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We consider a system where an optical cavity mode is parametrically coupledto a mechanical oscillator. A laser beam driving the cavity at its resonancefrequency will acquire red- and blue-shifted sidebands due to noise in theposition of the mechanical oscillator. In a classical theory without noise inthe electromagnetic field, the powers of these sidebands are of equalmagnitude. In a quantum theory, however, an asymmetry between the sidebands canbe resolved when the oscillator's average number of vibrational excitations(phonons) becomes small, i.e., comparable to 1. We discuss the interpretationof this sideband asymmetry in a heterodyne photodetection measurement schemeand show that it depends on the choice of detector model. In the opticalregime, standard photodetection theory leads to a photocurrent noise spectrumgiven by normal and time ordered expectation values. The sideband asymmetry isin that case a direct reflection of the quantum asymmetry of the position noisespectrum of the mechanical oscillator. Conversely, for a detector that measuressymmetric, non-ordered expectation values, we show that the sideband asymmetrycan be traced back to quantum optomechanical interference terms. This ambiguityin interpretation applies not only to mechanical oscillators, but to any degreeof freedom that couples linearly to noise in the electromagnetic field.Finally, we also compare the quantum theory to a fully classical model, wheresideband asymmetry can arise from classical optomechanical interference terms.We show that, due to the oscillator's lack of zero point motion in a classicaltheory, the sidebands in the photocurrent spectrum differ qualitatively fromthose of a quantum theory at sufficiently low temperatures. We discuss theobservable consequences of this deviaton between classical and quantumtheories.

Heterodyne photodetection measurements on cavity optomechanical systems: Interpretation of sideband asymmetry and limits to a classical explanation