity measurements, however, the intermediate state ($n=2$) has interesting properties of it’s own, as described in our latest article (Phys. Rev. Lett. 115, 183401).

Unlike regular atoms, Ps has the peculiar feature that it can self-annihilate into gamma-rays.  The amount of overlap between the positron and electron wave functions depends on the particular state the atom is in, and this determines how long before self-annihilation occurs (characterised by the average annihilation lifetime).  The quantum spin ($s=1/2$) of the electron and positron can combine in positronium to either cancel  ($S=0$) or sum ($S=1$), depending on the relative alignment between the two components.  In the former case (para-Ps) the atom has a very short ground-state lifetime of just 125 ps, whereas in the latter case (ortho-Ps) the atom lives in the $n=1$ state for an average of 142 ns (this may not sound very long but it’s actually plenty of time to do spectroscopy with pulsed lasers).

We produce $n=1$ ortho-Ps ($1^3S_1$) atoms then excite these using 243 nm laser light from our UV laser. The electronic dipole transition selection rules (principally, $\Delta S= 0$ and $\Delta \ell = \pm 1$) dictate that this single-photon transition drives the atoms to the $n = 2$, $\ell= 1$$S= 1$ state ($2 ^3P_J$).  For historical reasons the orbital angular momentum is written here as $S$ ($\ell= 0$) and $P$ ($\ell= 1$).

The fluorescence lifetime of an excited atom is the time it takes, on average, to spontaneously emit a photon and decay to a lower energy state. All of the $n=2, \ell = 1$ states have a fluorescence lifetime of 3.19 ns, and an annihilation lifetime of over 100 $\mu$s (practically infinite compared to the time-scale of our measurements, i.e., $2^3P$ states don’t annihilate directly, but can decay to a different state then annihilate). The $n=2, \ell = 0$ ortho and para states have annihilation lifetimes of 1136 ns and 1 ns, and they both fluoresce with a lifetime of $\simeq$ 0.24 s ($\approx \infty$).  The bottom line here is that there are a wide range of fluorescence and annihilation lifetimes for the various possible sub-states in the $n=1$ and $n=2$ manifolds.

In a magnetic field the short-lived $S=0$ and longer-lived $S=1$ states (with the same $\ell$) are mixed together (Zeeeman mixing).  Similarly, an electric field mixes states with different $\ell$ (but the same $S$) (Stark mixing).  By exciting Ps to $n = 2$ in a weak magnetic field then varying an electric field, we can tailor the extent of this mixing to increase or decrease the overall lifetime. This technique can be used to greatly increase the excitation efficiency to another state, since the losses due to annihilation can be reduced.  Conversely, increasing the annihilation rate can be used as an efficient way to detect excitation.

The polarization orientation of the UV  excitation laser gives us some control over which $M_J$ states are subsequently populated. More specifically, if the laser polarization is parallel to the applied magnetic field then only $\Delta M_J=0$ transitions are allowed, whereas if the polarization is perpendicular to it then  $\Delta M_J$ must change by $\pm 1$.

Below is a calculation of how the $n=2$ energy levels are shifted by an electric field, in zero magnetic field (red) and in a magnetic field of 13 mT (blue). Note the avoided crossing at 585 V/ cm in the 13 mT case.
So what can we actually measure? In most cases, laser excitation makes it more likely for ground state ortho-Ps to ultimately end up in the short-lived para-Ps state, thus applying the laser causes an increase in the annihilation gamma ray flux at early times. This change can be observed and quantified using the parameter $S$ (higher values means more gamma rays were detected compared to a measurement made without the laser). This is plotted below for various electric field strengths, and with the laser polarised either parallel (red) or perpendicular (green) to the magnetic field.  In both cases, the avoided crossing gives a sharp increase in annihilation rate (see the “ears” in both plots), whilst higher electric fields either reduce or increase the signal, depending on which $M_J$ states the laser initially populates.

Notice that when the laser polarisation is aligned parallel to the magnetic field (red), very high electric fields lead to negative $S$ values. This means that the lifetime of the Ps becomes longer than 142 ns (the ground-state ortho-Ps lifetime) if the laser is applied. This is due to the fact that in this field configuration there is significant mixing into the long lived $2^3S_1$ state.  This could be used to produce an ensemble of pure $2^3S_1$ states, by exciting Ps in this high field and then extracting the excited state into a region of zero field. These pure states could be exploited for $n=2$ microwave spectroscopy [3].

## High Temperature Coldhead for Positronium Photoemission

We have installed a new coldhead in our beamline with a high temperature heater, this will allow us to heat up samples up to 1000 K and cool them down to 10 K. The aim of this new addition to our system is to test Positronium emission from targets by implanting a positron pulse just after irradiating the sample with a high power laser. This has been done before with silicon samples [1]. In these previous studies samples of silicon were heated to similar temperatures and a green (532 nm) pulsed laser was fired at the samples before implanting bunched positron pulses, it was shown that heating the target increased the positronium yield, and likewise, increasing the laser power also enhanced the amount of positronium produced. It was also observed that the temperature of the target and the power of the laser pulse do not affect the energy of the produced positronium, only the yield. We plan to use this coldhead to repeat these measurements on germanium targets. Positronium produced out of these semiconductor targets has a very large emission energy, approximately 0.16 eV, compared to the 50 meV we can attain with porous silica. However, we can also cool these samples down to 10 K, potentially making efficient positronium emission at cryogenic temperatures more feasible if the same positronium photoemission mechanism is reproducible. This would be very useful for experiments in which antihydrogen will be produced at very low temperatures after interacting with positronium and trapped antiprotons [2].

