Collective modes of a one-dimensional trapped Bose gas in the presence of the anomalous density

TL;DR

This paper investigates the collective excitations of a one-dimensional trapped Bose-Einstein condensate, emphasizing the impact of anomalous density correlations at various temperatures using analytical and numerical methods.

Contribution

It provides analytical expressions for mode frequencies considering anomalous density and explores temperature effects on collective modes, extending understanding beyond previous models.

Findings

Anomalous density significantly influences collective mode frequencies.

Temperature affects breathing mode oscillations in the weak-coupling regime.

Zero-temperature predictions align with experimental and simulation data.

Abstract

We study the collective modes of a one-dimensional harmonically trapped Bose-Einstein condensate in the presence of the anomalous density using the time-dependent Hartree-Fock-Bogoliubov theory. Within the hydrodynamic equations, we derive analytical expressions for the mode frequencies and the density fluctuations of the anomalous density which constitutes the minority component at very low temperature and feels an effective external potential exerted by the majority component, i.e., the condensate. On the other hand, we numerically examine the temperature dependence of the breathing mode oscillations of the condensate at finite temperature in the weak-coupling regime. At zero temperature, we compare our predictions with available experimental data, theoretical treatments, and Monte carlo simulations in all interaction regimes and the remaining hindrances are emphasized. We show that the anomalous correlations have a non-negligible role on the collective modes at both zero and finite temperatures.