Motion-Induced Radiation Due to an Atom in the Presence of a Graphene Plane
Round 1
Reviewer 1 Report
Comments attached.
Comments for author File: 
Comments.pdf
Author Response
We thank the Referee for the careful reading of our manuscript, which allowed us to improve the presentation.
Regarding the comments in the report :
1. Please note that the fermion field describes the electrons in graphene, while the electron in the atom can be treated as a
nonrelativistic particle.
2. We included a derivation of Eq. (5).
3. $V(x)$ is the central potential with origin at the nucleus, as was already mentioned before Eq.(4).
4. We added a reference for Eq.(7).
5. We corrected the typo.
6. We explained the assumption after Eq.(10): the effective action is assumed to vanish in the free case.
7. We corrected the typo.
8. We included the definition of $\Delta_\omega$ after Eq.(16).
9. Regarding this point, please note that in that part of the paper we are discussing a two-level atom. This is why we only included
the states $|0\rangle$ and $|1\rangle$.
10. After Eq.(30) we clarified the relation between the divergent term in the correlation and the divergent contribution to the energy.
11. We have added a paragraph in the conclusions mentioning the relation between quantum friction and Cherenkov radiation. We also added the reference by Maghrebi et al, where this relation is discussed for the case of nondispersive dielectrics [24] .
Reviewer 2 Report
REPORT ON Motion-induced radiation due to an atom in the presence of a graphene plane
In this manuscript, the authors present a derivation of the emission of an atom with a center of mass oscillation nearby a graphene plate. The authors evaluate the additional emission arising from the dynamical atomic motion when compared to an atom at rest. Their main conclusions is that 1) the contribution tdepends strongly on the orientation of the motion with respect to the plate, yielding an increase/decrease when the oscillation 2) when the atomic motion is constant and parallel to the plate, quantum friction occurs only for a velocity above a threshold v_F. This threshold is lower than in other systems, enabling an easier derivation of the quantum friction.
The authors use the in-out effective action formalism to describe the effect of the graphene sheet. Fermionic modes of the graphene sheet are coupled to the EM field and the atom is coupled through the EM field through a dipole operator. The graphene and EM field degrees of freedom can be integrated on with Feynmann-Vernon path integrals, leaving an influence phase associated to the influence of the graphene plate, which imaginary part reflects the radiation.
The authors perform a perturbative expansion of the effective action, integrating the connected vacuum field diagrams. The imaginary part of this action yields the quantum friction. The authors use a perturbative expansion, with respect to the interaction S_int, and with respect to the atomic motion assumed at a small scale. The authors obtain in Eq.(62,69) spectral distribution associated the radiated field in perpendicular/parallel oscillations.
The results obtained by the authors are original and very interesting, and the method used is scientifically sound. The derivations are technical, but are described in sufficient details to be followed by an expert of the field, and the conclusions are sound. Thus, I recommend the paper for publication in the journal Universe.
This said, I have a few comments:
1) There is an existing literature on motional effects (interplay between atomic motion/quantum vacuum forces) that could be complemented, for instance by the references:
Stefan Scheel and Stefan Yoshi Buhmann Phys. Rev. A 80, 042902 (2009)
S Scheel, SY Buhmann Physical Review A 85 (3), 030101 (2010)
F Impens, RO Behunin, CC Ttira, PAM Neto EPL 101 (6), 60006 (2013)
Francesco Intravaia, Vanik E Mkrtchian, Stefan Yoshi Buhmann, Stefan Scheel, Diego A R Dalvit and Carsten Henkel J. Phys.: Condens. Matter 27 214020 (2015)
2) My only concern regarding the methodology obtention of the results is the following. The atomic dipolar should be taken in the comoving atomic frame, and there is thus a component associated to the vacuum fluctuations of the magnetic field (usually referred to as the “Rontgen term”) e v x B(r(t), t)/c. My question is whether this term could play a relevant role here, with respect to the photon emission in presence of oscillation, and with respect to the quantum friction. If this term can be neglected, it would be good to have an explanation.
3) Last, as suggestion: maybe the authors could do the parallel between the threshold in the frequency of the mechanical oscillation (62,69) – the mechanical oscillation needs to have enough power to excite the frequencies \nu, and the threshold in the velocity for the excitation of the graphene modes. To second order, there is no threshold for the photonic emission. My interpretation is that there is a continuum of available for emission in EM modes at arbitrary small frequencies, while there is a discrete excitation spectrum for the graphene modes.
4) Is there a simple physical interpretation (for instance with the image method, in terms of constructive/destructive interferences) why the emission is reduced when the atom oscillates perpendicular to the plate and enhanced when is oscillates parallel to the plate? In case there is one, that would be a nice complement to the author’s work.
To conclude, in view of the above, I recommend this work for publication.
Author Response
We thank the Referee for the careful reading of our manuscript, which allowed us to improve the presentation.
