Talk

Speaker

Oleksandr Marchukov, Tel Aviv University

Title

Quantum fluctuations and uncertainty relations in NLS solitons and breathers

Abstract

We consider the quantum fluctuations of the macroscopic variables associated with a breather, a second-order soliton solution of nonlinear Schrödinger equation. This solution is known to be governed by eight macroscopic parameters: number of atoms, global phase, center-of-mass position, center-of-mass velocity, relative mean amplitude, relative phase, relative velocity and relative position of the constituent solitons.

Linearizing the evolution of the bosonic quantum field around the Bose condensate in a breather state, we express the quantum fluctuations of the macroscopic variables through the fluctuations of the full quantum field, themselves known. 

First we calculate the initial quantum uncertainties of the macroscopic parameters and compare them to the similar relations for the fundamental soliton. Then, we calculate the time evolution of uncertainties of the parameters and compare them to the initial ones. We finally describe how the macroscopic fluctuations affect the time evolution of the atomic density and estimate the propagation time needed for an experimental detection of the predicted effects. Of the eight parameters, the relative distance between the constituent solitons is the most empirically appealing: we surmise that the observation of the temporal increase of this distance, due to the quantum fluctuation of the relative velocity may be within the experimental reach.