  In lossless acoustic systems, mode transitions are always time-reversible,
consistent with Lorentz reciprocity, giving rise to symmetric sound
manipulation in space-time. To overcome this fundamental limitation and break
space-time symmetry, nonreciprocal sound steering is realized by designing and
experimentally implementing spatiotemporally-modulated acoustic metamaterials.
Relying on no slow mechanical parts, unstable and noisy airflow or complicated
piezoelectric array, our mechanism uses the coupling between an ultrathin
membrane and external electromagnetic field to realize programmable, dynamic
control of acoustic impedance in a motionless and noiseless manner. The fast
and flexible impedance modulation at the deeply subwavelength scale enabled by
our compact metamaterials provides an effective unidirectional momentum in
space-time to realize irreversible transition in k-{\omega} space between
different diffraction modes. The nonreciprocal wave-steering functionality of
the proposed metamaterial is elucidated by theoretically deriving the
time-varying acoustic response and demonstrated both numerically and
experimentally via two distinctive examples of unidirectional evanescent wave
conversion and nonreciprocal blue-shift focusing. This work can be further
extended into the paradigm of Bloch waves and impact other vibrant domains,
such as non-Hermitian topological acoustics and parity-time-symmetric
acoustics.
