Perhaps my question was unclear.

I was trying to understand whether it is actually whether phase is preserved by a convetional balanced mixer. My interest is in the implementation of fourier zeugmatography, where preservation of the phase is required. My impression was that a mixer degrades the phase, hence the example below would not be possible using a simple mixer - and instead would require a quadrature mixer.

Take the scenario - I record a multi-frequency signal from time t - x, to t + x, with the property that at time t, all the components of the signal are at phase 0. (i.e. the signal begins with its components out of phase, they gradually drift into phase because of their differening frequencies, before drifting apart in the opposite direction).

I wish to repeat the recording multiple times, under varying conditions, so that some of the components begin to drift away from 0 phase at time t. However, I require that the subsequent demodulated signal accurately represent the phases of the individiual components between multiple recordings. The idea is to take these multiple recordings, 'stack' them up into a multidimensional array - and then perform multi-dimensional FT (1 dimension in the time domain, the other dimensions in the repetition domain). Clearly if the phase isn't maintained between experiments - then the FT in the higher dimensions will be meaningless.