In a classic homodyne balanced scheme, the difference current is read out that contains only a GW signal and quantum noise of the dark port:
Whatever quadrature the GW signal is in, by proper choice of the homodyne angle one can recover it with minimum additional noise. That is how homodyne detection works in theory.However, in real interferometers, the implementation of a homodyne readout appears to be fraught with serious technical difficulties. In particular, the local oscillator frequency has to be kept extremely stable, which means its optical path length and alignment need to be actively stabilized by a lownoise control system [79]. This inflicts a significant increase in the cost of the detector, not to mention the difficulties in taming the noise of stabilising control loops, as the experience of the implementation of such stabilization in a Garching prototype interferometer has shown [60, 75, 74].
Let us discuss how it works in a bit more detail. The schematic view of a Michelson interferometer with DC readout is drawn in the right panel of Figure 11. As already mentioned, the local oscillator light is produced by a deliberatelyintroduced constant difference of the lengths of the interferometer arms. It is also worth noting that the component of this local oscillator created by the asymmetry in the reflectivity of the arms that is always the case in a real interferometer and attributable mostly to the difference in the absorption of the ‘northern’ and ‘eastern’ end mirrors as well as asymmetry of the beamsplitter. All these factors can be taken into account if one writes the carrier fields at the beamsplitter after reflection off the arms in the following symmetric form:
In the case of a small offset of the interferometer from the dark fringe condition, i.e., for , the readout signal scales as local oscillator classical amplitude, which is directly proportional to the offset itself: . The laser noise associated with the pumping carrier also leaks to the signal port in the same proportion, which might be considered as the main disadvantage of the DC readout as it sets rather tough requirements on the stability of the laser source, which is not necessary for the homodyne readout. However, this problem, is partly solved in more sophisticated detectors by implementing power recycling and/or Fabry–Pérot cavities in the arms. These additional elements turn the Michelson interferometer into a resonant narrowband cavity for a pumping carrier with effective bandwidth determined by transmissivities of the power recycling mirror (PRM) and/or input test masses (ITMs) of the arm cavities divided by the corresponding cavity length, which yields the values of bandwidths as low as 10 Hz. Since the target GW signal occupies higher frequencies, the laser noise of the local oscillator around signal frequencies turns out to be passively filtered out by the interferometer itself.
DC readout has already been successfully tested at the LIGO 40meter interferometer in Caltech [164] and implemented in GEO 600 [77, 79, 55] and in Enhanced LIGO [61, 5]. It has proven a rather promising substitution for the previously ubiquitous heterodyne readout (to be considered below) and has become a baseline readout technique for future GW detectors [79].
Up until recently, the only readout method used in terrestrial GW detectors has been the heterodyne readout. Yet with more and more stable lasers being available for the GW community, this technique gradually gives ground to a more promising DC readout method considered above. However, it is instructive to consider briefly how heterodyne readout works and learn some of the reasons, that it has finally given way to its homodyne adversary.
The idea behind the heterodyne readout principle is the generalization of the homodyne readout, i.e., again, the use of strong local oscillator light to be mixed up with the faint signal light leaking out the dark port of the GW interferometer save the fact that local oscillator light frequency is shifted from the signal light carrier frequency by several megahertz. In GW interferometers with heterodyne readout, local oscillator light of different than frequency is produced via phasemodulation of the pumping carrier light by means of electrooptical modulator (EOM) before it enters the interferometer as drawn in Figure 12. The interferometer is tuned so that the readout port is dark for the pumping carrier. At the same time, by introducing a macroscopic (several centimeters) offset of the two arms, which is known as Schnupp asymmetry [134], the modulation sidebands at radio frequency appear to be optimally transferred from the pumping port to the readout one. Therefore, the local oscillator at the readout port comprises two modulation sidebands, , at frequencies and , respectively. These two are detected together with the signal sidebands at the photodetector, and then the resulting photocurrent is demodulated with the RFfrequency reference signal yielding an output current proportional to GWsignal.
This method was proposed and studied in great detail in the following works [65, 134, 60, 75, 74, 104, 116] where the heterodyne technique for GW interferometers tuned in resonance with pumping carrier field was considered and, therefore, the focus was made on the detection of only phase quadrature of the outgoing GW signal light. This analysis was further generalized to detuned interferometer configurations in [36, 138] where the full analysis of quantum noise in GW dualrecycled interferometers with heterodyne readout was done.
Let us see in a bit more detail how the heterodyne readout works as exemplified by a simple Michelson interferometer drawn in Figure 12. The equation of motion at the input port of the interferometer creates two phasemodulation sideband fields ( and ) at frequencies :
Unlike the homodyne readout schemes, in the heterodyne ones, not only the quantum noise components falling into the GW frequency band around the carrier frequency has to be accounted for but also those rallying around twice the RF modulation frequencies :
The analysis of the expression for the heterodyne photocurrent gives a clue to why these additional noise components emerge in the outgoing signal. It is easier to perform this kind of analysis if we represent the above trigonometric expressions in terms of scalar products of the vectors of the corresponding quadrature amplitudes and a special unitlength vector , e.g.:

where
It is instructive to see what the above procedure yields in the simple case of the Michelson interferometer tuned in resonance with RFsidebands produced by pure phase modulation: and . The foregoing expressions simplify significantly to the following:
For more realistic and thus more sophisticated optical configurations, including Fabry–Pérot cavities in the arms and additional recycling mirrors in the pumping and readout ports, the analysis of the interferometer sensitivity becomes rather complicated. Nevertheless, it is worthwhile to note that with proper optimization of the modulation sidebands and demodulation function shapes the same sensitivity as for frequencyindependent homodyne readout schemes can be obtained [36]. However, inherent additional frequencyindependent quantum shot noise brought by the heterodyning process into the detection band hampers the simultaneous use of advanced quantum nondemolition (QND) techniques and heterodyne readout schemes significantly.
http://www.livingreviews.org/lrr20125 
Living Rev. Relativity 15, (2012), 5
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