The response of classical or quantum harmonic oscillators coupled linearly to a classical field is strictly linear; all nonlinear response functions vanish identically. We show that, if the oscillators interact with quantum modes of the radiation field, they acquire nonlinear susceptibilities. The effective third order susceptibility induced by four interactions with quantum modes contains collective resonances involving pairs of oscillators. All nonlinearities are missed by the conventional approximate treatment based on the quantum master equations.
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Glenn et al. (2015) studied this question.
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