A previous post of ours (found here) described how our measurements of the energy intervals of the n = 2 positronium (Ps) fine structure produced asymmetric line shapes [1], see Figure 1(a). A line shape represents the probability of transferring an atom from one quantum energy state to another as a function of the applied photon energy. In this case the photons are in the microwave regime at a frequency of ~8.6 GHz as we are looking at the 2 3S1 to 2 3P2 state transition, known as ν2. For details on how we make and measure these lineshapes, and what 2 3S1 means see the previous post linked above.
The reason we do these measurements is that they are tests of quantum electrodynamics, and can reveal new physics beyond the standard model [2]. The energy interval ν2, given in MHz, can be retrieved as the central frequency of the line shape and compred to theoretical calculations. But if there is something distorting the measurement that we cannot account for then the precision we obtain will be limited and the test not as effective. Thus the asymmetry in the previous measurement meant that a value of ν2 could not be extracted from the line shape due to the lack of a suitable theoretical model that would account for the asymmetry.
The previous measurement used a waveguide, which is a structure designed to allow certain microwave frequencies to propagate with high intensity and uniformity. The cause of the line shape asymmetry was reflection effects, whereby microwaves escaped the open ends of the waveguide and were reflected back in [3]. The power reflected back into the waveguide varied as a function of microwave frequency because the changing wavelength altered the reflections in the chamber. This frequency dependent power distorted the line shapes, introducing asymmetry and apparent shifts to the energy interval we want to measure.
So having performed a measurement suffering from reflection effects we decided to make them much much worse. For the peer reviewed work summarised in this article click here [4]. Instead of a waveguide we used a horn antenna which allows microwave radiation to be coupled from a source into free space, removing the spatial restrictions of the waveguide (which was 12.6 mm x 25.8 mm in size, a WR-112 as it is known). In this experiment we placed the horn antenna outside the vacuum chamber where the Ps is made at a distance of up to 34 cm from the Ps, see Figure 2. The microwaves entered the chamber through a fused silica window where they could address the Ps atoms.
The distance between the horn antenna and the chamber should allow the radiation to propagate and become plane waves (radiation that has each peak of the wave travelling parallel to one another), in what is known as the far-field regime [5]. Plane waves should have uniform polarisation and power distribution. However, due to the metal chamber and electrodes there was a significant amount of reflection inside the chamber, much more than in the waveguide. This can be seen in Figure 3 (a & c) which shows a 2-D map of the simulated microwave field strength inside the vacuum chamber, and 3 (b & d) which shows the polarisation of the same data. In an ideal world these would show a uniform block of colour indicating uniform field strength and polarisation, but it really does not. This effectively randomised microwave field increases the frequency dependent power variation felt by the Ps atoms, amplifying distortions to the line shape.
The lineshape you see in Figure 1(b) is symmetric, unlike the previous measurement of ν2. However, this measurement does show a shift from the theoretical prediction of the energy interval. There were two causes we thought most likely to explain this shift: (a) the atoms had a preferential motion towards/away from the horn creating a Doppler shift (the change in frequency of light due to the motion of the target, i.e. when moving towards something you percieve the peaks of the wave being closer together and so see a higher frequency of light), or (b) the microwave reflections were causing a shift even without an asymmetry. The way we tested this was by varying the horn antenna angle θH with respect to the Ps. By rotating the horn we can select the subset of Ps atoms moving towards or away from the microwave radiation and change the Doppler shift with a certain angular dependency.
What we found was a ~300 kHz/degree shift, see Figure 4, which is much larger and of opposite magnitude compared to the expected Doppler shift of -40 kHz/degree. We therefore ruled out Doppler shifts as a possible explanation. In fact the shift we saw would have to come from all atoms moving directly towards the antenna at -10o and away from the antenna at +10o which, given our experiment, was implausible. Other possibilities such as ac Stark shift, spatial selection effects, polarisation effects, and stray electric fields were excluded for being too small in magnitude or not dependent on the horn orientation.
It would appear that this shift is therefore due to reflection effects, which is not surprising given the distorted line shapes observed in waveguide measurements where reflections were much less dominant. We therefore concluded that a horn antenna as a source of free space microwaves is not an ideal way to perform precision measurements of Ps. But the technique further demonstrates the nature of reflection effects in line shape measurements over a broad frequency range. An interesting feature is that the line shapes show no asymmetry but display large shifts, confirming the previously simulated data that showed a shift can manifest without an associated asymmetry [3] and therefore removal of reflections must be demonstrated beyond verification of symmetric line shapes.
If we wish to test QED in Ps using these microwave regime transitions we must remove reflections as a source of error. We believe that by using a different chamber with less reflective surfaces at the ends of the waveguide we can remove these reflections. Simulations with this new chamber have demonstrated this is indeed the case. Figure 5 shows the change in strength of the microwave field in a waveguide inside a new, modified vacuum chamber (called the Cube) versus the one used to make the previous asymmetric measurements (called the Cross) [1]. The field is over three times more uniform in the newly designed chamber than the old. Thus we intend to replicate the waveguide measurement with the new chamber (and other improvements) to probe bound state QED.
[1] Observation of asymmetric line shapes in precision microwave spectroscopy of the positronium 2 3P1 → 2 3PJ (J = 1, 2) fine-structure intervals. L. Gurung, T. J. Babij, J. Pérez-Ríos, S. D. Hogan and D. B. Cassidy; Phys. Rev. A.103, 042805 (2021)
[2] Precision physics of simple atoms: QED tests, nuclear structure and fundamental constants. S. G. Karshenboim; Phys. Rep. 422, 1 (2005)
[3] Line-shape modelling in microwave spectroscopy of the positronium n = 2 fine-structure intervals. L. A. Akopyan, T. J. Babij, K. Lakhmanskiy, D. B. Cassidy and A. Matveev; Phys. Rev. A. 104, 062810 (2021)
[4] Microwave spectroscopy of positronium atoms in free space. R. E. Sheldon, T. J. Babij, S. H. Reeder, S. D. Hogan, and D. B. Cassidy; Phys. Rev. A 107, 042810 (2023)
[5] Microwave Engineering. David M. Pozar; 4th Edition (2012)
[6] Tests of Quantum Electrodynamics Using n = 2 Positronium. R. E. Sheldon; PhD Thesis, University College London (2024)
[7] Precision microwave spectroscopy of the positronium 2 3S1 →2 3P2 interval. R. E. Sheldon, T. J. Babij, S. H. Reeder, S. D. Hogan, and D. B. Cassidy; Phys. Rev. Lett.131, 043001 (2023)
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