Question

The effective theory of photons in medium is usually obtained by inserting the electric susceptibility χ (linear or nonlinear) into ∫dD⋅E

and complete the integral. We can calculate χ by introducing Hdipole=−d⋅E as a perturbation to the electron part of the system, where E is treated as a given external field, and then calculating d. This is equivalent to "integrating out" the electron degrees of freedom and getting an effective Hamiltonian of photons.

In real materials, dissipation (by phonon scattering or spontaneous emssion) always exists, and the behavior of the electrons has to be treated by a quantum master equation, instead of a zero-temperature formalism; now χ, defined as the response of d to E, no longer captures how the state of photons evolve in the material: if we inject a coherent state (a pure state by definition) into the material, the output will be a mixed state, but this piece of information can't be captured by χ. I'm therefore curious about whether in this case, it's still possible to write down an effective theory for photons in the medium - possibly a quantum master equation as well?

This question may have some practical values since if you are to do a quantum optics experiment, it might be instructive to know what the lenses really do to the optical field; but I'm not an experimentalist and what I heard from experimentalist is "well you just need to lower the temperature to avoid anything weird".

Answer 1

To develop an effective theory for photons in a medium with dissipation, one must consider quantum effects and potentially use a quantum master equation that captures the complex interactions and loss of coherence in the system, going beyond the classical understanding illustrated by the photoelectric effect.

Step-by-step explanation:

The quest to formulate an effective theory for photons in a medium with dissipation involves complex quantum considerations. When exploring the interaction of light with matter, Albert Einstein's explanation of the photoelectric effect provides foundational insights. According to this effect, light, or electromagnetic (EM) radiation, can be thought of as a stream of particles—photons—each with energy E = hv (where h is Planck's constant and v is the frequency).

Upon striking a metal, photons with sufficient energy (above a certain threshold frequency) can eject electrons, imparting upon them kinetic energy. This ejection is independent of light intensity, instead depending on the energy of individual photons. In materials, photons interact with electrons and other lattice vibrations (phonons), with dissipation leading to non-trivial effects not captured by the linear susceptibility χ. For a real system where coherence is lost due to interactions with the environment, a quantum master equation, which takes into account dissipation and decoherence effects, might be necessary to describe the evolution of the photon states in the material.