The aim of precision spectroscopy is to carry out new measurements that will be compared to theoretical calculations. Measuring these energy structure provide a way of verifying the predictions made by theory. Atomic systems like hydrogen and helium are widely studied for QED testing, but the presence of heavy hadrons like protons introduces complications. One does not need to worry about such complications in positronium as there are no hadrons involved.

Within positronium there are many energy levels one could choose to measure. The separation of the triplet and singlet states of the *n*=1 level (i.e., the hyperfine structure interval), the 1S-2S interval, and the 2S-2P intervals are all excellent candidates [2]. The theoretical calculations for these three intervals have been very precisely calculated, and have also been previously measured. The last measurement of the fine structure intervals [3], however, is now over 25 years old and is much less precise than theory. Because Ps is very well defined by QED theory, any disagreements between calculations and measurements could be an indication of new physics. To be sensitive to new physics, the experiments have to done with precision comparable to calculations.

Recently we have measured the 2S-2P fine structure intervals of positronium [4]. There are three transitions within this branch and in this post, we’ll talk about the *ν*_{0} transition (2^{3}S_{1} – 2^{3}P_{0}) which is resonant around 18 GHz. This transition, including the other two, is illustrated in figure 1. Initially, the Ps atoms (which are formed in the 1S state) have to be excited to the 2S state. This can be done in several ways (direct 1S-2S transition with one photon is not allowed), and we will cover our method in detail in another blog post soon. For now, let’s assume that the atoms are already in the 2S state. These atoms then fly into a waveguide where the microwaves drive them to the 2P state (via stimulated emission) as shown in figure 2. The atom then emits a 243 nm photon and drops down to the 1S state, where it will annihilate into gamma-rays after 142 ns (remember the lifetime of Ps in the ground state?). If nothing happens in the waveguide, the 2^{3}S_{1} state atom will annihilate after 1 *μ*s.

We placed gamma-ray detectors (D1-D4) around the target chamber, as shown in figure 2, to monitor the annihilation signal. The detector signal was then used to quantify the microwave radiation induced signal, S_{γ}. We scanned over a frequency range to generate a lineshape that describes the transition; the centre describes the resonance frequency and the width is due to the lifetime of the excited state. A Lorentzian function was fitted to extract this information and for the example shown in figure 3, the centroid and line width are 18500.65 MHz and 60 MHz respectively. The centroid is slightly off from theory because the lineshape was measured in a magnetic field which introduces Zeeman shift to the centroid. The measured width is 60 MHz, slightly wider than the expected 50 MHz, and is due to the time taken to travel through the waveguide.

Similar lineshapes were measured over a range of magnetic fields in order to account for the Zeeman shift. These data are shown in figure 4. Extrapolating to zero with a quadratic function allows us to obtain the field free resonance frequency, free of Zeeman shifts. However, all of the measured points, including the extrapolated number, are offset from theoretical calculation (dashed curve) by about 3 MHz. There are a few systematic effects to consider and the largest of them is the Doppler shift arising from the laser and waveguide misalignment, which amounts to 215 kHz. Our result, compared with theory and previous measurements, is shown in figure 5 and disagrees with theory by 2.77 MHz (4.5 standard deviations). While the precision has improved by over a factor of 6, the disagreement with theory is significant.

Precision measurements can be vulnerable to interference effects and there are two main types of effects that can cause lineshape distortion and/or shifts in line centre. Whenever the radiation emitted from the excited state (2P state in our case) is monitored to generate the signal, the emitted radiation can interfere with the incident/driving radiation (microwaves in our case)[5]. This leads to shift in the resonance frequency, but we are not sensitive to this kind of effect as we monitor the gamma-rays instead of the 243 nm emitted radiation (figure 1). Another type of interference arises from the presence of neighbouring resonance states [6], such as the two other 2P states in the Ps fine structure. The further apart the states are, the lesser the interference effect is and we expect a shift of 200 kHz in our line shape. This is, however, over 10 times smaller than the observed shift, and therefore, cannot be the reason for the disagreement.

There are two more transitions in the fine structure we have measured and they reveal interesting new features which were not previously seen. These additional data will provide a broader picture that will help us explain the shift we see in this transition. We’ll discuss those results in the next blog post.

