# Talk:Dicke model

**Reviewer comments copied from original location at w:User_talk:Mimigdal/sandbox**

## Contents

### Review by Dr. Nathan Shammah

The Wikipedia article is excellent: informative, clear, well structured, coherent, well edited, comprehensive. Moreover, it is important that such a page is now present in Wikipedia.

As voiced to the Editors of Plos ONE, I believe that there are some concerns, in general, in the "Topical Pages" program. That is, that the content needs to be tailored for the general public, avoiding citations to currently explored research lines and self-citations.

1. I suggest to remove any reference that is not a textbook reference, beyond the first two historical papers of Refs. 1 and 2 (Hepp-Lieb's and Dicke's paper), the existing reviews. All other references could be removed, in my opinion, maybe keeping Esslinger's lab experiment. If the text seems requiring such references, it means that the discussion may have become very technical and not completely suitable for the purposes of a Wikipedia page. In this regard, details on experiments, mathematical generalizations and descriptions, could be reduced in length. — Preceding unsigned comment added by Nathan.shammah (talk • contribs) 05:11, 27 September 2019 (UTC)

Permamnent link to the page reviewed: https://en.wikipedia.org/w/index.php?title=User:Mimigdal/sandbox&oldid=885327026 — Preceding unsigned comment added by Nathan.shammah (talk • contribs) 05:16, 27 September 2019 (UTC)

### Review uploaded by *PLOS ONE* on behalf of Dr. Tobias Donner. Uploaded March 28, 2019.

The text is a competent and timely introduction to one of the most important models of quantum optics. It is well structured and clearly written. Besides some minor corrections, I mostly have suggestions for additions which in my view should be explained or at least find mentioning. I understand that this brevity might be related to the specific wiki-type format, but believe that some more details could help the reader.

**“The model and its symmetries”**

Corrections:

1. The name of Elliott H. Lieb is misspelled in the text (“Leib”).

2. The name of Max Planck is misspelled in the definition of the Planck constant (“Plank”)

3. Equation (1) misses Planck’s constant in the second and third term on the right-hand side.

Suggestions:

4. In the definition of the Dicke model it might be helpful to explicitly tell the reader that the sum over the spins can also be replaced by one macroscopic spin operator, again obeying the spin algebra. This thought is connected to the fact that in the Dicke model all spins are assumed to be equally coupled to the light field mode, which should also be mentioned in words.

5. I would suggest to skip the second definition of Planck’s constant right after Equation (1) since it was defined earlier.

6. I would suggest to mention that the effect of the global symmetry breaking corresponds to the system’s choice of a definitive phase of both the light field and the atomic spins. I understand that this is obvious when looking at equation (2), but would add this for pedagogical reasons.

7. I was missing the mentioning of the debate about the no-go-theorem for the Dicke phase transition. This could be mentioned here or at the experiments.

**“The superradiant phase transition”**

Suggestions:

8. It should be mentioned that this is a second order phase transition.

9. Since it is an important feature of second order phase transitions, I would suggest to also mention the softening of the first excited mode. Staying in the language of quantum optics, the description could mention the polaritonic character of the new eigenmodes of the coupled system. Then it could be specified that the first excited state is softened until its energy reaches zero, where the system undergoes the phase transition. For larger couplings the new ground state carries excitations although the (closed) system was never driven. These excitations origin from the coupling rate which exceeds the bare eigenfrequencies of the system (see equation (6)).

10. The statement that the order parameter is zero in the normal phase is sufficient, I would not mention that it does not depend on N.

**“The open Dicke model”**

I was wondering whether this section should not rather be shifted to after the section “Mean-field description…” to make the article more coherent.

Suggestions: 11. The author states that experiments realized the open Dicke model which allows for loss of both cavity photons and the decay of two-level systems. Equally important is however to mention, that these systems thus are driven systems and that the phase transition is realized in a frame rotating at a frequency which is given by the difference between the drive frequency and the bare cavity mode frequency. This is so far the only way to produce large enough coupling rates such that the phase transition can be reached.

12. Since the previous section gave the critical exponent of 0.5, it could here be mentioned that beta=1 for the open (i.e. effectively thermal) system.

