Topological pumping of multi-frequency solitons

TL;DR

This paper demonstrates topological pumping of quadratic optical solitons, revealing a power-dependent phase transition from non-topological to topological transport governed by Chern numbers, with distinct behaviors from cubic media.

Contribution

It introduces the phenomenon of topological pumping in quadratic solitons and details the transition from non-topological to topological phases influenced by nonlinearity and pumping velocity.

Findings

Quantized transport observed in quadratic solitons.

Transition from non-topological to topological phase with increasing nonlinearity.

No breakup or fractional pumping at high power levels in quadratic media.

Abstract

We report on the topological pumping of quadratic optical solitons, observed through their quantized transport in a dynamic optical potential. A distinctive feature of this system is that the two fields with different frequencies, which together form the quadratic soliton, evolve in separate yet topologically equivalent dynamic optical potentials. Pumping in this system exhibits several notable differences from pumping in cubic media. While Chern indices characterizing quantized transport for uncoupled fundamental and second harmonic waves are nonzero, small-amplitude solitons with narrow spectra do not move, thus revealing a non-topological phase. As the nonlinearity increases, the system undergoes a sharp transition, depending on the velocity of one of the sublattices forming dynamical potential, into the phase where the quantized transport of quadratic solitons governed by nonzero Chern numbers is observed. The power level at which this transition occurs increases with increase of pumping velocity, and the transition is observed even in the regime when the adiabatic approximation no longer applies. Unlike in cubic media, in a quadratic medium neither breakup of topological pumping nor fractional pumping at high power levels are observed.