The low-energy excitation spectrum of one-dimensional dipolar quantum gases

TL;DR

This study uses quantum Monte Carlo simulations to analyze the excitation spectrum of one-dimensional dipolar quantum gases, revealing the absence of a roton minimum and confirming a Luttinger-liquid state across different densities.

Contribution

First detailed simulation of excitation spectrum in 1D dipolar gases showing the absence of roton minimum and confirming Luttinger-liquid behavior.

Findings

Excitation energy vanishes at the reciprocal lattice vector across all densities.

Gaps at higher reciprocal vectors close with increasing density.

No long-range order exists in the strongly correlated system.

Abstract

We determine the excitation spectrum of a bosonic dipolar quantum gas in a one-dimensional geometry, from the dynamical density-density correlation functions simulated by means of Reptation Quantum Monte Carlo techniques. The excitation energy is always vanishing at the first vector of the reciprocal lattice in the whole crossover from the liquid-like at low density to the quasi-ordered state at high density, demonstrating the absence of a roton minimum. Gaps at higher reciprocal lattice vectors are seen to progressively close with increasing density, while the quantum state evolves into a quasi-periodic structure. The simulational data together with the uncertainty-principle inequality also provide a rigorous proof of the absence of long-range order in such a super-strongly correlated system. Our conclusions confirm that the dipolar gas is in a Luttinger-liquid state, significantly affected by the dynamical correlations. The connection with ongoing experiments is also discussed.