Overcoming dispersive spreading of quantum wave packets via periodic nonlinear kicking

TL;DR

This paper introduces a method to suppress dispersive spreading of quantum wave packets using periodic nonlinear kicks, enabling stable, dispersionless states that can move freely, with potential experimental realizations in ultracold gases.

Contribution

It develops a novel approach to create stroboscopically-dispersionless quantum states through periodic nonlinear modulation, differing from traditional soliton solutions.

Findings

Analytical construction of dispersionless quantum states

Numerical simulations confirm stability and dispersion suppression

Potential for experimental realization in ultracold atomic gases

Abstract

We propose the suppression of dispersive spreading of wave packets governed by the free-space Schr\"odinger equation with a periodically pulsed nonlinear term. Using asymptotic analysis, we construct stroboscopically-dispersionless quantum states that are physically reminiscent of, but mathematically different from, the well-known one-soliton solutions of the nonlinear Schr\"odinger equation with a constant (time-independent) nonlinearity. Our analytics are strongly supported by full numerical simulations. The predicted dispersionless wave packets can move with arbitrary velocity and can be realized in experiments involving ultracold atomic gases with temporally controlled interactions.