Quantum fluctuations of the center-of-mass and relative parameters of NLS breathers

TL;DR

This paper investigates quantum fluctuations of NLS breathers, deriving uncertainty relations and comparing models for quantum noise, with implications for observing macroscopic quantum effects in Bose-Einstein condensates.

Contribution

It introduces a comparison of white noise and correlated noise models for quantum fluctuations of NLS breathers, extending analysis to large particle numbers.

Findings

Uncertainty relations for breather parameters are derived.

Correlated noise model aligns with creation from fundamental solitons.

Results suggest feasible experimental observation of quantum fluctuations.

Abstract

We study quantum fluctuations of macroscopic parameters of an NLS breathers, i.e., the second-order soliton solution of the nonlinear Schr\"odinger equation. Uncertainty relations for the parameters are derived and compared to similar relations for fundamental solitons. We compare two models for the state of the quantum field of fluctuations surrounding the classical field of the Bose-Einstein condensate: a conventionally used, computationally convenient "white noise", and a correlated noise which assumes that the breather has been created from a fundamental soliton, by means of the application of the factor-of-four quench of the nonlinearity strength. Theoretical methods used in the work are well suited for a large number of particles, $N$. We thus confirm the possibility of experimental observation of macroscopic quantum fluctuations, which is suggested by an extrapolation to large $N$ of recently reported low-$N$ Bethe-ansatz results [Phys. Rev. Lett. 119 220401 (2017)].