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.

n19ionThe 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!

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.

Point-of-view of a Ps atom entering a quadrupole guide

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.]

Stark broadening of n=12 Ps in an electric field.

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.

Rydberg positronium source, lasers, gamma-ray detectors, and quadrupole guide.

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.

Electric field strength and trajectory calculation for low-field-seeking (blue),  high-field-seeking (red), and unaffected (green) Rydberg-Stark states of positronium in a quadrupole guide.

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.

The number of Rydberg Ps atoms entering (red) and passing all the way through (blue) the quadrupole guide.

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.

Antimatter annihilation, gamma rays, and Lutetium-yttrium oxyorthosilicate

Doing experiments with antimatter presents a number of challenges. Not least of these is that when a particle meets its antiparticle the two will quickly annihilate. As far as we know we live in a universe that is dominated by matter. We are certainly made of matter and we run experiments in matter-based labs. How then can we confine positrons (anti-electrons) when they disappear on contact with any of our equipment?

Paul Dirac – the theoretical physicist who predicted the existence of antiparticles almost 90 years ago – proposed the solution even before there was evidence that antimatter was any more than a theoretical curiosity. In 1931 Dirac wrote,

“if [positrons] could be produced experimentally in high vacuum they would be quite stable and amenable to observation.”

P. A. M. Dirac (1931) 

Our positron beamline makes use of vacuum chambers and pumps to achieve pressures as low as 12 orders of magnitude less than atmosphere. Inside of our buffer-gas trap, where the vacuum is deliberately not so vacuous, the positrons can still survive for several seconds without meeting an electron. And as positrons are electrically charged they can easily be prevented from touching the chamber walls using a combination of electric and magnetic fields. (For neutral forms of antimatter the task is more difficult.  Nevertheless, the ALPHA experiment was able to trap antihydrogen for 1000 s using a magnetic bottle.)

An antiparticle can be thought of as a mirror image of a particle, with a number of equal but opposite properties, such as electric charge. When the two meet and annihilate, these properties sum to zero and nothing remains. Well, almost nothing. Electrons and positrons have the same mass (m = 9.10938356 × 10-31 kg), and when the two annihilate this is converted to energy in accordance with Einstein’s well-known formula

 E = m c2,

where c is the speed of light (299792458 m/s). For this reason antimatter has long fascinated science fiction writers: there is a potentially vast amount of energy available – e.g., for propelling spaceships or destroying the Vatican – when only a small amount of antimatter annihilates with matter. However, the difficulty in accumulating even minuscule amounts means that applications in weaponry and propulsion are a very long way from viable.

When an electron and positron annihilate the energy takes the form of gamma-ray photons. Usually two, each with 511 keV of energy. Although annihilation raises some difficulties, the distinct signature it produces can be very useful for detection purposes. Gamma rays are hundreds of thousands of times more energetic than visible photons. To detect them we use scintillation materials that absorb the gamma ray energy and then emit visible light. Photo-multiplier tubes are then used to convert the visible photons into an electric current, which can then be recorded with an oscilloscope.

Many materials are known to scintillate when exposed to gamma rays, although their characteristics differ widely. The properties that are most relevant to our work are the density (which must be high to absorb the gamma rays), the length of time that a scintillation signal takes to decay (this can vary from a few ns to a few μs), and the number of visible photons emitted, i.e., the light output.


Encased sodium iodide crystal 

Sodium iodide (NaI) is a popular choice for antimatter research because the light output is very high, therefore individual annihilation events can easily be detected.  However, for some applications the decay time is too long (~1 μs).


PMT output for individual gamma-ray  detection with NaI

The material we normally use to perform single-shot positron annihilation lifetime spectroscopy (SSPALS) is lead tungstate (PbWO4) – the same type of crystal is used in the CMS electromagnetic calorimeter. This material has a fast decay time of around 10 ns, which allows us to resolve the 142 ns lifetime of ground-state positronium (Ps).  However, the amount of visible light emitted from PbWO4 is relatively low (~ 1% of NaI).

Recently we began experimenting with using Lutetium-yttrium oxyorthosilicate (LYSO) for SSPALS measurements, even though its decay time of ~40 ns is considerably slower than that of PbWO4.  So, why LYSO?  The main reason is that it has a much higher light output (~ 75% of NaI), therefore we can more efficiently detect the gamma rays in a given lifetime spectrum, and this significantly improves the overall statistics of our analysis.


An array of LYSO crystals

The compromise with using LYSO is that the longer decay time distorts the lifetime spectra and reduces our ability to resolve fast components. However, most of our experiments involve using lasers to alter the lifetime of Ps (reducing it via magnetic quenching or photoionisation; or extending it by exciting the atoms to Rydberg levels), and we generally care more about seeing how much the 142 ns component changes than about what happens on shorter timescales.   The decay time of LYSO is just about fast enough for this, and the improvement in contrast between signal and background measurements – which comes with the improved statistics – outweighs the loss in timing resolution.


SSPALS with LYSO and PbWO4

This post is based on our recent article:

Single-shot positron annihilation lifetime spectroscopy with LYSO scintillators, A. M. Alonso, B. S. Cooper, A. Deller, and D. B. Cassidy, Nucl. Instrum. Methods :  A  828, 163 (2016) DOI:10.1016/j.nima.2016.05.049.