**“The superradiant transition and Dicke superradiance”**

Correction:

13. The table summarizing the differences between superradiance and the superradiant phase transition should not mention “cavity field” but simply “field” (or “electromagnetic field”) in the first column since it refers both to the free space and the cavity mode case.

Suggestions:

14. The sentence “This is in contrast to spontaneous…” could mention that without superradiance the decay time of the ensemble equals the decay time of a single atom.

15. Figure 2 is slightly misleading in my view: While the Dicke superradiance is related to an open system, the superradiant transition can in principle also occur in a closed system, i.e. without the pump field. If the pump field is shown it should be stated that the driven-dissipative case is sketched. In addition, the cavity output should be displayed, as well as a graph showing emission vs time in analogy to the left panel. Alternatively, the closed system could be sketched with “half-way” excited atoms.

**“Mean-field description of the transition”**

Suggestions:

16. Here or in another section of the article I would very much like that the zero-temperature case is also discussed. This discussion should encompass the idea that this phase transition can take place at T=0 (cite e.g. C. Emary and T. Brandes, Phys. Rev. E 67, 066203 (2003)). Also, the scaling of fluctuations in the thermodynamic limit should be discussed, together with whether this transition should be regarded as a quantum phase transition.

**“Experimental Realization of the Dicke model”**

It should be mentioned that these realizations are in the rotating frame corresponding to the detuning between pump field and cavity resonance.

Suggestions:

17. I suggest to mention in the third sentence that the Raman transition is established by the combination of external pump and the cavity field.

18. The phrase “change its state from down to up, or vice versa, and emit a photon into the cavity” is not fully precise since also the process of scattering a cavity photon back into the pump needs to be mentioned.

19. The up state in the momentum space realization of the model corresponds actually to two recoil (i.e. twice the momentum of a photon), since the scattering is a two-photon process.

**“The generalized Dicke model and lasing”**

Question:

20. To me, an important difference between lasing and the superradiant phase transition is that lasing occurs when gain overcomes losses, while the superradiant transition occurs when two energy scales compete. Is this the case also here?

Suggestions:

21. Figure 3, left panel shows a situation that never was realized experimentally, while entire the figure has the title “Experiments on the Dicke model”. This should be clarified. At the same time, the relevant energy scales could be visualized, especially \omega_z.

## Tobias Donner, posted with permission by *PLOS ONE*

### Author's reply

Mimigdal (talk) 13:55, 13 January 2020 (UTC)

Uploaded reply in MediaWiki format Moroses (talk) 21:55, 16 January 2020 (UTC)

#### Letter To The Editor

Dear Editor,

We would like to thank the referees, Dr. Nathan Shammah and Prof. Tobias Donner, for reviewing our work and helping us improve it. We were happy to learn that they enjoyed our topic page, albeit some reservations. As suggested by Nathan, we removed all the technical references from the topic page. Tobias pointed out a few imprecisions and typos in our topic page, which we have now fixed. We also took into consideration the various suggestions proposed by him and implemented some of them.

Mor and Emanuele

#### First Referee

Dr. Nathan Shammah: The Wikipedia article is excellent: informative, clear, well structured, coherent, well edited, comprehensive. Moreover, it is important that such a page is now present in Wikipedia. As voiced to the Editors of Plos ONE, I believe that there are some concerns, in general, in the "Topical Pages" program. That is, that the content needs to be tailored for the general public, avoiding citations to currently explored research lines and self-citations. 1. I suggest to remove any reference that is not a textbook reference, beyond the first two historical papers of Refs. 1 and 2 (Hepp-Lieb's and Dicke's paper), the existing reviews. All other references could be removed, in my opinion, maybe keeping Esslinger's lab experiment. If the text seems requiring such references, it means that the discussion may have become very technical and not completely suitable for the purposes of a Wikipedia page. In this regard, details on experiments, mathematical generalizations and descriptions, could be reduced in length.

