The origin of the period-$2T/7$ quasi-breathing in disk-shaped Gross-Pitaevskii breathers

TL;DR

This paper investigates the origin of the observed quasi-periodic breathing in 2D Bose condensates, revealing a coincidence that links hydrodynamic collapse to the quasi-breathing period and extending the analysis to all spatial dimensions.

Contribution

It uncovers a coincidence causing the quasi-breathing period to mimic hydrodynamic collapse times and generalizes the phenomenon across different spatial dimensions.

Findings

The collapse time acts as a 'skillful impostor' for the quasi-breathing period.

The phenomenon persists in all scale-invariant gases across dimensions.

The half-period of quasi-breathing is given by an arctangent function of the dimension.

Abstract

We address the origins of the quasi-periodic breathing observed in [Phys. Rev.\ X vol. 9, 021035 (2019)] in disk-shaped harmonically trapped two-dimensional Bose condensates, where the quasi-period $T_{\text{quasi-breathing}}\sim$~$2T/7$ and $T$ is the period of the harmonic trap. We show that, due to an unexplained coincidence, the first instance of the collapse of the hydrodynamic description, at $t^{*} = \arctan(\sqrt{2})/(2\pi) T \approx T/7$, emerges as a `skillful impostor' of the quasi-breathing half-period $T_{\text{quasi-breathing}}/2$. At the time $t^{*}$, the velocity field almost vanishes, supporting the requisite time-reversal invariance. We find that this phenomenon persists for scale-invariant gases in all spatial dimensions, being exact in one dimension and, likely, approximate in all others. In $d$ dimensions, the quasi-breathing half-period assumes the form $T_{\text{quasi-breathing}}/2 \equiv t^{*} = \arctan(\sqrt{d})/(2\pi) T$. Remaining unresolved is the origin of the period-$2T$ breathing, reported in the same experiment.