We analyze the strong-coupling dynamics of a driven harmonic oscillator whose energy is modulated by a continuum of other bosonic modes. This type of system-bath interaction appears, for example, in optomechanical or equivalent circuit QED setups, where the frequency of a confined photonic mode depends linearly on a fluctuating boundary. Compared to the canonical spin-boson model, where coupling to bath modes only leads to decoherence, the role of the environment in such systems is more complex, since it also provides the only source of nonlinearity. We show that even for an unstructured bath, these environment-induced nonlinearities can dominate over decoherence processes resulting in Rabi oscillations and the formation of highly non-classical states. These findings provide important insights into the non-Markovian dynamics of higher-dimensional open quantum systems and for realizing few-photon optical nonlinearities through strong interactions with a bath.
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