Stability of quasicrystalline ultracold fermions to dipolar interactions

TL;DR

This study investigates how long-range dipolar interactions influence the stability and phase diagram of quasicrystalline phases in ultracold fermions within quasiperiodic optical lattices, revealing stabilization of intermediate phases and new localization phenomena.

Contribution

It provides the first detailed analysis of the effects of dipolar interactions on quasicrystalline phases, including the emergence of resonance-like behavior and interaction-induced localization.

Findings

Dipolar interactions stabilize the intermediate phase.

Strong interactions induce density oscillations resembling resonances.

Deep primary lattices can localize particles without quasiperiodicity.

Abstract

Quasiperiodic potentials can be used to interpolate between localization and delocalization in one dimension. With the rise of optical platforms engineering dipolar interactions, a key question is the stability of quasicrystalline phases under these long-range interactions. In this work, we study repulsive ultracold dipolar fermions in a quasiperiodic optical lattice to characterize the behavior of interacting quasicrystals. We simulate the full time evolution of the typical experimental protocols used to probe quasicrystalline order and localization properties. We extract experimentally measurable dynamical observables and correlation functions to characterize the three phases observed in the noninteracting setting: localized, intermediate, and extended. We then study the stability of such phases to repulsive dipolar interactions. We find that dipolar interactions can completely alter the shape of the phase diagram by stabilizing the intermediate phase, mostly at the expense of the extended phase. Moreover, in the strongly interacting regime, a resonance-like behavior characterized by density oscillations appears. Remarkably, strong dipolar repulsions can also localize particles even in the absence of quasiperiodicity if the primary lattice is sufficiently deep. Our work shows that dipolar interactions in a quasiperiodic potential can give rise to a complex, tuneable coexistence of localized and extended quantum states.