__
Dear Dr. Nathan Shammah,
__

__We sincerely thank you for your enthusiastic comments and for your thoughtful suggestions on how to improve our topic page.
We agree with you that our previous version of the topic page had become too technical in some points.
__

__Following your suggestion, we have removed most of the technical references that appeared in the topic page.
The only references that we kept are: (I) the original theory paper by Dicke and Hepp and Lieb; (ii) the first theoretical proposals and experimental realizations of the open Dicke model; and (iii) review articles and books regarding the Dicke model.
__

__Furthermore, we removed some technical details, in order to make the topic page as accessible as possible.
In particular, we removed the Green’s function description of the superradiant transition of the open Dicke model. (This is probably what you had in mind when you spoke about “self-referencing”?).
We decided not to remove the part on the counter-lasing transition. Although this part is a bit technical, it addresses a fundamental concept, namely the difference between the Dicke transition and lasing, which can be appreciated by nonprofessionals as well.
__

#### Second Referee

Dr. Tobias Donner: The text is a competent and timely introduction to one of the most important models of quantum optics. It is well structured and clearly written. Besides some minor corrections, I mostly have suggestions for additions which in my view should be explained or at least find mentioning. I understand that this brevity might be related to the specific wiki-type format, but believe that some more details could help the reader.

__
Dear Dr. Tobias Donner,
__

__We sincerely thank you for your thoughtful and informative review of our topic page.
We corrected the topic page according to your comments and took into considerations all your suggestions.
While most of them were implemented in the new version, a few were left because we felt that they would become too technical (see also the comments by the other Referee).
__

**"The model and its symmetries"**

Corrections:

1. The name of Elliott H. Lieb is misspelled in the text (“Leib”).

2. The name of Max Planck is misspelled in the definition of the Planck constant (“Plank”)

__
We thank you for highlighting these spelling mistakes, which were now fixed.
__

3. Equation (1) misses Planck’s constant in the second and third term on the right-hand side.

__
In this Topic page we chose to follow the notation used by Wikipedia Spin-½, where spin operators have units of .
__

__In this notation, appears explicitly in the spin commutation relation rather than in the Hamiltonian.
__

Suggestions:

4. In the definition of the Dicke model it might be helpful to explicitly tell the reader that the sum over the spins can also be replaced by one macroscopic spin operator, again obeying the spin algebra. This thought is connected to the fact that in the Dicke model all spins are assumed to be equally coupled to the light field mode, which should also be mentioned in words.

__
We
agree that there is a benefit to introduce the collective spin
operators. This is especially true for the case of the closed Dicke
model, where the collective spin is a conserved quantity. We have now
added a new paragraph that includes the definition of the collective spins and the Dicke model in the collective spin notation.__

5. I would suggest to skip the second definition of Planck’s constant right after Equation (1) since it was defined earlier.

__
We
have removed the redundant definition of Planck’s constant.__

6. I would suggest to mention that the effect of the global symmetry breaking corresponds to the system’s choice of a definitive phase of both the light field and the atomic spins. I understand that this is obvious when looking at equation (2), but would add this for pedagogical reasons.

__
We
now mention this point in the section on the superradiant transition,
where we discuss the nature of the phase transition and of its order
parameter.__

7. I was missing the mentioning of the debate about the no-go-theorem for the Dicke phase transition. This could be mentioned here or at the experiments.

__
We
now open the experimental part by mentioning that the dipole coupling
is insufficient to observe the Dicke transition and that periodic
drives were used to realize it.__

**"The superradiant phase transition"**

Suggestions:

8. It should be mentioned that this is a second order phase transition.

__
Done.__

9. Since it is an important feature of second order phase transitions, I would suggest to also mention the softening of the first excited mode. Staying in the language of quantum optics, the description could mention the polaritonic character of the new eigenmodes of the coupled system. Then it could be specified that the first excited state is softened until its energy reaches zero, where the system undergoes the phase transition. For larger couplings the new ground state carries excitations although the (closed) system was never driven. These excitations origin from the coupling rate which exceeds the bare eigenfrequencies of the system (see equation (6)).

__
We agree that polaritons are very relevant to this topic, but decided not to mention them here.
We felt that explaining this point would require too many technical details.
__

__Incidentally, we found that the Wikipedia page on polaritons is not well developed.
Perhaps your point can be added at a later state, one the page on polaritons is improved.
__

10. The statement that the order parameter is zero in the normal phase is sufficient, I would not mention that it does not depend on N.

__
We
followed your suggestion and erased this technical detail.__

**"The open Dicke model"**

I was wondering whether this section should not rather be shifted to after the section “Mean-field description…” to make the article more coherent.

