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Engineering ground-state pair interactions by Rydberg Optical Feshbach Resonance Schemes

Periodic Reporting for period 1 - ROFeRS (Engineering ground-state pair interactions by Rydberg Optical Feshbach Resonance Schemes)

Reporting period: 2017-06-01 to 2019-05-31

Laser control of atomic and molecular states has been an important staple of quantum optics and the experimental realization of quantum computing systems. In the present project, we proposed a new tool to broaden the possibilities for precise control of the interaction between ground state atom-pairs and concentrated on a thorough analysis of its usability. The proposed new tool, called Rydberg optical Feshbach-resonance (ROFER), is based on Rydberg molecular states, which is a special bound state of two or three atoms, provided by the Rydberg-excitation of one of the atoms' valence electrons. The essence of the ROFER method is to non-resonantly couple a set (2,3) of ground-state atoms to the Rydberg-molecular state. As a result, the ground-state atoms inherit the binding interaction of the molecule. The interaction engineered among the set of atoms is well controllable: the interaction strength is tunable by the properties of the coupling laser field and the characteristic length scale by changing the principal value of the Rydberg-state used to couple to.

These properties allow the proposed scheme to become an important tool in quantum optics for experiments where the precise control on atom-atom interaction is a requirement. Furthermore, the characteristic length scale of the ROFER methods represents a new regime in optical experiments.

The overall objective of the project was to design and analyze experimentally feasible interaction schemes based on ROFER in various important cases, for example, atoms in continuous space and optical lattices and different atomic species. We also aimed for describing many-body phenomena in atomic ensembles.

The main conclusion of our investigations is that the ROFER method proposed in this project is a useful tool for changing interactions between ground-state atomic pairs in continuous space. The experimental feasibility was not only demonstrated by our theoretical work, but also proved by an experimental group shortly after our proposal. Our calculations also suggest that the technique is well applicable for different species of atoms with one or two valence electrons. in contrast, our analysis for atoms trapped in optical lattices showed that the robustness of the scheme in continuous space is significantly reduced by the confinement of the ground-state atoms.

Regarding the description of many-body phenomena in atomic ensembles, we started a new approach by developing a machine learning algorithm based on Gaussian process regression to describe charge transport in a chain of ground-state atoms and perform extrapolation for a larger number of atoms. Although the results of this part of the project are not yet ready for dissemination, the software package that we developed is a useful basis for further research and it also allowed the researcher to acquire skills to further her carrier as a data scientist.
The work performed in the frame of the project was organized in the following three work packages:
WP1. Characterization of Rydberg-molecular and - molecular ion states
WP2. Derivation of the effective ground-state pair-interaction and scattering length
WP3. Analysis of many-body behavior of ultracold ensembles

In the first work package, the Born-Oppenheimer potentials and wave-functions for several types of Rydberg-molecular states were derived for:
a.) Rb and Sr dimers in free-space
b.) Rb and Sr dimers and trimers in one-dimensional lattice space.
We also investigated the existence of Rydberg molecular ions, we did not find a stable enough parameter regime that would suggest stable molecular ion states.

The second work package was built on the results of the first package. We calculated the Franc-Condon factor between ground-state atomic pair and symmetric Rydberg-molecular states. We described the short-range interaction between the two ground-state particles using the Fermi pseudopotential approach. The results of these calculations were published in PRA and were also presented in 2 workshops as poster contributions.

An effective interaction among ground-state lattice triples was also calculated in the presence of coupling to Rydberg-trimers. Unfortunately, an experimentally stable parameter range was not possible to identify for the considered cases (Rb and Sr trimers) due to the effects of the optical lattice that is used to create the lattice gas.

In the frame of the third work package, we developed a software package based on machine-learning algorithms to describe charge transport in a chain of ground-state atoms. This work package allowed both the researcher and the research group to acquire new skills in this new and highly developing field. The dissemination of this work was unfortunately highly affected by the COVID-19 crisis. On one hand, we were planning to present our preliminary results at two conferences, both canceled due to the pandemic. On the other hand, our calculations were also highly delayed on the university cluster to ensure priority for COVID-related research and thus the data-set we were planning to build could bot be finished within the duration of the action.
In the frame of the project, a new tool for tuning interaction between ground-state atoms was proposed and numerically analyzed. The new tool is based on the extension of optical Feshbach resonance to Rydberg molecules, which introduced a substantially new lengthscale (order of 100 nm) into the engineering of interparticle interactions. Furthermore, since the Rydberg-molecular states have a much longer lifetime than the ordinary excited states previously used in optical Feshbach resonance schemes, this method is much easier applicable in a variety of atomic species. The proposed method was successfully realized experimentally short after the theoretical proposal.

The third part of our project including machine learning methods has aided both the hosting research group and the researcher acquiring knowledge in this rapidly developing field. This knowledge, on one hand, has already secured the researcher a position at a highly innovative startup company, on the other hand, will allow the hosting group to create and strengthen links to industrial companies.
Scattering resonance created by the ROFeR scheme
Sketch of a Rydberg optical Feshbach resonance