Soliton turbulence of a strongly driven one-dimensional Bose gas

TL;DR

This paper investigates the out-of-equilibrium dynamics of a driven one-dimensional Bose gas, revealing soliton behavior and turbulence-like regimes characterized by distinct power-law momentum distributions.

Contribution

It introduces a detailed analysis of soliton turbulence in a driven Bose gas, linking momentum distribution power-laws to different dynamical regimes, with potential for experimental observation.

Findings

Weak driving leads to weakly perturbed solitons with a $k^{-2}$ momentum decay.

Strong driving induces turbulence with a $k^{-eta}$ decay, $eta$ in [7,9].

The regimes are characterized by space-time maps and inverse scattering transform analysis.

Abstract

We study the out-of-equilibrium dynamics of a weakly interacting one-dimensional Bose gas in a box trap, subjected to a drive realized by a periodically oscillating linear potential. After a transient regime, the gas reaches a quasi-steady state, characterized by the presence of several solitons. At weak driving amplitude, the solitons are only weakly perturbed by one another, while at strong driving amplitude a regime analogous to turbulence is reached, where the solitons are strongly intertwined with each other. We show that a hallmark of both regimes can be found in the momentum distribution, which displays a power-law decay $n(k) \sim k^{-2}$ at weak driving amplitude and $n(k) \sim k^{-\alpha}$ with a power-law exponent $\alpha\in [7,9]$ at large amplitude. We further characterize each of the two regimes by following the space-time maps and characterizing the solitons using the inverse scattering transform. The protocol analyzed in this study is amenable to experimental realization in current experimental setups.