Quantum Dynamics in Ultracold Rydberg Atomic Gases

Abstract

Engineering interactions in ultracold atomic systems is the primary focus of AMO physics in the recent times, which opens up various possibilities to explore exotic quantum many-body phases. Ultracold Rydberg AMO provides us with a wide scope of research. We can manipulate the existing systems to form new systems having exciting dynamics. A two-level atom is well explored when studying its interaction with a classical field, but if we adjust the system to increase the number of atoms and make them interact, we attain different and interesting dynamics. One can even adjust it to change the classical field to quantized, leading to novel dynamics. In this thesis, we explore different aspects of the two-level scheme, from single atom – light dynamics to many-atoms – light dynamics. We also explore quantized field and compare the definitions of basic parameters such as blockade radius in a quantized field to that in a classical field. For the purpose of two-level scheme, we develop our studies using the time-dependent Schrödinger equation for non-dissipative systems to the master equation for dissipative systems. In addition to the two-level scheme, we touch upon the three-level scheme and four-level scheme, studying the exotic nature of the effective interaction curve in these systems. For the purpose of the three-level and four-level scheme, we limit our analysis to numerical solutions of the master equation. Our goal is to explore different aspects of AMO ultracold physics in the realm of Rydberg atoms. We have attained interesting and novel dynamics in few-body systems and many-body systems while studying the two-level scheme. We have also attained interesting results while studying effective interactions in three-level and four-level scheme. This thesis opens up new directions of research such as attaining a potential system for exploring the collapse and revival behavior and studying entanglement, or extending the Jaynes-Cummings model to many atoms system and getting new dynamics. It even acts as a motivation for considering three-body interactions for three-level atoms