Ultracold dipolar gases of long-lived excited neodymium atoms – NeoDip

Determining the feasibility of laser-cooling requires the knowledge of physical quantities characterizing the interactions between atoms and lasers, such as energy levels and transition dipole moments. In the case of neodymium, some of those quantities are known, if they have been measured using spectroscopic techniques, but not all of them. The main goal of the project is thus to acquire an exhaustive information about neodymium (energy levels, transition dipole moments, etc.) using numerical modeling, in order for instance to find the most suitable wavelengths for the cooling lasers.

Those calculations are performed using Cowan’s semi-empirical method, implemented in a well-established computer program in atomic physics. The general idea is to make a first calculation of the relevant atomic properties using first principles of quantum physics. Afterwards, some parameters on which the energies and transition dipole moments depend are adjusted using least-square fitting, so as to obtain the best possible agreement between computed and experimental quantities. If one is able to compute accurate values of experimentally known quantities with a given parameter set, then one can expect the quantities without experimental counterpart to be accurately calculated too.

With a PhD student hired for this project, we started by working on the energy levels of neodymium, with three objectives in mind: (i) to reproduce as accurately as possible the energy levels already known experimentally; (ii) to interpret (i.e. label according to the laws of quantum physics) levels known experimentally but not interpreted; and (iii) to predict the energy of levels not observed experimentally. In this way, we were able to interpret almost 400 energy levels over a range of 25000 cm-1, with a standard deviation (which characterizes the average disagreement between theory and experiment) of less than 100 cm-1.

We then attempted to apply a similar method to calculate transition dipole moments (more precisely Einstein Aik coefficients of spontaneous emission). Given the complexity of the neodymium spectrum i.e. the number of possible transitions, the number of experimentally characterized transitions is in fact limited, hence the interest of these calculations. However, to date, we have not been able to complete these calculations, as we have not reproduced the most intense experimental transitions with good accuracy. Using the experimental data available in the scientific literature, we have nevertheless identified 7 interesting cooling transitions. But we still need to characterize possible leakage from these transitions.

In lanthanide atoms and ions, the number of transitions calculated can amount to several hundred thousand. To make all those data accessible to the community, we have developed, with a Master student, the CaDDiAcS database (https://vamdc.icb.cnrs.fr/caddiacs), with a search form allowing results to be filtered according to various criteria such as transition wavelength. Results can be displayed on screen or saved in a text file, which can be used as input by another program. Currently, transitions in Er+ ion are available.

In parallel, we have worked on the spectra of lanthanide ions used as dopants in solid materials, such as crystals. The transitions are described by the well-established Judd-Ofelt theory, whose accuracy we have sought to improve. We have therefore proposed an extension of this theory, which notably allows for describing more transitions, for example in the europium ion Eu3+. We have also validated our model in the case of erbium and neodymium ions in various host materials.

The first prospect is to continue calculating the transition dipole moments and Einstein coefficients for the neodymium atom. If the semi-empirical method proves unsuccessful, we plan to use a purely ab initio method, i.e. without least-square fitting, but with more advanced numerical calculations. This could be done using the GRASP2018 program, which takes full account of relativistic effects in atoms. As for the CaDDiAcS database, we plan to extend it with transitions in other atoms or ions, in particular lanthanides. Finally, concerning transitions in lanthanide-doped solids, we have prospects for improving our model, for example to describe transitions in polarized light or between Stark sublevels.

This theoretical project aims at proposing a new experiment with ultracold dipolar gases, based on long-lived excited levels of neodymium atoms (Nd). Since it belongs to the left part of the lanthanide row, Nd presents a dense spectrum in the range 8000-15000 cm-1 above its ground level, in striking contrast with yet laser-cooled lanthanide atoms like dysprosium or erbium, that belong to the right part of the row. That large density of states results in pairs of near energy levels that may be mixed by an external, static or oscillating, electric field, thus inducing a significant electric dipole moment, in addition to the large magnetic moment of lanthanides. Such a dense spectrum, though, makes it very challenging to compute quantities like Einstein coefficients, necessary to determine the feasibility of an experiment with ultracold Nd.

In order to fully characterize that future experiment, this project comprises the five following objectives:

- Proposing laser-cooling transitions for Nd;
- Identifying pairs of metastable near energy levels coupled by an oscillating electric field in the terahertz frequency range;
- Calculating the dynamic dipole polarizability of the relevant levels;
- Improving the spectroscopic knowledge of Nd;
- Determining the dipolar interaction energy between neighbouring atoms.

In order to fulfil those objectives, we will use the semi-empirical method of atomic-structure calculations based on the Cowan suite of codes, and extended by us to increase the precision of Einstein coefficients. Due to the large density of levels in Nd and the strong configuration-interaction mixing, our method will still be improved, in particular by simultaneous least-square fittings of energies and Einstein coefficients. The large amount of computed spectroscopic data will be made available in open access on various data portals.