Suggestions:

11. The author states that experiments realized the open Dicke model which allows for loss of both cavity photons and the decay of two-level systems. Equally important is however to mention, that these systems thus are driven systems and that the phase transition is realized in a frame rotating at a frequency which is given by the difference between the drive frequency and the bare cavity mode frequency. This is so far the only way to produce large enough coupling rates such that the phase transition can be reached.

__
We
now mention that the Dicke system was realized in a rotating frame.__

12. Since the previous section gave the critical exponent of 0.5, it could here be mentioned that beta=1 for the open (i.e. effectively thermal) system.

__
The exponent beta=0.5 is the same for all cases.
The quantum and open/thermal cases differ in the value of the critical exponent alpha, which sets the divergence of the fluctuations close to the transition.
To keep the text as simple as possible, we do not mention this critical exponent.
__

__Perhaps, at a later stage one may decide to add a paragraph on the fluctuations and their role in establishing the type of phase transition.
__

**"The superradiant transition and Dicke superradiance"**

Correction:

13. The table summarizing the differences between superradiance and the superradiant phase transition should not mention “cavity field” but simply “field” (or “electromagnetic field”) in the first column since it refers both to the free space and the cavity mode case.

__
We
have corrected the table.__

Suggestions:

14. The sentence “This is in contrast to spontaneous…” could mention that without superradiance the decay time of the ensemble equals the decay time of a single atom.

__
We
opted not to mention this point in order to keep the text as simple
as possible.__

15. Figure 2 is slightly misleading in my view: While the Dicke superradiance is related to an open system, the superradiant transition can in principle also occur in a closed system, i.e. without the pump field. If the pump field is shown it should be stated that the driven-dissipative case is sketched. In addition, the cavity output should be displayed, as well as a graph showing emission vs time in analogy to the left panel. Alternatively, the closed system could be sketched with “half-way” excited atoms.

__
We
now explicitly show the emission of the cavity and specify that the
graph refers to the open Dicke model.__

**"Mean-field description of the transition"**

Suggestions:

16. Here or in another section of the article I would very much like that the zero-temperature case is also discussed. This discussion should encompass the idea that this phase transition can take place at T=0 (cite e.g. C. Emary and T. Brandes, Phys. Rev. E 67, 066203 (2003)). Also, the scaling of fluctuations in the thermodynamic limit should be discussed, together with whether this transition should be regarded as a quantum phase transition.

__
We
now briefly mention that at zero temperature one obtains a quantum
phase transition. The roles of classical vs quantum fluctuations are
not discussed for the sake of brevity.__

**"Experimental Realization of the Dicke model"**

It should be mentioned that these realizations are in the rotating frame corresponding to the detuning between pump field and cavity resonance.

__
Done.__

Suggestions:

17. I suggest to mention in the third sentence that the Raman transition is established by the combination of external pump and the cavity field.

__
Done.__

18. The phrase “change its state from down to up, or vice versa, and emit a photon into the cavity” is not fully precise since also the process of scattering a cavity photon back into the pump needs to be mentioned.

__
We
mention that the photon can be also absorbed.__

19. The up state in the momentum space realization of the model corresponds actually to two recoil (i.e. twice the momentum of a photon), since the scattering is a two-photon process.

__
We
now mention that the “up” state has the sum of the momenta of
both the cavity photon and the pump photon.__

**"The generalized Dicke model and lasing"**

Question:

20. To me, an important difference between lasing and the superradiant phase transition is that lasing occurs when gain overcomes losses, while the superradiant transition occurs when two energy scales compete. Is this the case also here?

__
Yes, and no.
The counter-lasing transition is very similar to the lasing transition, so the gain vs. loss is the focus point.
For the superradiant transition the transition can occur even in the absence of loss and gain.
__

__However, in certain cases, e.g. strong single atom decay rates, the discussion can be shifted to gain vs. losses as well.
__

Suggestions:

21. Figure 3, left panel shows a situation that never was realized experimentally, while entire the figure has the title “Experiments on the Dicke model”. This should be clarified. At the same time, the relevant energy scales could be visualized, especially .

__
We
now mention that the left side of the panel was not realized (as of
yet) in the figure caption and we also provide a short discussion
about the no-go theorem in the paragraph. __