Nonreciprocal Breathing Solitons

Breathing solitons consist of a fast beating wave within a compact envelope of stable shape and velocity. They can propagate and carry information and energy in a variety of contexts such as plasmas, optical fibers, and cold atoms, but propagating breathers have remained elusive when energy conservation is broken. Here, we report on the observation of breathing, unidirectional, arbitrarily long-lived solitons in nonreciprocal, nonconservative active metamaterials. Combining precision desktop experiments, numerical simulations, and perturbation theory on generalizations of the sine-Gordon and nonlinear Schrödinger equations, we demonstrate that unidirectional breathers generically emerge in weakly nonlinear nonreciprocal materials, and that their dynamics are governed by an unstable fixed point. Crucially, breathing solitons can persist for arbitrarily long times provided that (i) this fixed point displays a bifurcation when a delicate balance between energy injection and dissipation is struck and (ii) the initial conditions allow the dynamics to reach this bifurcation point. Importantly, discrete effects tend to stabilize these nonreciprocal breathers over a wider range of initial conditions. Our work establishes nonreciprocity as a promising avenue to generate stable nonlinear unidirectional waves and could be generalized beyond metamaterials to optics, soft matter, and superconducting circuits.