Non-local Order in Elongated Dipolar Gases

TL;DR

This paper investigates the quantum phase transition in elongated dipolar gases, revealing a non-local string order in the zigzag phase, and explores the associated edge states and experimental implications.

Contribution

It introduces a low energy effective theory showing long-range string order in the zigzag phase and confirms it with DMRG calculations, highlighting novel non-local order in dipolar gases.

Findings

Long-range string order characterizes the zigzag phase.

Zero energy edge states appear at phase interfaces.

Differences in tunneling spectra between bosonic and fermionic particles.

Abstract

Dipolar particles in an elongated trap are expected to undergo a quantum phase transition from a linear to a zigzag structure with decreasing transverse confinement. We derive the low energy effective theory of the transition showing that in presence of quantum fluctuations the Zigzag phase can be characterized by a long ranged string order, while the local Ising correlations decay as a power law. This is also confirmed using DMRG calculations on a microscopic model. The non local order in the bulk gives rise to zero energy states localized at the interface between the ordered and disordered phases. Such an interface naturally arises when the particles are subject to a weak harmonic confinement along the tube axis. We compute the signature of the edge states in the single particle tunneling spectra pointing to differences between a system with bosonic versus fermionic particles. Finally we asses the magnitude of the relevant quantum fluctuations in realistic systems of dipolar particles, including ultracold polar molecules as well as alkali atoms weakly dressed by a Rydberg excitation.