Two-dimensional Dipolar Quantum Gases: Fluctuations and Orders.

Ordering in two-dimensional (2D) worlds is fundamentally different from what we know in 3D: Thermal fluctuations preclude conventional long-range order. An unconventional ordering mechanism based on topological defects may occur. The resulting order is topological, remains fluctuating, and intimately depends on the interparticle interactions.

Many systems, including frustrated magnets, superconductors, colloids, and quantum gases, exhibit such orders.

Their topological origin confers them exotic properties, of high technological interest, yet still partly enigmatic.In ultracold Bose gases of magnetic atoms, short-range and long-range anisotropic dipolar interactions compete.

Recently, such gases were observed to stabilize despite attractive mean interactions, through the effect of quantum fluctuations.

This fueled the discovery of several new phases of matter in such 3D gases, a prominent example being supersolids, which show simultaneous superfluid and crystal orders.

Building on my expertise in both fields, I propose to expand the rich physics of magnetic-gas orders to the exotic and yet unexplored 2D universe, in a new experimental setup.

Due to the unique variety of orders featured in magnetic quantum gases – superfluid, crystal, plus their anisotropic features (orientational orders) – and their remarkable intertwining, an unprecedented playground for 2D topological ordering will be at hand. By exploring the phase diagram, I will aim to bring a deep understanding of ordering and reveal new quantum phases.

First, I will focus on the repulsive regime and characterize the interplay between long-range anisotropic interactions and topological superfluidity. I will then explore the fluctuation-stabilized attractive regime. Here, I will map the novel variety of orders that 2D worlds provide.

Focusing on their ordering mechanism will reveal unprecedented phenomena, such as topological supersolidity and (superfluid) liquid-crystals, opening new research avenues.