Balanced homodyne detectors and Casimir energy densities

TL;DR

This paper extends the analysis of balanced homodyne detectors to quantum fields in Casimir geometries, revealing position- and frequency-dependent responses that could enhance understanding of sub-vacuum energy densities.

Contribution

It generalizes the response analysis of BHDs to quantum fields influenced by external conditions like cavities, providing new insights into local energy densities in Casimir setups.

Findings

BHD responses depend on position and frequency in Casimir geometries.

The analysis predicts rich patterns of vacuum fluctuations.

Potential for new characterization of quantum fields beyond Casimir forces.

Abstract

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 one- and two-point functions of arbitrary states of quantum fields. We generalize the analysis of the response of BHDs to the case of quantum fields under influence of static external conditions such as cavities or polarizable media. By recalling the expressions for two-point functions of quantum fields in Casimir geometries we show, that a rich, position- and frequency-dependent pattern of BHD responses is predicted for ground states. This points to a potentially new characterization of quantum fields in Casimir setups 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.