Atomic Chains with Rydberg Excitations: Bose-Hubbard Parameters to Correlation Dynamics

Abstract

Synthetic quantum systems are simplified versions of real-world, complex, quantum many-body systems. They provide a versatile testbed for understanding the complex phenomenons of condensed matter physics, nuclear physics, high energy physics, and chemistry. In the context of quantum many-body physics, these systems have mainly been used to study various spin models and Hubbard-type models. The major advantage of synthetic quantum systems is the possibility to have control over system parameters such as dimension, scale, the strength of interaction, and range of the interaction. The tremendous experimental progress in the area of laser cooling and trapping has boosted the development of various synthetic quantum systems based on different architectures. The platforms based on ultracold atoms, ions, superconducting circuits, photons have emerged in the past two decades and have succeeded in revealing exotic quantum phenomena. Among all the platforms, Rydberg atom-based quantum systems stand out because of strong controllable interaction, single-site addressability, scalability, and large coherence times. These systems have been used to study both the ground state physics as well as non-equilibrium dynamics of various spin models. This work is focused on utilizing the properties of Rydberg atoms along with other tools to achieve control over the interactions, population dynamics, correlations, and entanglement in the system. In three independent setups, we show how the specific properties of the system along with the properties of Rydberg atoms can be used to achieve the same. Towards that goal, in Chapter 1, we give a brief overview of the developments in the field of ultra-cold atoms. We then discuss the basic properties of Rydberg atoms such as Rydberg blockade, Rydberg dressed interaction, Bose-Hubbard model, photonic crystal waveguides. These properties will be used in subsequent chapters. In chapter 2, we calculate the Hubbard parameters for Rydberg-dressed interaction using maximally localized Wannier functions. We show that by varying the external laser parameters we can vary the shape of Rydberg-dressed potential such that the extended Bose-Hubbard model can be realized. We also identify the dominant density-assisted tunneling processes for Rydberg-dressed interaction. In chapter 3, we study a chain of Rydberg atoms in which the detuning is periodically varied in time. We identify the correlated Rabi oscillations emerging due to Rydberg interaction and study the effect of periodic driving onto the correlation functions characterizing the correlated Rabi oscillations. Chapter 4 studies the single excitation dynamics of an atomic excitation coupled to a photonic crystal waveguide. The coupling of atoms to photonic modes of the photonic crystal waveguide gives rise to an effective exchange Hamiltonian with a controllable exchange interaction range. We study the excitation dynamics as a function of exchange interaction range and characterize the change in the dynamics using various parameters. In the final chapter, we introduce one more excitation to the system and study the effect of that excitation on the dynamics. Firstly, for the non-interacting excitations, we show the anti-bunching dynamics and quasi-localization. Secondly, for the Rydberg excitations, we take into account the van der Waals interaction and study its effect on the excitation dynamics. By varying the strength of vdW interaction we go from anti-bunching dynamics to bound state dynamics. We also investigate the effect of initial separation on the population dynamics and entanglement.