Manipulating Ultracold Atoms --- from One to Many

William Marsh Rice University, Houston TX

Investigators

Abstract

In the realm of physics and many other fields of natural science, reductionism --- a complicated system can be reduced to simpler constituents and the properties of the whole can be inferred from the study of each constituent parts --- has played an important role. However, there also exist many examples where a reductionistic method does not provide a complete picture. As more and more parts are added, new phenomena may emerge at different stages and these new phenomena cannot be fully understood from the properties of the simpler system that precedes it. Such emergent behavior is well known in science. The system of cold atoms represents an ideal platform to investigate the emergent phenomena. Experimentally, several labs have developed techniques to accurately control the number of atoms in their atom traps, from one, to a few, to many. This is made possible by the exquisite controllability of cold atoms. The proposed research aims to provide a theoretical understanding of various cold atomic systems. The central theme is to study how the properties of single atoms affect the physics of a few-atom or a many-atom system. This research is of fundamental nature --- the basic science of cold atoms. Fundamental issues that will be addressed include: How does an atom or an ensemble of atoms interact with a quantum field of light? Will an ensemble of atoms that are interacting with each other and prepared out of equilibrium reach equilibrium? If so, how? When the inter-atomic interaction becomes very strong, what exotic properties will emerge? Many of these issues are at the forefront of the field of cold atoms and quantum many-body systems. This work will therefore significantly advance the relevant fields. In this project, the connection among single-body, few-body and many-body physics using the platform of cold atoms is investigated. There are four main topic areas: cold atoms inside an optical cavity, coupling both the internal and the external degrees of freedom of the atoms; cold atoms subject to synthetic spin-orbit coupling; quantum magnetism with 1D quantum gases; and far-off-equilibrium quantum dynamics. Each of these topics represents a relatively independent research direction, though there also are strong connections among different topics. A number of different theoretical techniques will be used to tackle these problems, including the mean-field method, the variational method, perturbation calculations, exact diagonalization, time-evolving block decimation (TEBD) for example.