Insights Vacuum Fluctuations in Experimental Practice - Comments

[Cthugha]

As already pointed out in the other thread, I disagree with many of the conclusions drawn in this insights article. Maybe the most important point I disagree with is:

What is called (not only in this paper, but everywhere where quantum field theory is used) the vacuum is just a mathematical state used in the computations of quantum electrodynamics (QED) with which predictions about experimentally realizable situations are computed in perturbation theory.

As most people outside of high energy physics, here they do not go beyond the simple Jaynes-Cummings model of cavity QED, which of course shares part of the name of the all-out relativistic quantum field theory QED is, but is usually not even treated relativistically.

In cavity QED, accordingly people are interested in vacuum states of cavity modes. For any realistic scenario, these will have a finite quality factor. This may be insanely high as in Haroche's experiments on resonators with millisecond lifetimes or it may be as bad as a piece of glass where reflections occur at the facets. In any case, the fundamental photon mode of the system is now one of finite spectral width and of finite lifetime. And most importantly, it is necessarily coupled to the environment and accordingly an open quantum system. One can easily see this in the finite coherence time one gets for the cavity field. And for open quantum systems I do not see any problems with converting the ensemble average into a time average as long as the averaging time window is much longer than the coherence time of the system.

Outside of high energy physics, any reasonable article on vacuum fluctuations (yes, of course there are also plenty of bad and unreasonable ones) either considers open quantum systems or situations similar to those considered by Glauber in his seminal paper on quantum optics in dielectric media (https://journals.aps.org/pra/abstract/10.1103/PhysRevA.43.467), where he finds that the ground state of the light field inside a dielectric becomes a squeezed state, when analyzed using empty-space photon operators. People usually talk about stuff like that, when they talk about virtual particles in dielectric media and not about internal lines in Feynman diagrams.

Similar things can be said about reference 32 which you discredit for unclear reasons. While active, Zimmermann was one of the most distinguished many-body theorists out there and questioning this is a very daring claim. And of course virtual states have a different meaning when considering ultrafast optics as compared to high energy QED. Edit: this should not have read virtual, but vacuum states.

One does not have to find this terminology useful or elegant, but one should at least acknowledge that in contrast to all-out relativistic QED which is important for precise predictions of energies, cavity QED is interested first and foremost in dynamics and open systems. Of course this results in different meanings in different fields for the same terminology. If you really think that the Science paper is actually wrong, it would be good scientific practice to write a rebuttal.

 

[A. Neumaier]

In any case, the fundamental photon mode of the system is now one of finite spectral width and of finite lifetime.

I was not aware of this. Can you give me a good reference where this and its implications are discussed in some detail?

By the way, your quote environment in the previous post misses a ".

 

[Cthugha]

I was not aware of this. Can you give me a good reference where this and its implications are discussed in some detail?

I am not sure, I have a reference at the level you might be interested in. If I get it right, you are working on the really well defined mathematical side of physics, while I am an experimentalist that does too much semiconductor physics to be a quantum optics guy and too much quantum optics to be a semiconductor guy. What I guess might be something along the lines you could be interested in, are the lecture notes "An Open Systems Approach to Quantum Optics: Lectures Presented at the Université Libre de Bruxelles" by Howard Carmichael. Unfortunately, I am not sure whether there is an easily accessible version on the web. The RMP article by Plenio and Knight (https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.70.101) is also interesting, but might not be what you are looking for (However, it also focuses on quantum jump approaches, which you seem to be interested in). I remember some book chapter or article about the question of how to quantize light fields subject to loss, but I do not remember where exactly I found it. I will let you know when I find it.

edit: This was not the article, I was looking for, but at least it goes into the right direction: https://arxiv.org/abs/quant-ph/9702030
It might have been some other article by Gardiner.

By the way, your quote environment in the previous post misses a ".

Oh, thanks a lot. I corrected that.

 

[A. Neumaier]

I am not sure, I have a reference at the level you might be interested in.

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.

If I get it right, you are working on the really well defined mathematical side of physics, while I am an experimentalist that does too much semiconductor physics to be a quantum optics guy and too much quantum optics to be a semiconductor guy.

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.

