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

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 one-, 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.