Superballistic center-of-mass motion in one-dimensional attractive Bose gases: Decoherence-induced Gaussian random walks in velocity space

TL;DR

This paper demonstrates that decoherence can induce superballistic spreading of the center-of-mass in one-dimensional attractive Bose gases, combining analytical solutions and simulations to identify regimes of experimental interest.

Contribution

It introduces an analytical model for superballistic spreading in attractive Bose gases under decoherence, validated by simulations, linking quantum superpositions to classical random walks.

Findings

Superballistic spreading occurs under weak decoherence.

Analytical solutions match numerical simulations.

Identifies experimental parameter regimes for superballistic behavior.

Abstract

We show that the spreading of the center-of-mass density of ultracold attractively interacting bosons can become superballistic in the presence of decoherence, via single-, two- and/or three-body losses. In the limit of weak decoherence, we analytically solve the numerical model introduced in [Phys. Rev. A 91, 063616 (2015)]. The analytical predictions allow us to identify experimentally accessible parameter regimes for which we predict superballistic spreading of the center-of-mass density. Ultracold attractive Bose gases form weakly bound molecules; quantum matter-wave bright solitons. Our computer-simulations combine ideas from classical field methods ("truncated Wigner") and piecewise deterministic stochastic processes. While the truncated Wigner approach to use an average over classical paths as a substitute for a quantum superposition is often an uncontrolled approximation, here it predicts the exact root-mean-square width when modeling an expanding Gaussian wave packet. In the superballistic regime, the leading-order of the spreading of the center-of-mass density can thus be modeled as a quantum superposition of classical Gaussian random walks in velocity space.