 

[A. Neumaier]

Glauber in his seminal paper on quantum optics in dielectric media (https://journals.aps.org/pra/abstract/10.1103/PhysRevA.43.467), where he finds that the ground state of the light field inside a dielectric becomes a squeezed state, when analyzed using empty-space photon operators. People usually talk about stuff like that, when they talk about virtual particles in dielectric media and not about internal lines in Feynman diagrams.

Similar things can be said about reference 32 which you discredit for unclear reasons. While active, Zimmermann was one of the most distinguished many-body theorists out there and questioning this is a very daring claim. And of course virtual states have a different meaning when considering ultrafast optics as compared to high energy QED.

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?

 

[Cthugha]

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.

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.

 

[A. Neumaier]

I fully agree that both are very different.

But this leaves me confused about your criticism in #31. Why did you mention virtual states at all? Is your complaint that I interpret their virtual excitations and virtual photons as virtual particles whereas I should interpret them as virtual states of photons? Then how would you interpret their statement about ”photons, which spontaneously arise and vanish in the ground state”? I can understand that a photon in an unstable ground state can vanish spontaneously but how could it be created spontaneously?

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.

Thanks.

 

[Cthugha]

But this leaves me confused about your criticism in #31. Why did you mention virtual states at all? Is your complaint that I interpret their virtual excitations and virtual photons as virtual particles whereas I should interpret them as virtual states of photons? Then how would you interpret their statement about ”photons, which spontaneously arise and vanish in the ground state”? I can understand that a photon in an unstable ground state can vanish spontaneously but how could it be created spontaneously?

Oh, I see. This was probably hard to understand. The comment was mainly due to your defense of Carmichael as a well-respected and honored theorist (which he is - without any doubt) with respect to the question of terminology of quantum jumps, while simultaneously dismissing reference [32] as just another paper by the authors. While indeed one of the authors is also a coauthor of reference [32], that paper is first and foremost a paper by Zimmermann, who is just as renowned, both as a scientist with respect to his work on many-body physics and as a person with respect to how he pursued his scientific career in the GDR without being an informer. However, I do not get what virtual states have to do with it.

edit: Argh, sorry. Now I see what you mean: it should have been vacuum states, not virtual states. Sorry. This happens, when students come rushing in while typing.

With respect to your other question: Well, in the overall true vacuum state this of course cannot happen, but I do not see this problem in an open system. The loss channel is something like tunneling through the cavity mirrors. However, the same mirror also offers a way for scattering into the cavity. This is your mechanism for spontaneous photon creation. Of course this results in a ground state that depends on the environment.

Is this in the sense of QFT? No, absolutely not. However, I have no better idea on how to describe the state of a system in contact with an environment I can neither control, nor have much information about. All of this is inherently non-equilibrium physics.
Still, what should be criticized about the paper is definitely the fact that the authors should have emphasized the role of the electro-optical crystal. This is really important.

 

[A. Neumaier]

Oh, I see. This was probably hard to understand. The comment was mainly due to your defense of Carmichael as a well-respected and honored theorist (which he is - without any doubt) with respect to the question of terminology of quantum jumps, while simultaneously dismissing reference [32] as just another paper by the authors. While indeed one of the authors is also a coauthor of reference [32], that paper is first and foremost a paper by Zimmermann, who is just as renowned, both as a scientist with respect to his work on many-body physics and as a person with respect to how he pursued his scientific career in the GDR without being an informer.

Ok; I see. I'll check again the content of that paper and will then word more carefully.

I do not see this problem in an open system. The loss channel is something like tunneling through the cavity mirrors. However, the same mirror also offers a way for scattering into the cavity. This is your mechanism for spontaneous photon creation. Of course this results in a ground state that depends on the environment.

Ok.

People usually talk about stuff like that, when they talk about virtual particles in dielectric media and not about internal lines in Feynman diagrams.

This comment is too fuzzy for me to comprehend. What is their usage of the term virtual particle and virtual photon? And is a virtual excitation just the excitation to a quickly decaying metastable level? I may need to update the definition part of the other Insight article.

 

[Cthugha]

This comment is too fuzzy for me to comprehend. What is their usage of the term virtual particle and virtual photon? And is a virtual excitation just the excitation to a quickly decaying metastable level? I may need to update the definition part of the other Insight article.

