## 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.

## 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.

## How long does Rydberg positronium live?

Time-of-flight (TOF) is a simple but powerful technique that consists of accurately measuring the time it takes a particle/ atom/ ion/ molecule/ neutrino/ etc. to travel a known distance.  This valuable tool has been used to characterise the kinetic energy distributions of an exhaustive range of sources, including positronium (Ps) [e.g. Howell et al, 1987], and is exploited widely in ion mass spectrometry.

Last year we published an article in which we described TOF measurements of ground-state (n=1) Ps atoms that were produced by implanting a short (5 ns) pulse of positrons into a porous silica film.  Using pulsed lasers to photoionise (tear apart) the atoms at a range of well-defined positions, we were able to estimate the Ps velocity distribution, finding mean speeds on the order of 100 km/s. Extrapolating the measured flight paths back to the film’s surface indicated that the Ps took on average between 1 and 10 ns to escape the pores, depending on the depth to which the positrons were initially implanted.

When in the ground state and isolated in vacuum the electron and positron that make up a positronium atom will tend to annihilate each another in around 140 ns.  Even with a speed of 100 km/s this means that Ps is unlikely to travel further than a couple of cm during its brief existence.  Consequently,  the photoionisation/ TOF measurements mentioned above were made within 6 mm of the silica film. However, instead of ionising the atoms, our lasers can be reconfigured to excite Ps to high-n Rydberg levels, and these typically live for a great deal longer.   The increase in lifetime allows us to measure TOF spectra over much longer timescales (~10 µs) and distances (1.2 m).

The image above depicts the layout of our TOF apparatus.  Positrons from a Surko trap are guided by magnets to the silica film, wherein they bind to electrons and are remitted as Ps.  Immediately after, ultraviolet and infra-red pulsed lasers drive the atoms to n=2 and then to Rydberg states.  Unlike the positively charged positrons, the neutral Ps atoms are not deflected by the curved magnetic fields and are able to travel straight along the 1.2 m flight tube, eventually crashing into the end of the vacuum chamber.  The annihilation gamma rays are there detected using an NaI scintillator and photomultipler tube (PMT), and the time delay between Ps production and gamma ray detection is digitally recorded.

The plots above show two different views of time-of-flight spectra accumulated with the infra-red laser tuned to address Rydberg levels in the range of n=10 to 20.  The data shows that more Ps are detected at later times for the higher-n states than for lower-n states.  This is easily explained by fluorescence, i.e., the decay of an excited-state atom via spontaneous emission of a photon.  As the fluorescence lifetime increases with n, the lower-n states are more likely to decay to the ground state and then annihilate before reaching the end of the chamber, reducing the number of gamma rays seen by the NaI detector at later times. We estimate from this data that Ps atoms in n=10 fluoresce in about 3 µs, compared to roughly 30 µs for n=20.

This work brings us an important step closer to performing a positronium free-fall measurement.  A flight path of at least ten meters will probably be required to observe gravitational deflection, so we still have some way to go.

This post is based on work discussed in our article:

Measurement of Rydberg positronium fluorescence lifetimes. A. Deller, A. M. Alonso, B. S. Cooper, S. D. Hogan, and D. B. Cassidy. Phys. Rev. A 93, 062513  (2016)DOI:10.1103/PhysRevA.93.062513.

## 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].

## 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.

## 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.