Vacuum fluctuations and balanced homodyne detection through ideal multi-mode photon number or power counting detectors

TL;DR

This paper analyzes how vacuum fluctuations affect noise in balanced homodyne detection for gravitational-wave detectors, clarifying the quantum measurement process without relying on the two-photon formulation.

Contribution

It explicitly specifies the quantum operator measured in balanced homodyne detection and clarifies vacuum fluctuation contributions without using the two-photon approach.

Findings

Vacuum fluctuations contribute to noise spectral density from the main interferometer.

Vacuum fluctuations from the local oscillator are not included in the measured operators.

The analysis provides a clearer understanding of quantum noise in gravitational-wave detection.

Abstract

The balanced homodyne detection as a readout scheme of gravitational-wave detectors is carefully examined, which specifies the directly measured quantum operator in the detection. This specification is necessary to apply the quantum measurement theory to gravitational-wave detections. We clarify the contribution of vacuum fluctuations to the noise spectral density without using the two-photon formulation. We found that the noise spectral density in the two-photon formulation includes vacuum fluctuations from the main interferometer but does not includes those from the local oscillator which depends on the directly measured operators.