  Photonic gauge potentials are crucial for manipulating charge-neutral photons
like their counterpart electrons in the electromagnetic field, allowing
analogous Aharonov-Bohm effect in photonics and paving the way for critical
applications like photonic isolation. Normally, a gauge potential exhibits
phase inversion along two opposite propagation paths. Here we experimentally
demonstrate phonon-induced anomalous gauge potentials with non-inverted gauge
phases in a spatial-frequency space, where quasi-phase-matched nonlinear
Brillouin scatterings enable such unique direction-dependent gauge phases.
Based on this scheme, we construct photonic isolators in the frequency domain
permitting nonreciprocal propagation of light along the frequency axis, where
coherent phase control in the photonic isolator allows switching completely the
directionality through an Aharonov-Bohm interferometer. Moreover, similar
coherent controlled unidirectional frequency conversions are also illustrated.
These results may offer a unique platform for a compact, integrated solution to
implement synthetic-dimension devices for on-chip optical signal processing.
