Peer review of: Fast electrical modulation of strong near-field interactions between erbium emitters and graphen  (2020)

REVIEWER COMMENTS 
Reviewer #1 (Remarks to the Author): 

This manuscript shows that graphene can be used to electrically modulate the decay rate of 
nearby emitters (a few nm) by modulating the concentration of carriers in the graphene sheet. The 
authors clearly demonstrate two different decay channels (plasmon generation, e-h pair 
generation) by tuning the concentration, or Fermi energy, of the graphene in a ‘sweet spot’ where 
half the cycle is governed by interband transitions (e-h pair generation) and the other half of the 
cycle is governed by intraband transitions (plasmon generation). The authors exploit the high 
bandwidth of the AC response in graphene to demonstrate that this near-field interaction can be 
operated in the kHz regime and ingeniously use a combination of Si backgate and polymer top 
gate to be able to reach this regime without applying large AC voltages while having transparency 
to optical experiments. An extensive and thorough theoretical analysis corroborates their results. 
This is not surprising given the well established expertise of the authors in the field. The paper is 
very clearly written and the results are very convincing. 

I believe that this paper will be of great interest to the general physics community (plasmonics, 2D 
materials, optics, electronics) and given the remarkable high quality of the paper and the clarity of 
the results, I would recommend publication in Nature Communications. Nevertheless, the 
manuscript can be improved by addressing the following points: 

Abstract: 
-‘of a significant fraction of the erbium emitters’: what does significant mean? After reading the 
paper I see it is 25%. Maybe better to use this number in the abstract? 

Page 2: 

1st paragraph: 
-Going briefly through the references presented, it seems to me (although I might be wrong) that 
reference 11 does not ‘modulate the effective refractive index of the cavity’ because i fail to 
recognize an optical cavity. It does however modulate the strength of the interaction at high speed 
by using graphene. It seems to me that it is a very pertinent reference, but misleading in how it is 
presented. 

-2nd paragraph: The authors attempt to compare field confinement of graphene plasmons with 
noble metal plasmons, but offer numbers only for graphene plasmons: 100 times smaller than 
free-space photons. Could they also include the metric for noble metal plasmons? 

-2nd paragraph: In the manuscript the 10^6 mode volume confinement is referenced with ref 14. 
I can’t find this metric in the reference. Could the authors help me understand how they obtain 
this number from the reference? 

fig 1: 
-I am confused by panel b. It looks as if when the Fermi energy is 0.3eV, then plasmons are 
launched (intraband transitions) and when Ef=0.6eV e-h pairs are generated (interband). Surely 
this is not the case. I realize now that I was wrong, but it took me a while. The fig is correct, but it 
is confusing. Additionally, for a general audience it would be suitable to show the conical band 
structure with the two types of transitions. 

fig 2: 
-fig 2b shows the lifetime in the interband regime at Ef = 0.2eV, however in panel a 
measurements stop at Ef=0.3eV. Although fig 2a is already convincing, if measurements are 
available to show the plateau below Ef=0.3V it would make it even more complete. 

-Inset of fig 2b is not mentioned in the caption. 

Page 5: 
-2nd paragraph: at the end of the paragraph the authors show the % of energy flowing into the 
different quasiparticles. Just for the form, it would be easier to follow if the authors referred to 
either interband (intraband) or e-h (plasmons). And this could also be corrected throughout the 
paper (in the figures for example). 

Page 6: 
-2nd paragraph: I have difficulty following how to obtain the percentage of ions having a certain 
purcell factor Fp from fig 2d. Could the authors explain it better please? Also, what is the x-axis ‘p’ 
in the figure? 

Page 7: 
-2nd paragraph: define ‘gamma’. Just for the form, we know it’s the decay rate. 

Page 8: 
-1st paragraph: The authors state that for fig 4e, the modulation amplitude is higher in exp than in 
simulation. Could this be a margin of error issue (noting that 1/f noise could increase this error) 
instead of non-local effects in the plasmonic local field? 



Reviewer #2 (Remarks to the Author): 

In this paper, the authors realized fast modulation of the strong near interactions between a 
nanolayer of erbium emitters and graphene by in-situ electrical tuning the Fermi energy of 
graphene. In specific, strong interaction with over 1000-fold increased decay rate of the erbium 
emitters and interactions with frequencies up to 300 kHz were reached. In my opinion, dynamical 
tuning the strong emitter-graphene interaction is important, which can find applications for 
integrated quantum technologies. This work is a following one by the same authors (Nat. Phys. 11, 
281 (2015)), in which fast dynamical modulations is considered here. The work is interesting, the 
physics is clean and the results are well presented, I think it can be acceptable as long as following 
issues are considered. 
1. It is difficult to understand the meaning of the inset in Fig.2. It seems that the z dependent 
decay rate should be discussed here, but it is unclear because that there is a lack of clear 
description of coordinates and enough discussion in the main text. 
2. Overall the paper, the emission is dominated by the isolated erbium emitter with specific 
distributions, however, collective interactions between them may be another important effect in 
this extreme condition. Could the authors comment more about if there are collective effects for 
the erbiurm emitters? 
3. It is still unclear the ultimate limit for this kind of fast modulations. It is clear from Fig. (3) that 
the decay of the erbium emitters cannot follow the speed of the modulation in the high frequencies. 
I suggest the authors to give more clear consideration in this aspect. 
4. I suggest more applications for this modulation can be included in the revised one, especially on 
how to implement this kind of modulations in a specific quantum device. 
5. In Pape 4, the authors have stated that there is an increasing slope of the emission contrast for 
E_F > 0.6 eV. However, I cannot find find the phenomenon in the figure.