Artificial gauge fields on neutral atoms

The remarkable advances of the last decade in the manipulation of ultracold atomic systems have opened a novel field at the interface of quantum information, quantum optics and many-body physics. The unprecedented precision on the control of atomic gases allows one to shed a new light on fundamental problems originating from condensed matter physics, while benefiting from different observables to characterize the system. The goal of our project is to use two-dimensional gases of rubidium atoms to simulate the fractional quantum Hall effect that occurs when a planar electron fluid is placed in a strong transverse magnetic field. Since the atoms are neutral, we must simulate the orbital magnetism at the origin of the quantum Hall effect by a mechanism that reproduces the action of the Lorentz force and the Aharonov-Bohm phase. We will use an artificial gauge field induced either by rotating the gas, or by using a `Berry-type' geometrical phase. We will address both the case of `mesoscopic' atomic samples (typically ten atoms) and of `macroscopic' ones (typically a few ten thousands atoms). In the mesoscopic case, we will start from a microtrap that we will set in rotation, and we will subsequently detect the position of each particle with a good spatial resolution. We will perform in parallel an exact numerical analysis, which will take into account the geometry of the setup and finite-temperature effects. This will allow for a direct and accurate comparison between theory and experiment, and a non-ambiguous identification of the strongly correlated states that will be produced. In the macroscopic case, we will use the new concept of flux lattice, i.e., a periodic distribution of light that provides a single-particle band spectrum with a structure and a topology analogous to the Landau levels of a charge in a magnetic field. We will explore the phase diagram of this new system in the presence of atomic interactions, and we will identify the region of parameters where correlated phases can emerge. We will develop several ways for detecting them experimentally, such as the search for edge states and the transposition to the real world of the gedanken experiment at the basis of the definition of entanglement entropy. The completion of this project will provide us with a quantitative characterization of robust correlated states in the presence of a strong magnetic field, for example the Laughlin state, which is emblematic of fractional quantum Hall physics. The ability to measure individual atomic positions will give access to quantities that are complementary to those obtained with condensed matter samples, usually based on transport measurements. On the long term this project will open several fascinating perspectives, such as the study of anyonic statistics and gauge fields with a richer structure, e.g. non-Abelian.