The semiclassical theory of light-matter interactions describes theinteraction between a classical electromagnetic field with a quantum mechanicaltwo-level system.We show that the quantum mechanical two-level system can bemodeled by a system of two coupled classical harmonic oscillators whoseeigenstates are split in frequency according to the coupling strength and playthe roles of the two levels of the quantum mechanical two-level system. Theeffect of the light field on the mechanical system is modeled as a modulationof the spring constants of the individual oscillators. Using this fullyclassical model, we derive the Bloch equations for a two-level system anddiscuss the mechanical analogues of Rabi oscillations and coherent controlexperiments
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