Balanced homodyne detectors in QFT

Within the dipole approximation we describe the interaction of a photodiode with the quantum electric field. The diode is modelled by an electron in a bound state which upon interaction, treated perturbatively in the paper, can get excited to one of the scattering states. We furthermore analyze a balanced homodyne detector (BHD) with a local oscillator (LO) consisting of two photodiodes illuminated by a monochromatic coherent state. We show, that to the leading order the BHD’s output measures the expectation value of the quantum electric field, in the state without the LO, restricted to the frequency of the LO. The square of the output measures the two-point function of the quantum field. This shows that the BHDs provide tools for measurements of sub-vacuum (negative) expectation values of the squares quantum fields and thus for test of Quantum Energy Inequality like bounds, or other QFT effects under the influence of external conditions.