  The ability to control phonons in solids is key for diverse quantum
applications, ranging from quantum information processing to sensing. Often,
phonons are sources of noise and decoherence, since they can interact with a
variety of solid-state quantum systems. To mitigate this, quantum systems
typically operate at milli-Kelvin temperatures to reduce the number of thermal
phonons. Here we demonstrate an alternative approach that relies on engineering
phononic density of states, drawing inspiration from photonic bandgap
structures that have been used to control the spontaneous emission of quantum
emitters. We design and fabricate diamond phononic crystals with a complete
phononic bandgap spanning 50 - 70 gigahertz, tailored to suppress interactions
of a single silicon-vacancy color center with resonant phonons of the thermal
bath. At 4 Kelvin, we demonstrate a reduction of the phonon-induced orbital
relaxation rate of the color center by a factor of 18 compared to bulk.
Furthermore, we show that the phononic bandgap can efficiently suppress
phonon-color center interactions up to 20 Kelvin. In addition to enabling
operation of quantum memories at higher temperatures, the ability to engineer
qubit-phonon interactions may enable new functionalities for quantum science
and technology, where phonons are used as carriers of quantum information.
