In this work, we investigate the dc electric-field dependence of two F\"orster resonant processes in ultracold
85Rb, $37{D}_{5/2}+37{D}_{5/2}\ensuremath{\rightarrow}35L(L=O,Q)+39{P}_{3/2}$, as a function of the atomic density. At low densities, the
39P3/2 yield as a function of electric field exhibits resonances. With increasing density, the linewidths increase until the peaks merge. Even under these extreme conditions, where the F\"orster resonance processes show little electric-field dependence, the
39P3/2 population depends quadratically on the total Rydberg atom population, suggesting that a two-body interaction is the dominant process. In order to explain our results, we implement a theoretical model which takes into account the multilevel character of the interactions and Rydberg atom blockade process using only atom pair interactions. The comparison between the experimental data and the model is very good, suggesting that the F\"orster resonant processes are dominated by two-body interactions up to atomic densities of $3.0\ifmmode\times\else\texttimes\fi{}{10}^{12}\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$.
Systems of cold, interacting Rydberg atoms are of interest because they exhibit a wide range of collective quantum phenomena. This thesis describes experimental and theoretical work related to these systems with an emphasis on two phenomena: Rydberg excitation blockades and quantum-state-changing collisions. I begin by presenting a detailed calculation of the interaction energies of two Rydberg atoms for a variety of orientations, quantum states, and applied electric fields. The calculated energies are used to interpret the experimental results that follow. I then describe measurements showing that the widths of the distributions of Rydberg excitation number are related to the effectiveness of a Rydberg excitation blockade. These distributions are investigated as a function of principal quantum number, n, and applied electric field. In the presence of a Forster resonant field, sub-Poissonian distributions are measured. I next present a spectroscopic measurement of the energy level shift of a system of atoms which collectively shares two Rydberg excitations. The qualitative nature of the shift depends sensitively on the type of interactions between the atoms (van der Waals or dipole-dipole) and may be changed by changing the quantum state or applied electric field. This measurement provides the first spectroscopic proof that Rydberg excitation blockades are operative. Finally, I describe measurements of the probability for quantum state-changing and Penning-ionizing collisions to provide evidence for intrinsic, electric field-free-interaction resonances and complex many-body interactions in systems of cold Rydberg atoms.
Long-range interactions between cold Rydberg atoms, which are used in many important applications, can be enhanced using F\"orster resonances between collective many-body states controlled by an external electric field. Here we report on the first experimental observation of highly resolved radio-frequency-assisted F\"orster resonances in a few cold Rb Rydberg atoms. We also observed radio-frequency-induced F\"orster resonances which cannot be tuned by a dc electric field. They imply an efficient transition from van der Waals to resonant dipole-dipole interaction due to Floquet sidebands of Rydberg levels appearing in the rf field. This method can be applied to enhance the interactions of almost arbitrary Rydberg atoms with large principal quantum numbers.
We examine state mixing in a dense, cold Rydberg gas. Cold Rb atom clouds in an optical dipole trap are excited into
nD5/2 Rydberg levels using narrow-bandwidth laser pulses. For
n=43, two atoms excited to
43D5/2 states can be converted to
41F7/2 and
45P3/2 product states via a F\"orster resonance. We find, unexpectedly, that up to 50% of the Rydberg atoms are detected in such product states after only 100 ns of interaction time. The experiment is modeled using many-body quantum simulations. To reproduce the mixing fractions measured near F\"orster resonances, we use an exact, nonperturbative many-atom Hamiltonian in which product states are treated on an equal basis with the laser-excited
nD5/2 Rydberg level. Simplified many-body interaction models based on sums over pairwise atomic potentials cannot reproduce the measured mixing fractions.
In this work, we excite
nD5/2 Rydberg states in a dense and cold Rb atomic sample held in a 10.6 $\ensuremath{\mu}\mathrm{m}$ quasi-electrostatic trap using narrow-bandwidth laser pulses. Our goal is to study the F\"orster resonance process $n{D}_{5/2}+n{D}_{5/2}\ensuremath{\rightarrow}(n\ensuremath{-}2)F+(n+2){P}_{3/2}$ at zero electric field as a function of the total atomic density using pulsed-field ionization in the range
n=37−−47. Such a process is almost degenerate for
n=43. Younge and coworkers studied this process [K. C. Younge, A. Reinhard, T. Pohl, P. R. Berman, and G. Raithel, Phys. Rev. A 79, 043420 (2009)] and attributed the observed saturation to many-body effects. Our results show that as the ground-state atomic density increases, the
nD5/2 state population and the population transfer starts to saturate, which is consistent with the onset of Rydberg atom blockade and previously published results. However, since our experiment allows the independent measurement of the
nD5/2 and
(n+2)P3/2 state populations, we were able to obtain the
(n+2)P3/2 state population density dependence. Our results clearly show that the
(n+2)P3/2 state population depends quadratically on the total Rydberg atomic population, and consequently, the F\"orster resonance is a two-body process for a ground-state atomic density below $3\ifmmode\times\else\texttimes\fi{}{10}^{11}$ ${\mathrm{cm}}^{\ensuremath{-}3}$.