# Anomalous frequency shifts in a one-dimensional trapped Bose gas

## TL;DR

This paper investigates anomalous frequency shifts in a one-dimensional trapped Bose gas at a two-body resonance, revealing that effective three-particle interactions cause measurable upward shifts in collective mode frequencies.

## Contribution

It provides an exact solution to the three-body problem and predicts observable frequency shifts due to scale anomaly effects in trapped Bose gases.

## Key findings

- Exact three-body solution shows increased mode frequency due to anomaly.
- Weak-coupling regime also exhibits upward frequency shifts.
- Predicted shifts are experimentally observable with higher particle numbers.

## Abstract

We consider a system of interacting bosons in one dimension at a two-body resonance. This system, which is weakly interacting, is known to give rise to effective three-particle interactions, whose dynamics is similar to that of a two-dimensional Bose gas with two-body interactions, and exhibits an identical scale anomaly. We consider the experimentally relevant scenario of a harmonically trapped system. We solve the three-body problem exactly and evaluate the shifts in the frequency of the lowest compressional mode with respect to the dipole mode, and find that the effect of the anomaly is to increase the mode's frequency. We also consider the weak-coupling regime of the trapped many-boson problem and find, within the local density approximation, that the frequency of the lowest compressional mode is also shifted upwards in this limit. Moreover, the anomalous frequency shifts are enhanced by the higher particle number to values that should be observable experimentally.