I am not sure how to phrase that, because I am quite convinced that on the theory side you know much more about the topic than I do. Please note that I mentioned two usages of the term that describe very different scenarios. I will now do my best to describe one of them. This is the one used more in ultrastrong coupling, but not really in the paper your insights article was about. If you are interested rather in the other one, let me know.

One of the possible usages of the term is brought up with respect to the question of field quantization in dielectrics. I guess you are well aware that bare photons are not eigenstates of the electromagnetic field inside some material. The Glauber paper I cited earlier analyzes this situation and finds that if you want to describe the state of the light field inside the material based on empty space operators, you will find a squeezed state. A squeezed state has a photon number distribution containing only even photon numbers, so there is a natural connection to photon pair creation. Of course Glauber also discusses the choice of operators in detail. You can find some transformed creation and annihilation operators that describe effective modes inside the medium, where the vacuum state behaves like an ordinary vacuum state. Now the interesting question that arose decades later is, what happens if you introduce fast dynamics, which may mean that you introduce a modulation of the Rabi frequency on short timescales. In that case, the question about which set of operators describes your system adequately becomes a pretty nontrivial one and this is what one part of the virtual particle articles is about.

The Riek et al. paper is rather about the implications of open systems - although they hide that very well in their article. If the notion of virtual particles in that scenario was your main focus of interest, this is about the question of how to treat an environment you do not have detailed information about adequately. I can try to come up with a detailed example, if you want to, but the rough idea is that a virtual excitation is equivalent to the environment leaking into your system of interest.

 

[vanhees71]

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.

The "photon decay" is simply due to imperfect cavities. A perfectly reflecting mirror is a theoretical fictition, though nowadays they have amazingly good ones. For a real-world cavity there's thus always some probability for the photon to being absorbed by the walls of the cavity. Mathematically it's pretty much analogous to the same calculation as in classical electrodynamics. The reason is that a lot can be done in linear-response approximation, and as long as the models are linear in the fields, the "operator-valuedness" of the mathematical objects doesn't play much of a role. The observables are then calculated by taking the appropriate averages or evaluating the corresponding probabilities, using auto-correlation functions of the fields.

Of course, you have to distinguish the notion of "virtual particles" in the HEP community, where they deal with "vacuum QED", i.e., scattering processes of two incoming particles to some other particles (or elastic scattering). In quantum optics you deal with "in-medium QED". It's usually sufficient to treat the matter involved (dielectrics, metals, making up the usual optical equipment like lenses, mirrors, beam splitters) in non-relativistic approximation. As long as linear response is sufficient you can use, e.g., dispersion theory which has been developed very early in the history of QT in the semiclassical approach (treating the em. field classical and the matter with non-relativistic QM). In modern many-body QFT terms all these linear response functions for the photons is just described by the (retarded) in-medium photon-polarization tensor, or in other words, the em. current-current correlation function.

In my field of relativistic heavy-ion collisions we deal with the same quantity in the relativistic regime to evaluate the in-medium production rates of photons and "dileptons" (i.e., lepton-antilepton pairs).

Then, with the advent of the laser, you also deal with strong fields and non-linear optics, which is also well understood in terms of phenomenological response functions.

For me quantum optics is just a side-subject because of my interest in the fascinating (real-world physics!) possibilities to test the very foundations of QT by experiment. So I'm not an expert, but my favorite textbooks on Quantum optics are

Scully, Zubairy, Quantum Optics, Cam. Uni. Press
Garrison, Chiuao, Quantum Optics, Ox. Uni. Press

Then there's of course the comprehensive bible:

Mandel, Wolf, Optical Coherence and Quantum Optics, Cam. Uni. Press

 

[Cthugha]

Then there's of course the comprehensive bible:

Mandel, Wolf, Optical Coherence and Quantum Optics, Cam. Uni. Press

Which is a great book, but could use some revised edition as the notation used is somewhat outdated in some parts.

On the textbook level, the book most theorists I know consider as thorough and reasonably detailed, is:
Vogel, Welsch, Quantum Optics, Wiley VCH
It also contains at least a short discussion on non-monochromatic photon modes, which is missing in many basic introductory texts.

Also Schleich's book on quantum optics in phase space is good, if one is interested in continuous variables and phase space distributions.