Unlocking arbitrary fast wavepackets: controlled group velocity in non-Hermitian classical systems*

The ability to induce non-Hermitian dynamics in classical systems gives us the unique opportunity to realize fascinating phenomena that

originates in the quantum realm. One of such phenomena is the propagation of arbitrary fast wavepackets, which have a group velocity fully

determined by the non-Hermiticity parameters. The wavepackets can be made faster than its Hermitian counterpart upon the user request.

This phenomenon was originally spotted in photonic systems, where a burst of light was propagated across a two-dimensional graphene-like

stretched lattice constructed of coupled optical waveguides with gain and loss at the sites. Since in graphene-like photonic lattices excitation

near the dispersion singularities resembles Dirac particle physics, with a group velocity of light in vacuum in the Hermitian case, obtaining

higher velocities in the non-Hermitian case was of a major scientific interest. However, due to the instability of the non-Hermitian system,

the wavepacket amplitude turned out to grow without bound, impairing the applicability of the result. Here, we show how to obtain this

phenomenon in a stable form in the classical domain. The targeted stabilization approach that we propose directly serves this goal, helping to

produce arbitrary fast wavepackets propagating with a constant amplitude, where the group velocity is proportional to the square root of the

gain parameter. We demonstrate the phenomenon experimentally in an electrical transmission line, where the non-Hermiticity is generated

using embedded operational amplifiers in a feedback setup.