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I'm new in quantum optics and I need to know that when a detector operates in microwave frequency range, which of microwave photon or microwave radiation takes part in detection? I suppose that the detector has the same length as the incoming photon and/or radiation signal wavelength and the coupling can be made via a horn antenna or a cavity.

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Photons are elementary point particles, no length or other dimension, that have momentum and energy = h*nu, where h is plancks constant and nu is the frequency of the light wave that will be built up by zillions of this energy photons. That is , classical electromagnetic radiation, light is an emergent property of the superposition of zillions of photons.

Here is an experiment with individual footprints of photons which display the classical interference pattern when in large numbers.

Unless the experiment is designed to detect single photons at a time, one is working with the classical electromagnetic wave and can usually forget the photon aspect.

Individual photons can only be detected by interactions, as seen in the link above.

In quantum optics:

Quantum optics is the study of how individual quanta of light, known as photons, interact with atoms and molecules. This includes studying the particle-like properties of photons. Photons have been used to test many of the counter-intuitive predictions of quantum mechanics, such as entanglement and teleportation, and are a useful resource for quantum information processing.

It will depend on the particular experiment how the underlying photon structure is used and emerges in the classical light effects. The type of detection of the quantum effects will depend on the specific experiment

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