Resonant laser excitation of multiple Rydberg atoms are prohibited, leading to Rydberg blockade, when the long-range van der Waals interactions are stronger than the laser-atom coupling. Rydberg blockade can be violated, i.e., simultaneous excitation of more than one Rydberg atom, by off-resonant laser excitation, causing an excitation antiblockade. Rydberg antiblockade gives rise to strongly correlated many-body dynamics and spin-orbit coupling and also finds quantum computation applications. Instead of commonly used van der Waals interactions, we investigate antiblockade dynamics of two Rydberg atoms interacting via dipole-dipole exchange interactions. We study typical situations in current Rydberg atom experiments, where different types of dipole-dipole interactions can be achieved by varying Rydberg state couplings. An effective Hamiltonian governing underlying antiblockade dynamics is derived. We illustrate that geometric gates can be realized with the Rydberg antiblockade which is robust against the decay of Rydberg states. Our study may stimulate new experimental and theoretical exploration of quantum optics and strongly interacting many-body dynamics with Rydberg antiblockade driven by dipole-dipole interactions.
This thesis investigates new phenomena that arise when light is strongly coupled to an interacting atomic gas. For this, a new apparatus has been built which allows to create ultracold and dense atomic samples and to detect individual atoms in high-lying atomic states, so-called Rydberg atoms. Strong light-matter coupling is achieved using the collective coupling of the atomic cloud to the light field under conditions of electromagnetically induced transparency (EIT). In experiments on EIT involving non-interacting Rydberg states, we characterize the light-matter coupling and demonstrate the first combined optical and matter based probing of EIT. By coupling to strongly-interacting Rydberg states, we investigate the effect of interactions which we observe as a strong nonlinear optical \nresponse of the atomic gas as well as in the emergence of strong correlations between the hybrid quasiparticles associated with the strong light-matter coupling. We employ the nonlinear response of the atomic cloud to image Rydberg atoms immersed in the atomic cloud. In a theoretical proposal, we show that this novel imaging technique allows to investigate many-body Rydberg states with single particle sensitivity. Using the proposed imaging method, we demonstrate imaging of small numbers of Rydberg atoms with high time-resolution in single shot experiments. In experiments exploiting the dipolar exchange interaction between Rydberg atoms, we employ the new imaging technique to follow dipole-mediated transport of Rydberg excitations through the cloud. The transport dynamics is determined by the continuous spatial projection of the electronic quantum state under observation and features an emergent spatial scale of micrometer size induced by Rydberg-Rydberg interactions.
In this thesis I present several theoretical methods to explore the excitation dynamics of Ultracold Rydberg systems in various regimes. For some applications the details of interactions between Rydberg atoms have to be carefully examined, while for others, the many-body aspect of Rydberg excitation may be crucial. In both cases, the basic prerequisite is to know the interactions sufficiently well. I will review the basic concepts how to evaluate molecular potentials in various Hund's cases and approximations. Long-range Rydberg-Rydberg interactions between Rydberg atoms induce ℓ-mixing which in certain situations gives rise to molecular resonances. For these resonances, we calculate long-range potentials in Hund's case (c) by diagonalization of an interaction matrix. The excitation dynamics of the resonances is always modeled as pair excitation. At high principal quantum number n, the interactions between Rydberg atoms can blockade the excitation of many surrounding atoms in the range of few μm. The atoms within this range are strongly correlated so that many-body treatments are, in general, needed. To describe this blockading effect and other manifestations of the collective behavior of Rydberg excitation, such as the many-body Rabi oscillations, spatial correlations between atoms and the fluctuations of the number of excited atoms, I have used three different approaches. In the mean-field approach the interactions between different atoms is modeled by a distribution of mean-field shifts for which a distribution of probabilities is calculated, A good agreement between the theoretical model and experimental measurements is found. To study the correlations between atoms the many-body wavefunction is numerically computed. The possibility of observing the many-body Rabi oscillations of Rydberg excitation and other aspects of many-body dynamics is analyzed. Although strong interactions cannot be treated perturbatively other expansions may be feasible. I will show that the expansion in powers of the single atom Rabi frequency can be evaluated in the interaction and Heisenberg picture. The expansion is expected to behave well for arbitrary strong interactions. ^