Phenomenology of a Rydberg impurity in an ideal Bose-Einstein condensate

In a Bose-Einstein condensate, the long-range nature of Rydberg interactions are characterised by a scattering length that may rival or even surpass the average spacing between the surrounding bosons. The significance of these interactions depends on the density; when the average distance between Bosons is smaller then the scattering length, the system exhibits a rich absorption spectrum which extends typical polaron physics, with large shifts and complex molaron structures. However, within a dense bath, the absorption spectrum consists only of a broad single Gaussian, indicating an almost classical behaviour.

Extending the scope of interactions even further, and changing the electronic angular momentum of the Rydberg atom to l>0 can introduce anisotropic and non-additive interactions, breaking spherical symmetry and leading to  l(l+1)-degenerate electronic potential energy surfaces. This degeneracy leads to a non-additive interaction potential, where the full interaction between impurity and bath depends explicitly on the positions of each bosons. To capture these effects, we employ a multichannel version of the functional determinant approach for bosons  and scattering theory, revealing how anisotropy and non-additivity shape the absorption spectrum of a Rydberg impurity in an ideal BEC. 

The same framework is used to describe the dephasing dynamics of a Rydberg impurity in a thermal bosonic bath. This dephasing, measurable via Ramsey spectroscopy, is of particular interest for quantum information applications.