Rydberg Electrons as a Probe for Ultracold Systems

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This project seeks to utilize Rydberg excitations, promotion of an electron in an atom to a very high energy level, to probe novel properties of ultracold gases. Rydberg atoms within an ultracold gas move very slowly, resulting in long collision times and large cumulative effects of even very weak interatomic forces. The large spatial extent of the Rydberg electron also renders the Rydberg atom sensitive to local field environments. The combination of these two factors, slow speed and large spatial volume, makes ultracold Rydberg atoms ideal probes of delicate correlations and other novel phenomena within the ultracold environment. During the past few years, experimental progress in preparing and manipulating ultracold Rydberg atoms has led to many new developments in Atomic, Molecular, and Optical (AMO) Physics. For example, Rydberg atoms have made possible the detection of a new class of long-range molecules, the so-called "trilobite"-like molecules, and of fast quantum gates relevant to the quantum information revolution. They are now utilized to make small regions of an otherwise opaque gas transparent, using what is known as electromagnetically induced transparency. Rydberg atoms can also generate single photon sources and mediate photon-photon interactions. Accordingly, ultracold Rydberg atom research bridges AMO, condensed matter and mesoscopic physics, and quantum information science, as well as ultracold chemistry. This theory project models the interactions of Rydberg electrons with their environment in order to better understand and predict observed spectra, which are expected to depend sensitively on the distribution of atoms in the gas, and enhance their utilization in the range of areas mentioned above. This research program explores how Rydberg electrons can be used to investigate few- and many-body phenomena. Rydberg electrons provide a low-energy and well-localized probe for AMO, condensed-matter, and chemical systems. While their wave function extends to large volumes, Rydberg electrons, being excited near the ionization threshold, have a small kinetic energy that minimally perturbs a system to be investigated. Rydberg electrons can scatter from one, two, or many ground-state atoms depending on the density of neighboring atoms. The effect of those scatterers on the Rydberg electron wave function can be used to study the properties of the ground-state atoms, such as their distribution and correlation, including in degenerate Bose or Fermi gases. In particular, the special case of two scatterers can shed light on Efimov physics, a three-body system with peculiar properties introduced in nuclear physics. To carry out this research, accurate wave functions are essential ingredients that current methods struggle to provide. Here, a non-perturbative approach based on Green's functions to compute wave functions and potential energy surfaces for Rydberg trilobite-like dimers, trimers, etc., will be developed. These accurate wave functions will then be employed in the calculation of photo-association (PA) spectra whose detailed lineshapes will unlock the information about the ground-state atoms, including their correlation (from two, three, four, or N-body). Finally, together with the computation of the Efimov wave functions, the probing of those elusive states with spectroscopic accuracy will be made possible.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.