Balanced homodyne detectors and Casimir energy densities

We recall and generalize the analysis of the output of the so-called balanced homodyne detectors. The most important feature of these detectors is their ability to quantify the vacuum fluctuations of the electric field, that is expectation values of products of (quantum-) electric-field operators. More precisely, the output of BHDs provides information on the oneand two-point functions of arbitrary states of quantum fields. We compute the two-point function and the associated spectral density for the ground state of the quantum electric field in a Casimir geometry. Furthermore, we predict a positionand frequency-dependent pattern of BHD responses if a device of this type were to be placed between Casimir plates. This points to a potential new characterization of ground states in Casimir geometries, which would not only complement the current global methods (Casimir forces), but also improve understanding of sub-vacuum energy densities present in some regions in these geometries. Balanced homodyne detectors and Casimir energy densities 2