Observation of non-reciprocal harmonic conversion in real sounds

Reciprocity guarantees that in most media, sound transmission is symmetric between two points of space when the location of the source and receiver are interchanged. This fundamental law can be broken in non-linear media, often at the cost of detrimental input power levels, large insertion losses, and ideally prepared single-frequency input signals. Thus, previous observations of non-reciprocal sound transmission have focused on pure tones, and cannot handle real sounds composed of various harmonics of a low-frequency fundamental note, as generated for example by musical instruments. Here, we extend the reach of non-reciprocal acoustics by achieving large, tunable, and timbre-preserved non-reciprocal transmission of sound notes composed of several harmonics, originating from musical instruments. This is achieved in a non-linear, actively reconfigurable, and non-Hermitian isolator that can handle arbitrarily low input power at any audible frequency, while providing isolation levels up to 30dB and a tunable level of non-reciprocal gain. Our findings may find applications in sound isolation, noise control, non-reciprocal and non-Hermitian metamaterials, and analog audio processing.