Dynamics and Geometry in Ultracold Atoms

Chenwei Lv, Purdue University

Abstract

The rapid developments in technique bring simulation of quantum dynamics and precise coherence control to a new regime. The Atomic Molecular and Optical (AMO) platform provides a highly tunable means to control unitary and non-unitary time evolution. While the dissipation causes decoherence of a quantum system and is undesired in conventional understanding, manipulating dissipation in a controllable manner allows us to access a variety of peculiar non-Hermitian phenomena. This dissertation focuses on emergent geometry from SU(1,1) symmetry and non-Hermitian physics, two highly entangled concepts with different realizations in the AMO system. Like SU(2) symmetry, a fundamental symmetry in various physical systems, SU(1,1) symmetry plays an important role in coherent control of quantum dynamics, dynamical instability, emergent curved space, and non-Hermitian phenomena. In Chapters 2 and 3, we show how different geometric structures, including hyperbolic spaces and anti-de Sitter spacetimes, are generated by SU(1,1) symmetry. We also discuss several examples of coherent control of quantum systems based on their geometric representations. In Chapters 4 and 5, we move on to non-Hermitian physics. Chapter 4 discusses the quantum simulation of curved space in lattice systems. On the one hand, we demonstrate the simulation of any Riemann surfaces using a lattice system with tunable tunnelings. In particular, we consider hyperbolic spaces and show the emergences of the Efimov-like state and funneling effect on lattices. On the other hand, we build a duality between curved space and the non-Hermitian system, using a non-Hermitian generalization of the tight-binding model with chiral tunneling as an example. This duality and the highly controllable ultracold systems in laboratories allow experimentalists to simulate curved spaces using dissipation. Chapter 5 studies dissipations in ultracold molecules. While the ultracold molecules intrinsically suffer from losses caused by reaction or formation of complexes, we show that universality exists in ultracold reactive molecules. We apply contacts, a central quantity that captures many-body correlations in dilute quantum systems, to establish universal relations between various physical observables in reactive molecules. Ultracold molecules have emerged as a powerful platform in quantum simulation. The universal relations, which hold for any particle number, temperature, or interaction strength, provide physicists with a unique tool to explore and engineer ultracold molecules. In Chapter 6, we also point out that the unit rate of reaction of ultracold molecules at a short distance amounts to a perfect event horizon. The characteristic length scale of the intermolecular potential plays the role of the horizon’s radius. Therefore, the highly controllable ultracold molecules can be implemented as a simulator of black hole physics.

Degree

Ph.D.

Advisors

Zhou, Purdue University.

Subject Area

Physics|Energy|Astronomy|Astrophysics|Electromagnetics|Low Temperature Physics|Mathematics|Quantum physics|Theoretical physics

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