## What happens to a silica film at cryogenic temperatures?

Since we are interested in making positronium atoms we are always looking to shoot positron beams at various materials, and under different conditions. In some cases we might need our Ps atoms to be made in a cold environment, so they can be excited to Rydberg states without being harassed by black body radiation. One of the best positronium formation targets we have used are porous silica films, which we get from collaborators in Paris (Laszlo Liskay and co-workers from CEA Saclay) [1]. Because of the way these materials make Ps they are not very sensitive to the temperature, so it should be possible to cool them down without changing the amount or character of Ps produced after a positron beam is implanted. This has already been seen at around 50 K [2] but we decided to have a look for ourselves at a slightly lower temperature (12K) to see if the impact of the positron beam might cause some damage at these temperatures (it can happen [3]).

With a cold head installed in our new positronium interaction chamber, we have cooled one of Lazslo’s silica films [1] to 12 Kelvin (~261˚C) which is about 100˚C colder than the dark side of the moon. It turns out that our positron beam didn’t do any damage at all and the sample was basically fine, so just for fun we decided to blast it with a laser beam (UV light, at 243 nm).

When you cool something down any gas in the region will tend to freeze on it. In ultra-high vacuum there isn’t that much gas around, but there is always a bit (known as residual gas, for obvious reasons) and after a while we do observe some fairly minor effects from all this freezing gas. Fortunately this takes a long time, and the sample is still useable for a week or so, and if you warm it up it will be restored to its original condition (since the frozen gas just evaporates away from the target). Once you start shooting the silica with a laser, however, things are not so stable, as shown in the figure. We observe a drastic reduction in the positronium formation efficiency after the silica is irradiated at low temperature (nothing happens at room temperature).

The delayed fraction f (black data points) measured for different sample temperatures (solid red lines), with the UV laser fired during the times indicated. Since f measures the amount of long-lived Ps present (it is more or less proportional to the fraction of incident positrons that form positronium) the sharp drop indicates that either less Ps is being created, or that it is being destroyed shortly after creation. The latter process is consistent with the experiment of Saito et al. Note that there is no effect from the laser at room temperature, and that the paramagnetic centers created at low temperature can be annealed out when the temperature is raised.

This is not very surprising, researchers in Japan already saw this many years ago [4]. Although they did not use lasers, and their experiments were done with slightly different samples (not thin films as we have been using) the physical mechanism is expected to be essentially the same. At low temperatures disturbed molecules are not able to repair themselves and so if they are distorted in some way by radiation they tend to remain in that configuration. This can create something called a paramagnetic center which is bad news for positronium atoms. Why? Well paramagnetic centers are essentially unpaired spins, and interactions with these makes it very easy for a long-lived (triplet) Ps state to be converted into a short-lived (singlet) state. In other words, paramagnetic centers kill positronium atoms. These killer centers are not stable at room temperature, and molecular thermal fluctuations can restore the system to its normal state (which generally does not contain any paramagnetic centers). This means that after we create these troublesome centers with a laser all we have to do to get rid of them is to warm the target up. When we do this (see figure above) we get an annealing/recovery process quite similar to the results of Saito et al [4].

Refs.

## Time-resolved Doppler spectroscopy

Positronium atoms created by implanting positrons into porous silica initially have ~ 1 eV kinetic energy, but subsequently cool by colliding with the inner surfaces of the porous network.  The longer spent inside the pores before being emitted to vacuum, the closer the Ps can get to thermalising with the bulk (i.e. room temperature, ~ 25 meV).

Once the positronium atoms make it out of the pores and into vacuum we can excite them using a 243 nm (UV) pulsed laser to n = 2, then ionize these with a 532~nm (green) laser. The amount of positrons resonantly ionised can be measured using SSPALS as the UV wavelength is slowly varied.  This gives us the 1s2p Doppler-width, from which we estimate the Ps energy.  The delay between implanting positrons and firing the 6 ns laser pulse was varied to try and see how the width changes when hitting the Ps cloud at different times.

In the 3D plot above we see that at earlier times the Doppler width is broader than later on.  This is because Ps atoms that spend longer inside the silica have more collisions with the pores and therefore cool down further (narrowing the distribution at later times), mixed up with the simple fact that the fastest atoms reach the laser interaction region quickest, and pass through it more quickly too!