[1] Karshenboim, S.G., *Precision Study of Positronium: Testing Bound State QED Theory*. Int. J. Mod. Phys. A, **19** (2004)

[2] Rich, A., *Recent Experimental Advances in Positronium Research*. Rev. Mod. Phys., **53** (1981)

[3] Hagena, D., Ley, R., Weil, D., Werth, G., Arnold, W. and Schneider, H., *Precise Measurement of n=2 Positronium Fine-Structure Intervals*. Phys. Rev. Lett., **71** (1993)

[4] Gurung, L., Babij, T. J., Hogan, S. D. and Cassidy, D. B., *Precision Microwave Spectroscopy of the n=2 Positronium Fine Structure *. Phys. Rev. Lett., **125** (2020)

[5] Beyer, A., Maisenbacher, L., Matveev, A., Pohl, R., Khabarova, K., Grinin, A., Lamour, T., Yost, D.C., Ha ̈nsch, T.W., Kolachevsky, N. and Udem, T., *The Rydberg Constant and Proton Size From Atomic Hydrogen*. Science, **358** (2017)

[6] Horbatsch, M. and Hessels, E.A., *Shifts From a Distant Neighboring Resonance*. Phys. Rev. A, **82** (2010)

Following the discussion about producing Ps in MgO target, we decided to examine the effects of cavities on the positronium with laser spectroscopy [2]. Ps atoms produced by MgO were excited after being emitted in vacuum [Fig. 1(a)] or while they were still inside the powder [Fig. 1(b)]. The former will tell us the energy levels in vacuum, which are well known while the latter can tell us about the Ps-cavity interaction. The 1S->2P transition for both excitation cases are shown below in Fig. 2. Excitation in vacuum has a single curve centered around 243 nm as expected, with a Doppler width that implies kinetic energy of 350 meV. The reason for such a high energy and absence of cooling was discussed in a previous blogpost, which you may read here. But, when the Ps is probed inside the MgO, multiple peaks are visible. The redshifted peak (peak on the right, red dotted line) is due to some Ps which are already in vacuum and moving towards the lasers being excited. Another peak for atoms in vacuum moving away from the lasers (blue dotted) is also present. The third peak (blue dashed) arises from the excitation of Ps inside the MgO, which is shifted away from the vacuum resonance by 0.2 nm or 1000 GHz. The 1000 GHz shift is too large to be a confinement effect as the MgO cavities are too large. Similar measurement with silica was done previously by the Riverside Ps group [3] but not for Rydberg states as presented here.

Similar to the data in Fig. 2, excitation to Rydberg states (2P -> 11S/11D) was also measured and is shown below in Fig. 3. Again, the vacuum excitation results in only one peak at the expected resonance [Fig. 3(a)] but excitation inside MgO [Fig. 3(b)] has a blueshifted and a redshifted peak. Two observations are apparent from the data: the Rydberg atoms are able to leave the target even after several collisions, and more surprisingly, Rydberg states (for *n*= 10-17) are all shifted by the same amount as shown in Fig. 4.

Rydberg atoms which are more sensitive to interactions should have some *n* dependence, contrary to what was observed. This appears to be because MgO has photoluminescence (PL) absorption bands in the 240 nm range [4], which overlaps with the 1S-2P transition wavelength in Ps and are coupled resonantly. There are no PL bands that overlap with the Rydberg energies, thus, these states are unaffected. The resulting 1S and 2P energy levels in MgO are therefore shifted, with higher states unshifted as shown in Fig. 5. A detailed dipole-dipole treatment of the interaction of Ps and MgO crystals is outlined in the paper. These PL bands which are also present in silica may have caused the shift previously seen but without further Rydberg data we cannot tell if individual levels are shifted.

Thus, the presence of such PL absorption in other materials for Ps confinement purposes can also give rise to energy shifts and can affect the control of atoms, which is necessary for high-density Ps experiments. It may be possible to carefully engineer material which can confine Ps but will not exhibit these characteristics.

