Higher-order matter-wave solitons formed by inter- action quenches*

Solitons are 1D nonlinear waves that propagate without dispersion. Higher-order solitons, i.e$.$ coherent superpositions of fundamental solitons known as breathers, can be formed using a specific interaction quench. We experimentally produce and characterize higher-order matter-wave solitons. Using a $^7$Li BEC whose interactions are tuned using a Feshbach resonance, an $n$th order breather is created by suddenly increasing the strength of the attractive interactions by a factor of $n^2$, where $n$ is an integer. The breathing frequency is determined by the chemical potential difference between the constituent solitons\footnote{V. E. Zakharov and A. B. Shabat, Soviet Physics JETP, 34, 1 (1972)}$^,$\footnote{J. Satsuma and N. Yajima, Prog. Theor. Phys. Supp. 55, 284 (1974)}. We show that the breathing frequency depends on the aspect ratio of the confinement and the strength of the post-quench non-linearity. The frequency is independent of the axial confinement when it is sufficiently weak. We demonstrate the realization of both the second (n=2) and third (n=3) order breather.