Peer review of: Sub-picosecond thermalization dynamics in condensation of strongly coupled lattice plasmons (2020)



RR2
Reviewers' comments:
Reviewer #1 (Remarks to the Author): Dear editor and authors,
   the resubmitted manuscript by Väkeväinen et al. has significantly improved, and the conclusions
 are now much better backed up by the measured data. Before I can recommend publication, there
 are however a few points that need to be adressed:
 i) Just for my own curiosity: How stable are the real space images in fig. 2? If instead of single
 shot (in b, d and f) one would average over the same amount of shots as for the spectral data in c,
 e and g, which of the observed features do survive?
 ii) In Fig. 3 h and i, one should in principle see a thermal tail, however in the present color scale
 this nis just some shadow. Could one make this tail observable by e.gusing a logarithmic color
 scale, or does the blooming of the CCD somehow prevent this? Considering that the integrated
 signal does not suffer to severely from the blooming, I guess this should be an option?
 iii) As a suggestion, the authors might want to discuss the nature of the "multimode condensation"
 in a little more detail. It might indeed be a single mode condensate at any given time, but due to
 the blue shift which is a function of intensity and thus also of time due to the pump pulse temporal
 profile the condensate mode will change. Then the observed spectra would be somehow
 "dynamical single mode" instead of multimode. I am aware that temoral resolution is out-of-the
 way, but maybe there are other signatures that could help decide between the two options?
 iv) On page 12, the authors give the scale of 25μm after which the red shift occurs. With this part,
 I have a few points that should be adressed:
 - The 25μm is presented as something general, however it is only true for a given pump fluence.
 While this is clear from fig. 5i, it should be clearly adressed in the text also.
 - The authors hsould explain how they experimentally determine, at which point the red shift
 starts. Igot the feeling that this is done "by eye" when reading the text, but I assume there is a
 more clear-cut criterion for that?
 - The authors should discuss the existence of the saturation value of 18μm in more detail. It is
 unclear to me where it should come from, and if/how it could be at least estimated from system
 parameters? The 18μm correspond roughly to the distance a free space would travel during the
 pulse duration of 50 fs, but this is clearly a weird coincidence. However, it is quite striking that the
 Builup-Time model from Q-switching fits so nicely but then suddenly breaks down, thus this needs
 an explanation.
 v) In figure 5, integrated spectra would be quite convenient such that one can estimate the degree
 of thermalization "by eye". According to Fig. 2, the pump fluence of 2.2μJ is rather close to the
 condensation threshold, thus I believe this would be quite helpful (I think one of them corresponds
 to something slightly above the yellow line in Fig. S6, but a single, well readable spectrum in the
 supplementary for each lattice size would be quite helpful).
 vi) On page 17, the authors state "It seems that for a long excitation pulse...[]...as it competes
 from the same gain wtih the lasing...". However, the competition for gain is always the case,
 independent of the pump pulse length, so I do not quite get the intention of that statement. It
 does not really explain the difference between short and long pulses.
 vii) In fig. 7, the authors state that they chose the threshold for thermalization ( i.e. the data
 points for incomplete thermalization) from the point at which the interference patterns become
 visible. This seems a completely subjective measure, as "soemthing becoming visible" obviously is
 a matter of color scale, noise, personal taste, and such like. Correspondingly, for these data points
 
I would ask for a more reliabel measure such as "the visibility of the associated interference
 pattern is larger than xx", which is independent on the observer.
 viii) In their reply letter the authors state that in light of my previous comment (Reviewer 1,
 statement vii) they changed the conclusion to "These questions have become challenging for
 strongly coupled room temperature condensates", as most of the claimed points were discussed
 for the Photon BECs in Bonn and London. However, the first sentence of the discussion still gives
 the impression that nothing has been done in that direction. I would appreciate a reformulation in
 the sense "These questions have been adressed for weakly coupled photon BECs, but become
 challenging for strongly coupled systems..." or something in this spirit.
 Reviewer #2 (Remarks to the Author):
Reviewer #3 (Remarks to the Author):
 I have read the comments of all referees, the replies by the authors, and the revised manuscript &
 supplemental material in detail. The authors have replied in a lot of detail to all referee comments
 and questions and as a result have significantly improved the manuscript. I believe all important
 questions have been addressed and thus now recommend publication in Nature Communications
 without further revisions.
  During the revision process the manuscript has been considerably improved along the
 lines of the criticism of the referees. This has clarified the majority of points,
 which have been raised. But, partially due to the enormous scope of both the
 manuscript and the supplemental material, still some points are unclear to me, so I
 hope that the refereeing process of Nature Communications would allow also their
 clarification:
 1) The authors answered quite elaborately concerning the question whether the y
 observe a Bose-Einstein or a Maxwell-Boltzmann distribution. Partially I do not
 understandtheirextensiveargumentation.SomehowIwouldhaveexpectedthatthey
 plainly plot the experimental data in form of ln (1+1/n) as a function of energy E.
 In case of a Bose-Einstein distribution ln (1+1/n) would coincide with (E-mu)/(k_B
 T). Thus, the slope should yield the temperature and the axis section the chemical
 potential. As a consequence, the question is how well the temperature in the
 experiment is reproduced and how the result for the chemical potential could be
 understood in terms of the ground-state energy of the system.
 2) In view of the photon-photon interaction strength, the authors mention now a
 value of about 0.2 \mu e V \mu m^2. Here it would be helpful if the authors could
 also calculate the dimensionless interaction strength \tilde{g}=g m / hbar^2, which
 is possible to determine due to the two-dimensionality of the considered system. To
 this end one would have to know the polariton mass in the experiment. The resulting
 value would be important to judge whether the polaritons are in the state of a BEC,
 i.e. \tilde{g} < 0.5, or in a BKT, i.e. \tilde{g} > 0.5. Please note that this
 boundary value 0.5 is not a sharp one but just gives the order of magnitude.
 3) The plots in Fig. 4 are unclear to me. On the one hand, the contrast is defined
 in the method section in Eq. (3) locally, on the other hand the plots in Fig. 4 do
 not contain any spatial dependence. It is just mentioned that the contrast is
 plotted over the region of interest – but what does this mean concretely? Does a
 point in Fig. 4 correspond to the integral of the contrast in the region of interest
 
or is it the average or just the contrast value evaluated at half the size of the
 region of interest? Here a clarification would be appreciated by the readers.
 After the clarification of these points, the manuscript could be published in the journal Nature
 Communications.