[1] P. M. Platzman and A. P. Mills, Jr. *PRB*, **49**, 454 (1994)

[2] L. Gurung, B. S. Cooper, S. D. Hogan, and D. B. Cassidy, *PRA*, **101**, 012701 (2020)

[3] D. B. Cassidy, M. W. J. Bromley, L. C. Cota, T. H. Hisakado, H. W. K. Tom and A. P. Mills, Jr. *PRL*, **106**, 023401 (2011)

[4] C. Chizallet, G. Costentin, H. Lauron-Pernot, J-M. Krafft, M. Che, F. Delbecq, and P. Sautet, *J. Phys. Chem. C*, **112**, 19710 (2008)

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**Rydberg excitation in thermal Rydberg gases**

The creation of optical nonlinearities in atomic gases become a challenging task with increasing temperature, due to large Doppler effects. We study single photon excitation of electronically high-lying Rydberg states by nanosecond laser pulses that propagate in a high density thermal gas of alkali atoms. Fast Rabi flopping and strong Rydberg atom interactions, both in the order of GHz, overcome Doppler effects and dephasing due to thermal collisions between Rydberg electrons and surrounding atoms. The latter has not been taken into account appropriately so far. We show that a sizable dispersive nonlinearity is generated by strong interactions between Rydberg atoms. Despite the Rydberg optical nonlinearity, solitary propagation, i.e., self-induced transparency (SIT), of the light pulse can still occur. The existence of SIT allows to implement a conditional optical phase gate in the thermal gas through harvesting strong interactions. Our study paves the route to study nonlinear optics in thermal Rydberg gases and directly contributes to the current effort in realising scalable quantum information and communication devices with glass cell technologies.

]]>**Spatial and internal control of atomic ensembles with radiofrequency and microwave driving**

The ability to apply well-controlled perturbation to quantum systems is essential to modern methodologies to study their properties (e.g. in high-precision-spectroscopy), and developing quantum technologies (e.g. atomic-clocks and quantum processors). In most of the experimental platforms available today, such perturbations arise from the interaction of a quantum system with electromagnetic radiation, which creates harmonically oscillating couplings between the states of the system. Within this context, in this talk, I will describe our recent studies of the use of low-frequency electromagnetic radiation to control the external and internal degrees of freedom of ultracold atomic ensembles [1,2]. I will outline the relation of this problem with Floquet Engineering and the more general issue of describing the dynamic of the driven quantum systems. Finally, I will explain the challenges of describing the quantum dynamics of systems driven and highlight eh need for developing new conceptual and mathematical tools to identify universal characteristics and limitation of their dynamics.

[1] G. A. Sinuco-Leon, B. M. Garraway, H. Mas, S. Pandey, G. Vasilakis, V. Bolpasi, W. von Klitzing, B. Foxon, S. Jammi, K. Poulios, T. Fernholz, Microwave spectroscopy of radio-frequency dressed alkali atoms, Physical Review A, accepted (2019). [ArXiv:1904.12073].

[2] G. Sinuco-León and B.M. Garraway, Addressed qubit manipulation in radio-frequency dressed lattices, New Journal of Physics. 18, 035009 (2016)

**Optimal quantum control with poor statistics**

Learning how to control a quantum system based on experimental data can help us to exceed the limitations imposed by theoretical modeling. Due to the intrinsic probabilistic nature of quantum mechanics, it is fundamentally necessary to repeat measurements on individual quantum systems many times in order to estimate the expectation value of an observable with good accuracy. Control algorithms requiring accurate data can thus imply an experimental effort that negates the benefits of avoiding theoretic modelling. We present a control algorithm based on Bayesian optimisation that finds optimal control solutions in the presence of large measurement shot noise and even in the limit of single shot measurements. With the explicit example of the preparation of a GHZ state, we demonstrate in numerical simulations that this method is capable of finding excellent control solutions with minimal experimental effort.

