Quantum State Control of Two Interacting Rydberg Atoms

Abstract

The field of ultracold Rydberg atoms has made enormous progress in recent years and emerges at the forefront to probe quantum properties of matter. Individually controlled Rydberg atoms prove to be a versatile platform to test phenomena significant to condensed matter physics, quantum optics, atomic and molecular physics. Systems of many-body interacting Rydberg atoms have an enormous potential to solve long-standing problems in physics. On the other hand, the interest in two-body Rydberg systems is motivated by applications of local quantum control and deterministic local state preparation in a larger array. Our work pertains to manipulating the state dynamics of the two-atom system which is achieved by tuning the atom-light couplings and detunings, both in weakly and strongly interacting systems. First, we investigate the effect of an offset in Rabi coupling between two Rydberg atoms both in coherent and dissipative systems. The interplay of Rabi frequency offset and tunable interactions reveals fascinating features. In the strongly interacting regime, we find a novel phenomenon of Rydberg-biased freezing where amplification of the Rabi frequency of one atom suppresses the dynamics in the second atom. In the weak interaction regime, we discuss the double excitation dynamics as a function of interaction for very small offsets in the Rabi frequencies. We further propose a dynamic control over quantum correlations upon dynamic variation of the Rabi frequency of the second atom. In the second part of the thesis, we use time-dependent atom-laser detuning to manipulate collective quantum states. We first consider a linear variation of the detuning. We observe that for different values of Rydberg-Rydberg interaction, the system can emulate different three-level Landau-Zener models such as bow-tie and triangular Landau-Zener models. Our central result is that Landau-Zener excitation dynamics exhibit nontrivial dependence on the initial state, the quench rate, and the interaction strengths. We further use analytical techniques such as Adiabatic Impulse approximation in the strongly interacting regime to capture the non-trivial dynamics. In the last section, we consider the application of periodic atom-laser detuning on the pair of Rydberg atoms. We review the single two-level periodically driven atom and highlight the similarity of the final state population with the intensity pattern obtained in an antenna array. We further use a single atom to characterize the phenomenon of population trapping and dynamical stabilization using Floquet quasienergies and the Inverse participation ratio. In the two atom setup, we test the validity of the Adiabatic Impulse approximation under periodic driving. We further explain the interesting phenomenon of a state-dependent population trapping that emerges due to Rydberg-Rydberg interactions. We specify the regimes where populations in experimentally significant states such as product and Bell entangled states can be frozen for a significantly longer duration. This thesis is a study of the manipulation of coherent dynamics of a setup of two two-level Rydberg atoms. We achieve the above goal by tuning the atom-light couplings and detunings, both in weakly and strongly interacting systems. Our study shows that the minimal setup can be used to create non-trivial dynamics and exert local control, or as an atom-interferometer. Our investigations also serve as a building block that can be extended to multi atom setups.