Dipole modes of a trapped bosonic mixture: Fate of the sum-rule approach

TL;DR

This paper compares the sum-rule approach and full GP calculations for dipole modes in a trapped heteronuclear bosonic mixture, revealing regimes where sum rules deviate from GP predictions and interpreting this via Ehrenfest dynamics.

Contribution

It demonstrates the limitations of the sum-rule approach for dipole modes in certain interaction regimes and links it to Ehrenfest dynamics, providing new insights into collective excitations.

Findings

Sum-rule approach deviates from GP results in certain interaction regimes.

Ehrenfest approach is equivalent to the sum-rule method for dipole excitations.

Identifies conditions where the sum-rule approach fails to accurately predict dipole modes.

Abstract

We present a general discussion of the dipole modes of a heteronuclear bosonic mixture in a harmonic trap by comparing the prediction of the sum-rule approach with full Gross-Pitaevskii (GP) calculations. Yet in the range of interaction in which the mixture is miscible and stable at the mean field level, $g_{12}^2<g_{11}g_{22}$, we find that there are regimes where the sum rules displays significant deviations from the GP solution. We provide an interpretation for this behavior in terms of the Ehrenfest approach, which we show to be equivalent to the sum-rule approach for dipole excitations.