Degeneracy-breaking and Long-lived Multimode Microwave Electromechanical Systems Enabled by Cubic Silicon-Carbide Membrane Crystals

Cubic silicon-carbide crystals (3C-SiC), known for their high thermal conductivity and in-plane stress, hold significant promise for the development of high-quality ($Q$) mechanical oscillators. We reveal degeneracy-breaking phenomena in 3C-phase crystalline silicon-carbide membrane and present high-$Q$ mechanical modes in pairs or clusters. The 3C-SiC material demonstrates excellent microwave compatibility with superconducting circuits. Thus, we can establish a coherent electromechanical interface, enabling precise control over 21 high-$Q$ mechanical modes from a single 3C-SiC square membrane. Benefiting from extremely high mechanical frequency stability, this interface enables tunable light slowing with group delays extending up to an impressive duration of \emph{an hour}. Coherent energy transfer between distinct mechanical modes are also presented. In this work, the studied 3C-SiC membrane crystal with their significant properties of multiple acoustic modes and high-quality factors, provide unique opportunities for the encoding, storage, and transmission of quantum information via bosonic phonon channels.