Artificial gauge fields and quantum hall physics in optical lattices

The engineering of artificial gauge fields for ultracold atoms in optical lattices opens a new chapter for the quantum simulation of quantum Hall physics. Motivated by recent advances and refined techniques in controlling quantum gases in optical lattices, this thesis explores how the spatio-temporal control of optical lattice systems can be exploited for the engineering of artificial gauge fields, rapid state preparation, and for controlling and probing integer and fractional Chern insulator states and their excitations. The first example is about the implementation of local magnetic fluxes piercing single lattice plaquettes (analogous to those created by a thin solenoid), which plays an important role in Laughlin's gedankenexperiment of quantum Hall physics. By combining Floquet engineering of artificial magnetic fields with the ability of single-site addressing in quantum gas microscopes, we propose a scheme for the realization of such local solenoid-type magnetic fields in optical lattices. We show that it can be employed to manipulate and probe elementary excitations of a topological Chern insulator, including the quantized charge pumping along tailored paths inside the bulk, as well as the controlled population of edge modes. This possibility is due to the fact that it is the artificial vector potentials (in the form of Peierls phases) that are controlled experimentally, i.e.\ both the artificial magnetic and electric fields associated with it, rather than the artificial magnetic field alone. Based on such an observation, then we investigate protocols for adiabatic state preparation via ramping artificial gauge potentials in the form of Peierls phases. Taking an interacting bosonic flux ladder as a minimal model, we find that the time required for adiabatic state preparation dramatically depends on which pattern of Peierls phases is implemented. This can be understood intuitively by noting that different patterns of time-dependent Peierls phases that all give rise to the same magnetic field ramp, generally lead to different artificial electric fields during the ramp. As an intriguing result, we find that an optimal choice allows for preparing the ground state almost instantaneously in the non-interacting system. We show that this effect can be related to the concept of counterdiabatic driving. Remarkably, we find extremely short preparation time also in the strongly-interacting regime. This finding opens new possibilities for robust state preparation in atomic quantum simulators. The recent progress in engineering topological band structures in optical-lattice systems makes it promising to study fractional Chern insulator states in these systems. In the rest of the thesis, we consider a realistic finite system of a few repulsively interacting bosons on a square lattice with magnetic flux and sharp edges, as it can be realized in quantum-gas microscopes. We investigate under which conditions a fractional Chern insulator state corresponding to the Laughlin-like state at filling $\nu=1/2$ can be stabilized and its fractional excitations probed. Using numerical simulations, we find an incompressible bulk density at the expected filling for systems, whose linear extent is as small as 6-8 sites. This is a promising result, since such small systems are favorable with respect to the required adiabatic state preparation. Moreover, we also see very clear signatures of excitations with fractional charge in response both to static pinning potentials and dynamical flux insertion. These observations are robust against changes in various system parameters. Our results suggest that signatures of both a fractional Chern insulator state and its fractional excitations can be found under realistic experimental conditions.

Author dc:creator

• Wang, Botao

Advisor dc:contributor.advisor

• Eckardt, André

Licence dc:rights.uri

• https://creativecommons.org/licenses/by/4.0/

Language dc:language.iso

en

Identifier URI

http://dx.doi.org/10.14279/depositonce-15355

OAI identifier oai:identifier

oai:depositonce.tu-berlin.de:11303/16578