  Optomechanical systems show great potential as quantum transducers and
information storage devices for use in future hybrid quantum networks and offer
novel strategies for quantum state preparation to explore macroscopic quantum
phenomena. Towards these goals, deterministic control of optomechanical
interactions in the strong coupling regime represents an important strategy for
efficient utilization of quantum degrees of freedom in mechanical systems.
While strong coupling has been demonstrated in both electromechanical and
optomechanical systems, it has proven difficult to identify a robust
optomechanical system that features the low loss and high coupling rates
required for more sophisticated control of mechanical motion. In this paper, we
demonstrate robust strong coupling between multiple long-lived phonon modes of
a bulk acoustic wave (BAW) resonator and a single optical cavity mode. We show
that this so-called "multimode strong coupling" regime can be a powerful tool
to shape and control decoherence pathways through nontrivial forms of mode
hybridization. Using frequency- and time-domain measurements, we identify
hybridized modes with lifetimes that are significantly longer than that of any
mode of the uncoupled system. This surprising effect, which results from the
interference of decay channels, showcases the use of multimode strong coupling
as a general strategy to mitigate extrinsic loss mechanisms. Moreover, the
phonons supported by BAW resonators have a collection of properties, including
high frequencies, long coherence times, and robustness against thermal
decoherence, making this optomechanical system particularly enticing for
applications such as quantum transduction and memories. These results show that
our system can be used to study novel phenomena in a previously unexplored
regime of optomechanics and could be an important building block for future
quantum devices.
