Shengjie YU

PhD Student

Resarch activities at CPHT: Condensed Matter

Sujet de thèse : "Bosons ultra-froids dans des quasicristaux optiques"
Directeur de thèse : Laurent Sanchez-Palencia

Thesis: "Quantum Information and Entanglement in Correlated Quantum Matter"
Advisor: Laurent Sanchez-Palencia

Abstract

The aim of this project is to study the physics of quasiperiodic systems within the context of atomic, molecular, and optical (AMO) physics. We shall consider two ways of realizing quasiperiodic systems, both allowed by the high degree of control in ultracold-atom systems.

On the one hand, we shall consider cases where the quasiperiodic order is imposed by an external potential, ie optical laser fields in adequate geometries. This allows one to decouple the stability problem of the quasiperiodic structure from the dynamics of carriers (ie, here, the atoms). The latter are then subjected to a pure, defectless quasiperiodic potential, which, in addition, does not suffer thermal, phonon-like, fluctuations. The unique possibility to realize such systems is a major asset of ultracold-atom systems, and more generally of AMO systems, such as photonic systems, for instance. In the context of periodic systems, this has paved the way to the first, nonunambigously, demonstration the superfluid-to-Mott insulator transition in a pure realization of the Bose-Hubbard model (Greiner et al., 2002). Fermionic Mott insulators have been more recently demonstrated (Jördens et al., 2008; Schneider et al., 2008) as well as the onset of antiferromagnetic ordering (Mazurenk et al., 2017) in pure realizations of the two-dimensional Fermi-Hubbard model. Such an approach allows one to realize exact standard models of quasiperiodic systems. Here, we shall study localization transitions and fractal properties of Bose gases in quasicrystal potentials at both single-particle and many-body levels. Use of a combination of exact diagonalization, meanfied calculations and exact quantum Monte Carlo approaches will allow us to draw a complete picture. Special attention will be devoted to understand the nature of the Bose glass transition and to identify relevant probes accessible in current state-of-the-art ultracold-atom quantum simulators.

On the other hand, we shall study the quantum dynamics of self-organized quasicrystals, i.e. without imposing the quasicrystalline order by an external potential. Examples of structured interaction potentials that allow this have been demonstrated for classical systems (Barkan et al., 2014). However, the question whether a quasicrystalline order survives quantum fluctuations and can coexist with a significant superfluid fraction remains open. A primary motivation of this second part of the project is to explore possibilities to realize such self-stabilized quasicrystalline structures in AMO systems, and in the first place ultracold atoms. For instance, it was recently demonstrated that long-range interactions allows one to stabilize periodic structures, coexisting with a finite superfluid fraction, hence realizing a supersolid phase (Tanzi et al., 2019 ; Böttcher et al., 2019 ; Chomaz et al., 2019). Finding a realistic scheme that can be resonnably implemented in AMO experiments is definitely the most challenging aspect of the project. If successful, it would be a major result, which would pave the way to a number of further studies, both theoretical and experimental. It would then become possible to study the structural and dynamical properties of artificial quasicrystals in well-controlled and isolated AMO systems, resumably also in regimes that may not be accessible to solid-state systems. Careful analysis of the possibilities will be conducted before starting the concrete work of this part (planned for the second part of the PhD thesis). It is, however, not a strict pre-requisite for developing this part of the PhD project. There are known long-range interacting potentials that allow for the stabilization of a quasicrystalline structure. From a theoretical point of view, it remains of fundamental interest to understand the quantum dynamics of such systems. A fundamental question we shall address is to understand whether superfluidity can coexist with a self-organized quasicrystalline order. It would be a kind of quasiperiodic counterpart of the supersolid phase recently observed in dipolar quantum gases.