## Rydberg Positronium and Stark broadening

We have recently produced Rydberg positronium atoms in a two step excitation process, using 243 nm light from our broad band pulsed dye laser to excite 2P states, as in our previous Ps spectroscopy measurements. Then, instead of photoionizing with 532 nm light, we used ~ 750 nm light to excite 2p-nd transitions. This process is shown in the energy level diagram below, you can also see a photograph of the green light produced by our Nd:YAG laser pumping the infra red laser.

Once the Ps atoms have been excited to a Rydberg state, their lifetime is greatly increased, and they only annihilate once they collide with the vacuum chamber. This leads to a reduced delayed fraction in our positronium SSPALS signal, since there are less gamma ray events occurring on our delayed detection time (to read more about how we detect Ps, read here). This can be seen in our data below where we excited Ps atoms to n = 11.

When atoms are subjected to a high electric field different states are separated and shifted leading to an overall broadening of the spectral line, this effect is known as Stark broadening,  the mixing and shifting of the states is proportional to the strength of the electric field being applied. We are able to observe this effect by varying the voltage  applied to our porous silica target from which Ps atoms are produced, and therefore changing the electric field that the Ps atoms are subjected to. As the voltage is increased, the broadening grows with the eclectic field, thus producing a signal over a wider range of infra red wavelengths, this is shown in the figure above where we plot the delayed fraction over a range of 5.6 nm, changing the voltage applied to our target from from 1 kV to 2 kV and 3 kV.

## Positronium formation detected using annihilation radiation energy spectroscopy

When a positron and an electron annihilate directly, instead of forming a Ps atom, all of their energy is converted into two gamma ray photons, each with 511 keV (the rest mass energy of the electron/positron). However, if an electron and a positron form a Ps atom the annihilation can occur either into two or three photons, depending on the spin state of the Ps atom. The longer-lived Ps state is called ortho-positronium (o-Ps), and in this system the electron and positron spins point in the same direction, so the total spin of the atom is 1. This means that o-Ps has to decay into an odd number of gamma rays in order to conserve angular momentum. Usually this means three photons, as single photon decay can only happen if there is a third body present (this has been observed). The three photon energies are spread out over a large range (but they always add up to 2 x 511 keV). The short-lived Ps state is called para-positronium (p-Ps) and this usually decays into two photons. It is possible for a three photon state to have zero angular momentum, so singlet decay into three photons is not ruled out by momentum considerations, but this mode is suppressed and to a good approximation p-Ps decays into two gamma rays with well-defined energies (i.e., 511 keV). This means that p-Ps decays look very similar to direct electron-positron decays. It also means that we can detect the presence of o-Ps by looking at the energy spectrum of annihilation radiation, as is shown in the graph below.

We are able to measure gamma ray energies using a detector; in this case NaI(TI), or thallium doped sodium iodide. The data shown above were taken with a positron beam fired into a piece of untreated metal, from which we expect hardly any Ps to be made, and also in a silica film, which we know converts about 30% of the incident positrons into the Ps atoms. When the beam hits the metal many events at energies close to 511 keV are detected, since most positrons will annihilate directly into two 511 keV photons.
The production of Ps can be seen when we compare the two curves (red and black lines) shown in the figure. These spectra are normalised to have the same total area, so the excess of counts in the valley region (i.e., energies between about 300 and 500 keV), and the reduction of counts in the photopeak (at 511 keV) is exactly what you would expect if you made positronium: the decay into three photons means there are more photons with energies less than 511 keV.

## Ps Spectroscopy

We have used our ultraviolet laser (a pulsed dye laser), in addition to a green laser, to ionize a significant fraction of the positronium (Ps) atoms produced by our beamline (read here for more details).

We first tune the UV laser to a wavelength of 243 nm, for which the photons have the same energy as the interval between the ground state and the first excited state of the positronium atom.

We carefully time the laser pulse to pass through the cloud of Ps atoms shortly after they’re created, and so many of the atoms absorb the light and become resonantly excited.  The photons in the green laser have sufficient energy to then ionise these excited atoms – separating the positron and electron.  This technique is known as resonant ionisation spectroscopy (RIS).

The positrons are very likely to fall back into the target and annihilate shortly after ionisation occurs, causing more gamma rays to be detected during the prompt peak of our SSPALS traces; with fewer o-Ps annihilations subsequently detected at later times.  An example SSPALS trace, with and without the laser, is shown below.

We quantify the ionisation by measuring the fraction of delayed annihilations in our SSPALS traces,

f = ∫(B→C)/∫(A→C)

and comparing it to a background measurement without the laser:

S = (flaser onflaser off)/flaser off

The figure below shows how this ionization signal, S, varies as we tune the UV laser across the resonant wavelength, 243nm, for the 1S-2P transition.

The width of the roughly Gaussian line-shape is caused by Doppler broadening, where the atoms moving towards, or away from the laser see a slightly shorter, or longer, wavelength.

The different coloured points represent different voltages applied to the Ps converter. This voltage creates an electric field that attracts and accelerates the positrons, implanting them into the material.  The highest target bias has the narrowest RIS line-shape as the Ps atoms form deep inside the sample and therefore experience more collisions as they make their way back to the surface, which slows them down and reduces the Doppler effect.