Shifts of positronium energy levels in MgO

The observation of a positronium (Ps) Bose-Einstein condensate (BEC) has been a long sought after achievement in Ps physics. When an ensemble of identical particles collects into  the lowest energy state, i.e. approaching 0 K, a BEC is formed. A Ps BEC can be a source of a highly directional monoenergetic positronium beam, with applications in precision spectroscopy and gravitational interferometry. While BEC of normal atoms have been performed through evaporative cooling or laser cooling, the propensity of Ps to annihilate complicates this endeavour. One way to circumvent this problem was proposed by Platzman and Mills where Ps atoms are made and trapped inside a cavity [1]. However, a smaller cavity which has a higher cooling rate also has higher annihilation rates. One may use larger cavities at the expense of slower cooling, which can then perhaps be compensated by laser cooling.

Fig. 1: Excitation of Ps in vacuum (a) and inside MgO (b).

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.

Fig. 2: 1S-2P transition in Ps in vacuum (a) and inside MgO (b).

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.

Fig. 3: 2P-11S/11D transition in Ps in vacuum (a) and inside MgO (b).


Fig. 4: (a) Shift of Rydberg transitions and (b) 2P- nS/nD transition for n= 10-17 for vacuum and MgO excitation.

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.

Fig. 5: Representation of Ps energy levels in (a) vacuum and (b) inside MgO powder inferred from the data.

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)