Atoms in the lowest Landau level of a synthetic erbium quantum Hall system

Abstract

This thesis presents results on an experimental realisation of a synthetic Landau like system using ultracold erbium atoms in a two-dimensional quantum Hall ribbon geometry. The scheme used to realise artificial magnetic fields is based on spin-orbit coupling and uses a synthetic dimension encoded in the 13 internal Zeeman states of the erbium atom in its electronic ground state. The spin-orbit coupling is realised by two-photon Raman transitions and effectively creates unique pairs between the internal Zeeman state of atoms and its external momentum state. Therefore the atom’s momentum is bound to a specific position in the synthetic dimension and the spin-orbit coupling can be interpreted as a vector potential in the Hamiltonian. The spatial dependence of the vector potential required to generate artificial magnetic fields is realised by the momentum dependence of the position in the synthetic dimension, or in other words the internal Zeeman state. <br /> The experimental apparatus is introduced and the main properties are presented. The creation of a Bose-Einstein condensate, which lies at the very heart of this experiment, is introduced. The main properties of the experiment are presented as well as characterising measurements. <br /> The basic theory behind the quantum Hall effect for a two-dimensional electron gas subject to a perpendicular real magnetic field is introduced and characteristic observables are derived to create a basic understanding of the underlying physics before the transition to synthetic magnetic fields is introduced. Spin-orbit coupling is introduced in its use within the scope of this thesis by presenting the underlying theory following earlier work where another atomic species, dysprosium, was used. The implemented scheme allows for a system which follows a Landau like dispersion relation with clear distinct behaviour for the inner bulk region and outer edge regions. The behaviour of the bulk and the edge mode indicates the non-trivial topology of the system. Measurements including dispersion relations and excitation into higher energy bands are performed and show the expected and distinct behaviour of atoms in the bulk and near the edges respectively. The equivalent to closed cyclotron orbits is observed inside the bulk region, whereas skipping orbits are observed for edge regions. <br /> In addition to the observation of flat dispersion relations and cyclotron orbits the mobility and a local Chern marker are determined. It will be shown that the mobility of the synthetic system follows the behaviour of a real quantum Hall system. The local Chern marker is determined to have a value close to the value expected for a Landau system with infinite size in the bulk region. This shows that the synthetic dimension with its 13 positions is large enough to observe a clear difference between bulk and edge behaviour. <br /> The last section presents first measurements of a chiral edge current in a system of the size, which is presented in this thesis.