  We use a bulk acoustic wave resonator to demonstrate coherent control of the
excited orbital states in a diamond nitrogen-vacancy (NV) center at cryogenic
temperature. Coherent quantum control is an essential tool for understanding
and mitigating decoherence. Moreover, characterizing and controlling orbital
states is a central challenge for quantum networking, where optical coherence
is tied to orbital coherence. We study resonant multi-phonon orbital Rabi
oscillations in both the frequency and time domain, extracting the strength of
the orbital-phonon interactions and the coherence of the acoustically driven
orbital states. We reach the strong-driving limit, where the physics is
dominated by the coupling induced by the acoustic waves. We find agreement
between our measurements, quantum master equation simulations, and a
Landau-Zener transition model in the strong-driving limit. Using perturbation
theory, we derive an expression for the orbital Rabi frequency versus acoustic
drive strength that is non-perturbative in the drive strength and agrees well
with our measurements for all acoustic powers. Motivated by continuous wave
spin resonance-based decoherence protection schemes, we model the orbital
decoherence and find good agreement between our model and our measured
few-to-several nanoseconds orbital decoherence times. We discuss the outlook
for orbital decoherence protection.
