Collective excitations of trapped one-dimensional dipolar quantum gases

TL;DR

This paper predicts how the breathing mode frequency of a 1D dipolar quantum gas varies with interaction strength, using hydrodynamic and quantum Monte Carlo methods, revealing Luttinger-liquid behavior in experiments.

Contribution

It introduces a combined hydrodynamic and quantum Monte Carlo approach to accurately predict excitation modes in 1D dipolar gases, connecting theory with experimental observables.

Findings

Breathing mode frequency transitions from 2ω₀ to √5ω₀ with interaction strength.

Hydrodynamic Luttinger-Liquid theory agrees with sum-rule approach.

Predictions are applicable to current experimental setups.

Abstract

We calculate the excitation modes of a 1D dipolar quantum gas confined in a harmonic trap with frequency $\omega_0$ and predict how the frequency of the breathing n=2 mode characterizes the interaction strength evolving from the Tonks-Girardeau value $\omega_2=2\omega_0$ to the quasi-ordered, super-strongly interacting value $\omega_2=\sqrt{5}\omega_0$. Our predictions are obtained within a hydrodynamic Luttinger-Liquid theory after applying the Local Density Approximation to the equation of state for the homogeneous dipolar gas, which are in turn determined from Reptation Quantum Monte Carlo simulations. They are shown to be in quite accurate agreement with the results of a sum-rule approach. These effects can be observed in current experiments, revealing the Luttinger-liquid nature of 1D dipolar Bose gases.