Balanced homodyne detectors in quantum field theory

By examining balanced homodyne defectors (BHDs) from the general quantum-field-theoretical point of view we derive a number of generalizations of the standard analysis of their response. In particular, by allowing for interactions restricted in time (by a smooth function) we present general expressions for BHD output (in which the usual, simplifying limits can but need not be taken). Moreover, we point out the need for nonstrictly monochromatic local oscillators (i.e., the need for “pulsed” ones) in order to have well-defined quantum-field-theory (QFT) observables (the products of which, e.g., have finite vacuum expectation values). Furthermore, we show how the analysis of the detectors generalize to situations with BHDs in waveguides, Casimir cavities, or other time-independent but inhomogeneous γ and μ . The general treatment also allows us to comment on important QFT features of the detector observables such as locality (i.e., commuting for causally separated measurements) and non-null vacuum response. This leads to the conclusion that balanced homodyne-type detectors (and not single photodiodelike ones) are the appropriate tools in testing intriguing QFT predictions such as negative (subvacuum) energy densities. Finally, by recalling results on field-autocorrelation functions for QFT in Casimir cavities we show that interesting effects (large reductions of fluctuations) are to be expected if a version of BHDs were to be placed in such cavities.