]]>**Using the Zeeman effect to manipulate radicals and study ion-radical reactions**

In spite of their real-world importance, very few experimental methods can be applied to the precise study of gas-phase ion-radical reaction systems. This is primarily due to the significant difficulty associated with generating a pure beam of atomic or molecular gas-phase radicals with tuneable properties. In this seminar, I will present our work in generating a pure beam of velocity-selected radicals. Only the target radicals are transmitted into the detection region; all other components of the incoming beam (radical species travelling faster/slower than the target velocity. precursor molecules and seed gases) are removed. This control over the properties of the radical beam is achieved through the use of a magnetic guide, composed of four Halbach arrays (permanent magnets in a hexapolar configuration) and two skimming blades. Experimental measurements of Zeeman-decelerated H atoms transmitted through the guide, combined with extensive simulations, show that the magnetic guide removes 99% of H atoms travelling outside the narrow target velocity range [1,2]. We will shortly combined the Zeeman decelerator and magnetic guide with an ion trap, for the study of ion-radical reactions. I will present some recent work on the reaction of ions with polar molecules – and discuss how we intend to adapt this approach for the study of ion-radical processes.

[1] J. Toscano, C. J. Rennick, T. P. Softley and B. R. Heazlewood, J. Chem. Phys. 149, 174201, (2018).

[2] J. Toscano, M. Hejduk, H. G. McGhee and B. R. Heazlewood, Rev. Sci. Instrum. 90, 033201, (2019).

**Precursor of the Higgs Mode in Ultracold Few-Fermion Systems**

The emergence of collective modes from single-particle excitations is one of the most striking features of strongly interacting systems. Understanding such excitations is an ongoing challenge in nuclear physics, strongly correlated electron systems, and high-energy physics. Ultracold atoms in optical potentials provide a unique setting to precisely study the appearance of collective excitations in a tunable laboratory setting.

Here we experimentally observe the “birth” of a collective mode in a few-body system of ultracold Fermions. Using optical tweezers, we deterministically prepare few Fermions in the ground state of a two dimensional trap. This system exhibits a shell structure of stable “magic” numbers of 2,6,12… particles. We perform many-body spectroscopy through a modulation of the interaction strength find both single-particle and two-particle excitations. The latter consists of pairwise excitations akin to Cooper pairs and can be identified as the precursor of the Higgs mode in a two-dimensional Fermi gas.

In the future, we will probe such mesoscopic Fermi systems with single-particle detection. We recently demonstrated spin-resolved fluorescence imaging of individual atoms in free space, which will allow us to detect the momenta of every particle in the system in time-of-flight. We expect to directly see the formation of Cooper pairs and the momentum space signature of the BEC-BCS crossover.

]]>**Trapping long-lived hydrogenic Rydberg states of nitric oxide
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High Rydberg states of atoms or molecules can have extremely large static electric dipole moments, upon which an inhomogeneous electric field will exert a sizable force. Electrostatic or time-varying electric fields have been utilised to exploit this effect to guide or decelerate and trap H, He, Ps and also H2.

I will describe a compact chip-based Rydberg-Stark decelerator comprised of a linear array of 115 electrodes. And I will present the results of recent experiments in which this device was employed to decelerate and trap laser excited NO molecules. An average lifetime of approximately 300 us was measured for molecules in the cryogenic trap. These cold, trapped NO molecules are of interest for studying low-temperature inelastic scattering processes for which long-range interaction play an important role.

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A wide range of topics, from Ps physics to defect studies, were discussed by over 100 participants in the workshop. David outlined the recent experimental progress in Ps-laser physics in his talk, while Ross talked about the versatility of a multi-ring guide for possible Ps deceleration and trapping studies. Lokesh presented the results of the new precision microwave spectroscopy experiment (stay tuned for more details). The complete list of abstracts can be found here. It was a pleasure discussing the ongoing work in the field of slow positron physics in the wonderful city of Prague.

Click to view slideshow.We’d like to thank the local organising committee, led by Jakub Cizek, for organising an excellent meeting and we look forward to the next SLOPOS which will be held in Orléans, France in 2022.

]]>Our most recent work on the microwave spectroscopy of Ps *n*=2 fine structure (more on this in the next blog post) was presented by Lokesh. It was a great opportunity to discuss our research with the positron (positronium) and the electron community as well as explore ongoing and future research from other groups. The complete list of abstract is available here, as well as the photo gallery.

We’d like to thank the organisers for planning this excellent conference and we look forward to the next meeting. The UCL Ps Spectroscopy group will be attending SLOPOS-15 in Prague in September. See you then!

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