Etude d'états topologiques de la matière dans un gaz atomiques de dysprosium

Probing topological phase transitions and critical physics with ultracold atomic Dysprosium

• Auteur / Autrice : Nehal Mittal
• Direction : Sylvain Nascimbene
• Type : Projet de thèse
• Discipline(s) : Physique
• Date : Inscription en doctorat le 01/09/2022
• Etablissement(s) : Université Paris sciences et lettres
• Ecole(s) doctorale(s) : École doctorale Physique en Île-de-France (Paris ; 2014-....)
• Partenaire(s) de recherche : Laboratoire : Laboratoire Kastler Brossel
• Partenaire(s) de recherche : établissement opérateur d'inscription : Ecole normale supérieure

Mots clés

Mots clés libres

Topologie

Effet Hall quantique

Atome ultrafroid

Dysprosium

Topology

Quantum Hall Effect

Ultracold atoms

Entanglement Hamiltonian

Topological phase transition

Résumé

L'objectif de cette thèse est de sonder la physique topologique à l'aide de Dysprosium ultrafroid. En utilisant le spin de Dysprosium dans son état fondamental, nous avons sondé l'effet Hall quantique, en observant les modes de bord chiraux balistiques, les orbites cyclotron/saut, Lowest Landau Level (LLL), Local Chern Marker etc. Pour la thèse, nous prévoyons d'aller en régime d'interaction pour sonder l'effet Hall quantique fractionnaire.

Scienti fic context: Since the observation of Bose-Einstein condensation in 1995, the research field of ultracold atomic gases expanded towards the study of various types of complex quantum systems. Among them, the so-called topological states of matter (for which the 2016 Nobel prize in physics was awarded to J. M. Kosterlitz, D. Haldane and D. J. Thouless) recently attracted a lot of e orts, due to the very exciting and peculiar physical behaviours expected in such systems, such as the possible occurrence of anyons, which are quasi-particles that exhibit neither bosonic nor fermionic quantum statistics. Topology arising from light-spin coupling: Our experiment, which produces ultracold samples of atomic Dysprosium (both bosonic and fermionic isotopes), aims at realizing atomic instances of topological phases of matter. The basic ingredient required to induce a non-trivial topology is to couple the internal spin of the atoms with their movement, resulting in an artifi cial gauge eld. The speci c electronic structure of Dysprosium allows us to efficiently couple the spin to light and create gauge fields of strong amplitude. Thesis project: The experimental setup was built over the last years, and we now routinely produce ultracold samples of Dysprosium [1, 2]. In the last two years, we have performed several projects based on the manipulation of the spin degree of freedom via coherent light eld close to a narrow optical transition, leading to the production of highly non-classical spin states [3, 4, 5, 6]. We have recently extended these techniques to induce a coupling between the atom's motion and its spin. Such a coupling leads to an effective magnetic fi eld at low energy, such that one recovers the physics of the quantum Hall effect. In particular, we have been able to probe the underlying topological structure of quantum states, via the quantization of the Hall response [7]. We recently generalized this approach to engineer a quantum Hall system in a cylindrical geometry, which allowed one to reveal the band topology in a simple manner (`Laughlin pump' experiment) [8]. In the first part of the PhD, we will investigate the physics of weakly interacting gases of bosonic atoms in such a synthetic quantum Hall system. The atoms will organize into a Bose-Einstein condensate, pierced with a regular lattice of quantized vortices. The expected phenomenology of this system corresponds to the behaviour of super fluid liquid Helium or superconductors in a magnetic fi eld. The second part of the PhD will be devoted to the study of the strongly interacting regime. This regime will be reached with dilute gases, such that the quantum orbitals are not macroscopically fi lled. We expect to produce analogs of fractional quantum Hall states encountered in 2D electron gases under strong magnetic fields. These phases of matter have a very rich and exhibit a peculiar physical behaviour, e.g. elementary excitations with anyonic quantum statistics. We also plan to use fermionic atoms, also subjected to a light-induced gauge eld, to generate a different class of strongly-interacting topological phases, namely topological superconductors.