STAGE Pairing and topological phases in cold atoms with long-range interaction

Correlated quantum systems in low dimensions show fascinating properties that distinguish them

from their three dimensional counterparts as a consequence of the enhancement of quantum

fluctuations. Interacting fermions and bosons in one-dimension (1D) can exhibit many exotic

phases of matter. Although short-range interacting particles in 1D are rather well understood,

much less is known for long-range interacting systems.

Seminal efforts are underway in the control of artificial quantum systems to simulate arbitrary

model Hamiltonians which are now barely accessible to classical computation methods.

Ultra-cold dipolar or Rydberg-atom gases atoms can realize Bose gases with long-range

interactions.

In this internship we would like to study 1D hardcore bosons interacting via a long-range

potential. Taking only into account nearest and next-nearest interactions, it has been shown

recently that two distinct liquid phases emerge among which a cluster quantum liquid phase

where the essential granularity in the liquid is given not by individual atoms but rather by cluster

of two atoms like in a superconducting paired phase [1]. These two liquid phases are separated

by a quantum critical point with an emerging Ising degree of freedom. We want first to

characterize the topological properties of these phases by comparing them to well-tabulated

1D topological superconducting phases in condensed matter systems