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.

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.

UCL positronium spectroscopy beamline (the first two years)

The UCL Ps spectroscopy positron beamline began producing low-energy positrons almost two years ago, and it has since become slightly longer and somewhat more sophisticated. Though it’s not the most complex scientific machine in the world (compared to, e.g., the LHC) we still find regular use for a 3D depiction of it.  Our model is essentially a cartoon. Typically we use it to create (fairly) accurate schematics that help us to convey the configuration of our equipment at conferences or in publications.


The snap shot above shows the three main components of the beamline, namely the positron source (left), Surko trap (centre, cross-section), and Ps laser-spectroscopy region (right).  The 3D model is built from simplified forms of the various vacuum chambers and pumps, magnetic coils, and detectors.  And it shows where these all are in relation to one another.  The 45° angled line is being used right now for Rydberg Ps time-of-flight measurements.  The source and trap are based on the design developed by Rod Greaves and Jeremey Moxom of First Point Scientific Inc. (unfortunately now defunct).  You can read about the details of their design in this article.

To allow you to take a closer look we have created a 3D pdf file that you can download here * (licensed under a Creative Commons Attribution 4.0 License). Be aware we use this for illustration/ communication purposes and it is not an accurate technical model. Nonetheless, using this you can pan, zoom, and rotate around our virtual lab to your heart’s content! No need for 3D glasses, though you will need a recent copy of Adobe reader,  (the interactive features probably won’t work in your web browser).

*MD5 checksum c6028573596c9511d9ba0450cd2caa05

And here’s how the lab looks in real life,