  Matter-wave jets are ejected from a Bose-Einstein condensate subjected to a
modulation of the interaction strength. For sufficiently strong modulation
additional higher harmonic matter-wave jets emerge. Here we report the first
experimental observation of incommensurable "golden" $\frac{1+\sqrt{5}}{2}$
matter-wave jets in a Bose-Einstein condensate exposed to a single frequency
interaction modulation. We study the formation of higher-order jets and the
corresponding incommensurable density waves in quasi-one-dimensional geometry
with numerical one dimensional (1D) Gross-Pitaevskii equation simulation. We
explore the process of jet formation experimentally and theoretically for a
wide range of modulation amplitudes and frequencies and establish a phase
diagram delineating different regimes of jet formation.
