M. Brandenbourger

O. Gamayun

J. Veenstra

F. Gorp

H. Terwisscha-Dekker

J. Caux

C. Coulais

Producing the first examples of breathing solitons in one-dimensional non-reciprocal media allows their propagation dynamics to be analysed.

Breathing solitons consist of a fast-beating wave within a compact envelope of stable shape and velocity. The phenomenon has been demonstrated in plasmas, optical fibers and cold atoms but has yet to be experimentally observed in systems that dissipate energy. Here, we report breathing, unidirectional, arbitrarily long-lived solitons in non-reciprocal, non-conservative active metamaterials and analyse their dynamics.

Breathing solitons consist of a fast beating wave within a compact envelope of stable shape and velocity. They manifest themselves in a variety of contexts such as plasmas, optical fibers and cold atoms, but have remained elusive when energy conservation is broken. Here, we report on the observation of breathing, unidirectional, arbitrarily long-lived solitons in non-reciprocal, non-conservative 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 non-reciprocal materials, and that their dynamics are governed by an unstable fixed point. Crucially, breathing solitons can persist for arbitrarily long times provided: (i) this fixed point displays a bifurcation upon reachin a delicate balance between energy injection and dissipation; (ii) the initial conditions allow the dynamics to reach this bifurcation point. Our work establishes non-reciprocity as a promising avenue to generate stable nonlinear unidirectional waves, and could be generalized beyond metamaterials to optics, soft matter and superconducting circuits.

Non-reciprocal breather

Non-reciprocal breathing solitons