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Cthugha
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A. Neumaier said:Thanks for the references. It may take a while to find time to do the reading (and then also to respond to your previous post) as I have an upcoming deadline mid of June that takes a lot of my time.
I am interested both in mathematical physics (the really well defined mathematical side of physics) and in the modeling of applications in physics by the concepts from theoretical physics.
I'd need something that explains in quantum optics (or if necessary semiconductor) terms how the finite lifetime of the fundamental photon mode (a) arises, and (b) affects the modeling of typical experimental situations. I am not so much interested in experimental details, rather in the way the experiments are modeled. I understand the theory of quantum optics quite well.
I see. I will look for further references, but I am not sure how long it may take. But Carmichael and Gardiner are both well-known theorists and should be a good starting point.
However, in a nutshell the reason for the finite lifetime is the finite reflectivity of the cavity mirrors, which allows for some leakage of photons out of the cavity (and leakage of the reservoir outside into the cavity). This finite lifetime of course also results in a finite line width in the Fourier domain. Now, the natural choice for field quantization inside the cavity is a field mode with the same spectral characteristics as the cavity cannot sustain a monochromatic mode anyway. This of course also results in the coherence time of the cavity becoming a natural time scale of the system.
With respect to modeling: good question. I know that typical approaches include quantum Ito-type stochastic differential equations ans similar approaches, but I know too little about these approaches to give any details.
A. Neumaier said:There is an important difference between virtual particles and virtual states. Do you agree with my definitions in https://www.physicsforums.com/insights/physics-virtual-particles/ ? If not, what is different in the usage of these terms in quantum optics?
I fully agree that both are very different. I can start by giving some examples for these terms outside of high-energy physics.
The most prominent appearance of virtual states besides high-energy I know of is in non-linear optics. For example in two-photon absorption, the intermediate state one photon energy above the ground state would be considered a virtual state. Again, the focus here is on the dynamics of the system, so I cannot say with confidence how this compares to high-energy physics.
For virtual particles, a prominent topic is the ultrastrong coupling regime, which is essentially the Jaynes-Cummings model at coupling strengths, where the rotating wave approximation breaks down and you need to consider the terms that do not conserve energy explicitly or the question of quantization in a dielectric medium - or both. The article by Glauber, which I linked earlier is on the dielectric part. I am no expert on ultrastrong coupling, but this article cites a lt of the relevant references in this field:
(https://www.nature.com/articles/s41467-017-01504-5).
However, it is my impression that all of these topics in the non-high energy sense are more or less always based on the question of field quantization in non-trivial systems, which means lossy ones or dielectrics or similar problems. I cannot really judge, but I have the impression that your definition is pretty complete for the case of empty space and relativistic quantum field theory.