# Static-response theory and the roton-maxon spectrum of a flattened dipolar Bose-Einstein condensate

## TL;DR

This paper develops a static-response approach to analyze the roton-maxon spectrum in a flattened dipolar Bose-Einstein condensate, enabling accurate predictions and a potential experimental method for dispersion relation measurement.

## Contribution

It introduces a static perturbation method combined with sum rules and Gross-Pitaevskii equation solutions to predict the excitation spectrum of dipolar BECs, validated by Bogoliubov calculations.

## Key findings

- Excellent agreement between static-response predictions and Bogoliubov calculations.
- Oscillatory behavior of density modulations reveals excitation spectrum features.
- Measurement of oscillation periods offers a practical way to determine dispersion relations.

## Abstract

Important information for the roton-maxon spectrum of a flattened dipolar Bose-Einstein condensate is extracted by applying a static perturbation exhibiting a periodic in-plane modulation. By solving the Gross-Pitaevskii equation in the presence of the weak perturbation we evaluate the linear density response of the system and use it, together with sum rules, to provide a Feynman-like upper-bound prediction for the excitation spectrum, finding excellent agreement with the predictions of full Bogoliubov calculations. By suddenly removing the static perturbation, while still maintaining the trap, we find that the density modulations -- as well as the weights of the perturbation-induced side peaks of the momentum distribution -- undergo an oscillatory behavior with double the characteristic frequency of the excitation spectrum. The measurement of the oscillation periods could provide an easy determination of dispersion relations.