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.

Photoemission of Ps from single-crystal p-Ge semiconductors

The production of positronium in a low-temperature (cryogenic) environment is in general only possible using materials that operate via non-thermal processes. In previous experiments we showed that porous silica films can be used in this way at temperatures as low as 10 K, but that Ps formation at these temperatures can be inhibited by condensation of residual gas, or by laser irradiation.

It has been known for several years now that some semiconductors can produce Ps via an exciton-like surface state [12]. Si and Ge are the only semiconductors that have been studied so far, but it is likely that others will work in a similar way. The electronic surface state(s) underlying the Ps production can be populated thermally, resulting in temperature dependent Ps formation that is very similar to what is observed in metals (for which the Ps is actually generated via thermal desorption of positrons in surface states). Since laser irradiation can also populate electronic surface states, and is known to result in Ps emission from Si at room temperature, the possibility exists that this process can be used at cryogenic temperatures.

We have studied this possibility using p-type Ge(100) crystals. Initial sample preparation involves immersion in acid (HCl) and this process leaves the sample with Chlorine-terminated dangling bonds which can be thermally desorbed. We attached the samples to a cold head with a high temperature interface  that can be heated to 700 K and cooled to 12 K. The heating is necessary to remove Cl from the crystal surface, which otherwise inhibits Ps formation. Fig 1 shows the initial heating cycle that prepares the sample for use. The figure shows the delayed annihilation fraction (which is proportional to the amount of positronium) as a function of temperature.


FIG. 1:  Delayed fraction as a function of sample temperature after initial installation into the vacuum system. After the surface Cl has been thermally desorbed the amount of Ps emitted at room temperature is substantially increased.

As has been previously observed [2] using visible laser light at 532 nm can increase the Ps yield. This occurs because the electrons necessary for Ps formation can be excited to surface states by the laser. However, these states have a finite lifetime, and as both the laser and positron pulses are typically around 5 ns wide these have to be synchronized in order to optimise the photoemission effect. This is shown in FIG 2.  These data indicate that the electronic surface states are fairly short lived, with lifetimes of less than 10 ns or so. Longer surface states were observed in similar measurements using Si.

phototime web

FIG 2: Delayed fraction as a function of the arrival time of the laser relative to the incident positron pulse. These data are recorded at room temperature.  The laser fluence was ~ 15 mJ/cm^2

When Ge is cooled the Ps fraction drops significantly. This is not related to surface contamination, but is due to the lack of thermally generated surface electrons. However, surface contamination does further reduce the Ps fraction (much more quickly than is the case for silica. This effect is shown in FIG 3. If a photoemission laser is applied to a cold contaminated Ge sample two things happen (1) the laser desorbs some of the surface material and (2) photoemission occurs .This means that Ge can be used to produce Ps with a high efficiency at any temperature, and we don’t even have to worry about the vacuum conditions (within some limits).


FIG 3: Delayed fraction as a function of time that the target was exposed to showing the effect that different laser fluences has on the photoemission process. During irradiation, the positronium fraction is noticeably increased.

There are many possible applications for cryogenic Ps production within the field of antimatter physics, including the formation of antihydrogen formation via Ps collision with antiprotons [3], Ps laser cooling and Bose Einstein Condensation [4], as well as precision spectroscopy.

[1] Positronium formation via excitonlike states on Si and Ge surfaces. D. B. Cassidy, T. H. Hisakado, H. W. K. Tom, and A. P. Mills, Jr. Phys. Rev. B, 84, 195312 (2011). DOI:10.1103/PhysRevB.84.195312.

[2] Photoemission of Positronium from Si. D. B. Cassidy, T. H. Hisakado, H. W. K. Tom, and A. P. Mills, Jr. Phys. Rev. Lett. 107, 033401 (2011). DOI:10.1103/PhysRevLett.107.033401.

[3] Antihydrogen Formation via Antiproton Scattering with Excited Positronium. A. S. Kadyrov, C. M. Rawlins, A. T. Stelbovics, I. Bray, and M. Charlton. Phys. Rev. Lett. 114, 183201 (2015). DOI:10.1103/PhysRevLett.114.183201.

[4] Possibilities for Bose condensation of positronium. P. M. Platzman and A. P. Mills, Jr. Phys. Rev. B 49, 454 (1994). DOI:10.1103/PhysRevB.49.454.

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= 1S= 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 \mus (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.
StarkmapFigSo 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].

[1] Selective Production of Rydberg-Stark States of Positronium. T. E. Wall, A. M. Alonso, B. S. Cooper, A. Deller, S. D. Hogan, and D. B. Cassidy, Phys. Rev. Lett. 114, 173001 (2015) DOI:10.1103/PhysRevLett.114.173001.

[2] Controlling Positronium Annihilation with Electric Fields.  A. M. Alonso, B. S. Cooper, A. Deller, S. D. Hogan, D. B. Cassidy, Phys. Rev. Lett. 115, 183401 (2015) DOI:10.1103/PhysRevLett.115.183401.

[3] Fine-Structure Measurement in the First Excited State of Positronium. A. P. Mills,  S. Berko, and  K. F. Canter, Phys. Rev. Lett. 34 1541 (1975) DOI:/10.1103/PhysRevLett.34.1541.