Soliton resuscitations: asymmetric revivals of the breathing mode of an atomic bright soliton in a harmonic trap

TL;DR

This paper investigates the non-Markovian dynamics of atomic bright solitons in harmonic traps, revealing asymmetric breathing mode revivals caused by atom emission and reabsorption, and provides an analytical explanation for these phenomena.

Contribution

It introduces a detailed analysis of non-Markovian revivals in atomic solitons and derives an analytical approximation for the Bogoliubov-de Gennes spectrum explaining the asymmetry.

Findings

Revivals exhibit asymmetric amplitude envelopes with gradual increases and sudden drops.

Emitted atoms oscillate and return, causing periodic breathing mode revivals.

Analytical approximation matches observed revival patterns.

Abstract

An atomic bright soliton realised in a quasi-one-dimensional Bose-Einstein condensate can be considered as an open quantum system. The soliton's breathing mode, for example, is damped by emission of atoms from the soliton to spatial infinity, which thus acts as a Markovian environment for the soliton. If the soliton is held in a shallow harmonic trap, however, the environment becomes non-Markovian: emitted atoms oscillate in the trap and eventually return to the soliton, interfering with it, producing periodic revivals of the breathing mode (``resuscitations''). The amplitude envelopes of these breathing revivals shows a curious asymmetry, with a gradual increase in breathing amplitude followed by sudden drop in amplitude that becomes more and more pronounced in later revivals. We explain this asymmetrical revival pattern in the non-Markovian revivals by deriving a close analytical approximation to the Bogoliubov-de Gennes frequency spectrum for the weakly trapped soliton.