In the report, the Referee highlights three aspects of our results and asks about the relation with the corresponding ones for dielectric/metal plates:
" 1) for QF, the threshold is the same as for two graphene planes sliding relative to each other 2) the effect of graphene plane increases the emission probability when the atom oscillates in the perpendicular direction, and decreases when the atom performs parallel oscillations; 3) when the approximation of small amplitudes for harmonic motion is not used, the system can receive excitations also from harmonics of the fundamental frequency. All these conclusions are a consequence of the massless behavior of the Dirac fermions in graphene propagating with the Fermi velocity Vf=0.003c. If all this is true, then the system under consideration behaves completely differently than more conventional ones, such as an electromagnetic field-atom-metal (dielectric) plate. "
Taking into account (1), in the conclusions we have added a discussion on the relation between quantum friction and Cherenkov radiation. We also added the reference by Maghrebi et al, where this relation is discussed for the case of nondispersive dielectrics [24]. Therefore, we pointed out that in this respect graphene behaves as a nondispersive dielectric.
Regarding point (2), we would like to stress that these results are reminiscent of those for atoms in the presence of perfect mirrors, which can be understood in terms of the images method. This was already mentioned in the manuscript, at the end of Section V.
About point (3), we would like to stress that this result is not related to the presence of a graphene sheet. Indeed, in the manuscript, we showed that higher harmonics enter in the imaginary part of the effective action even for an atom oscillating in vacuum. We also mentioned that the relevance of the harmonics of the fundamental frequency in the DCE has been previously pointed out in Ref.[23], for the case of semitransparent mirrors.
We also added two of the references mentioned by the Referee, and corrected all the typos listed in the report.
Regarding the comment about the use of upper and lower indices in both sides of some equations, please note that we are using that notation in order to avoid confusion. In any case, we have mentioned explicitly that we are using the metric signature $(+ - - -)$ (we have taken into account the eventual changes of signs induced by our notation).
Reviewer 3 Report
The authors use the quite complicated mathematical formalism developed in line with their previous publications [17–20]. I have not a possibility to go into the details of the mathematics, but I have no reason to expect anything else than that the formal calculations in the paper are performed in a competent way, and therefore, I have to rely on the results obtained.
My main concern is the presence (absence) of the velocity threshold for radiation and quantum friction (QF) in the system electromagnetic field-atom-graphene plane. The authors claim that: 1) for QF, the threshold is the same as for two graphene planes sliding relative to each other 2) the effect of graphene plane increases the emission probability when the atom oscillates in the perpendicular direction, and decreases when the atom performs parallel oscillations; 3) when the approximation of small amplitudes for harmonic motion is not used, the system can receive excitations also from harmonics of the fundamental frequency. All these conclusions are a consequence of the massless behavior of the Dirac fermions in graphene propagating with the Fermi velocity Vf=0.003c. If all this is true, then the system under consideration behaves completely differently than more conventional ones, such as an electromagnetic field-atom-metal (dielectric) plate. I was missing a discussion of the absolute assessments of the QF, the intensity of radiation and its directionality. This is desirable in order to compare (at least QF) with the known results for the systems mentioned above. In this regard, some references are worth to be cited which are absent in the list:
- Høye, S., Brevik, I., Milton, K.A. Casimir friction between polarizable particle and half-space with radiation damping at zero temperature. J. Phys. A, 2015, 48, 365004.
- Intravaia, F., Behunin, R.O., Henkel, C.; Busch, K.; Dalvit, D.A.R. Failure of local thermal equilibrium in quantum friction. Rev. Lett. 2016, 117, 100402.
- Dedkov, G.V., Kyasov, A.A. Fluctuation-electromagnetic interaction under dynamic and thermal nonequilibrium conditions. Physics-Uspekhi 2017, 60, 1–27.
In summary, I believe that the paper has met the threshold for acceptance, and I support its publication in Universe. There are several typos and additions, however, that should be addressed and made before publication. A list is given below.
- Please, specify the definition of χ before (20) and N after (22)
- Check the exponential factor in (36)
- Please, use the same upper (lower) indices in both parts of equations (p3 or p3, k3 or k3) in (46), (47), (49)-(52); why do you use the upper and lower indices for the Kroenecker symbol in, in (30), (38) ?
- Check the denominator in (33)
- Line 190: “in one assumes” should be replaced by ”if one assumes”
- Check Ref. 17 (Decca npj)
Author Response
We thank the Referee for the careful reading of our manuscript, which allowed us to improve the presentation.
Regarding the comments in the report:
1) We have included the references suggested.
2) We believe that the magnetic dipole contribution can be neglected in our nonrelativistic approximation.
3) Thank you for your suggestion. We are not completely sure about the parallelism between the two thresholds, but certainly is a point that deserves further analysis.
4) Regarding this point, we would like to stress that the results are reminiscent of those for atoms in the presence of perfect mirrors, which can be understood in terms of the images method. This was already mentioned in the manuscript, at the end of Section V.
Reviewer 4 Report
This is an interesting study of the motion-induced radiation due to the non-relativistic motion of an atom. The latter is coupled to the vacuum electromagnetic field by an electric dipole term in the presence of a static graphene plate. It is shown that the effect of the plate is to increase the probability of emission when the atom is near the plate and oscillates along a direction perpendicular, while for parallel oscillations there is a suppression. They also show that there is a threshold for quantum friction. These are well justified results and deserve publication to Universe.
Author Response
Thank you very much for your remarks.
