  We consider a system where an optical cavity mode is parametrically coupled
to a mechanical oscillator. A laser beam driving the cavity at its resonance
frequency will acquire red- and blue-shifted sidebands due to noise in the
position of the mechanical oscillator. In a classical theory without noise in
the electromagnetic field, the powers of these sidebands are of equal
magnitude. In a quantum theory, however, an asymmetry between the sidebands can
be resolved when the oscillator's average number of vibrational excitations
(phonons) becomes small, i.e., comparable to 1. We discuss the interpretation
of this sideband asymmetry in a heterodyne photodetection measurement scheme
and show that it depends on the choice of detector model. In the optical
regime, standard photodetection theory leads to a photocurrent noise spectrum
given by normal and time ordered expectation values. The sideband asymmetry is
in that case a direct reflection of the quantum asymmetry of the position noise
spectrum of the mechanical oscillator. Conversely, for a detector that measures
symmetric, non-ordered expectation values, we show that the sideband asymmetry
can be traced back to quantum optomechanical interference terms. This ambiguity
in interpretation applies not only to mechanical oscillators, but to any degree
of freedom that couples linearly to noise in the electromagnetic field.
Finally, we also compare the quantum theory to a fully classical model, where
sideband asymmetry can arise from classical optomechanical interference terms.
We show that, due to the oscillator's lack of zero point motion in a classical
theory, the sidebands in the photocurrent spectrum differ qualitatively from
those of a quantum theory at sufficiently low temperatures. We discuss the
observable consequences of this deviaton between classical and quantum
theories.
