The multi-level system $^{55}$Mn$^{2+}$ is used to generate two pseudo-harmonic level systems, as representations of the same electronic sextuplet at different nuclear spin projections. The systems are coupled using a forbidden nuclear transition induced by the crystalline anisotropy. We demonstrate Rabi oscillations between the two representations in conditions similar to two coupled quasi-harmonic quantum oscillators. Rabi oscillations are performed at a detuned pumping frequency which matches energy difference between electro-nuclear states of different oscillators. We measure a coupling stronger than the decoherence rate, to indicate the possibility fast information exchange between the systems.
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