From what I understand, it seems like you can only "add" beams together. You can use a beam combiner, basically using a beam splitter in reverse, to combine two beams. In homodyne detection, you use a local oscillator beam to mix with the signal beam so you can decipher the difference in phase change which would give you information about the system your signal beam is probing. Homodyne detection can give information regarding the position of an atom.
Say I wanted to detect the relative distance of two atoms. Each atom/ion is stuck inside an electric harmonic potential. The location of the harmonic potentials are known, (if this is possible) Now, let's say I turn off the harmonic potential trap and at the same time I use the homodyne measurement technique to determine the position of both of the atoms. This means shining a laser to detect the atom's position. (The light is absorbed and re-emitted?, or reflected?) In any case, light that comes out of the atom/ion cavity is related to the atom's position/momentum and it is combined with a local oscillator beam to determine the position and momentum of the atom. The light hits photodetectors which then integrate the signals together producing a photocurrent. The analysis of this photocurrent will allow one to figure out the atom's position relative to the center of the harmonic trap.
To figure out the relative position of the atoms from each other, I'll need to "subtract" the position of one atom with the other. If one atom's position is labeled x1 and the other is labeled x2, than wouldn't we simply do x2 - x1? If so, how is one to do this?! How does one "subtract" the position of one from the other using light beams?