Localization engineering by resonant driving in dissipative polariton arrays

1- Does a good job of situating the work as relevant within the context of recent developments in the field, and noting throughout where results of the theory being presented correspond with experimental observations in the references.
2- Describes both the most general application of the theory to arbitrary geometries, as well as specific cases of common interest in the field such as the SSH model.
3- Is clearly and logically structured, demonstrating how the method works for the simplest cases with one or two driven sites before progressing to arbitrary geometries and nonlinear interactions.

1- There are some places where the formatting of equations or figures needs to updated to fit properly in the style and layout of SciPost.
2- Some of the figures could be adjusted for improved readability.
3- While the manuscript does clearly explain how the method can be used for arbitrary lattice geometries, results are only presented for 1D examples.

This work details a theoretical framework for calculating the conditions for generating localised occupation in driven-dissipative lattices by tuning the frequency and amplitude (modulus and phase) of coherent driving on specific lattice sites. It is demonstrated throughout the manuscript how the results of this method can explain various recent experimental results, and I also agree with the author's conclusion that it should be useful for designing driving schemes for future theoretical and experimental studies of driven-dissipative bosonic lattice models e.g., in the context of microcavity polaritons. To facilitate such future use, the manuscript presents itself in a clear step-by-step manner, starting with calculations of the simplest examples and proceeding to cases of additional complexity. While it is noted in both this manuscript and ref. [24] that these two works have independently produced some very similar results around the same time, I do think this work still sufficiently distinguishes itself in terms of originality both by addressing the extension to arbitrary lattice and driving geometries, and also by considering a case with non-uniform hopping of significant interest within this field given by the SSH model.

The complaints I have about the manuscript in its current form are mostly matters of presentation. There a few instances where it looks like the manuscript has not been properly updated to account for the formatting in SciPost: for instance, there is an ambiguous construction $(H)_{ij} = H_{ij}/\hbar$ on line 79 and similarly on line 191; I noticed in the ArXiv version these are properly distinguished by font, but in SciPost all equation text is bold so the two quantities $H$ need to be distinguished from each other in some other way. There is also figure 3, whose dimensions are currently such that the caption is clipping into the page number. I noticed a few cases where it looked like some of the axes labels or captions of figures had not been properly updated from some older version; I will include a full list of corrections I noticed in the "Requested changes" below. I also thought that some of the figures could be adjusted slightly to improve readability: in particular, often the density of points is such that it can be difficult to distinguish "open symbols" and "solid symbols", especially in panels b) and d) of figure 6 where they are only really distinguishable in the small region of dynamical instabilities; perhaps since the data points look almost continuous solid/dashed lines could be used instead of solid/open symbols.

Finally, I had a few questions for the author that I was curious about, which they may also want to further elaborate on in the manuscript if they so choose. First, since all the results presented in the manuscript are for 1D models, I was wondering what the author's assessment was of how difficult it might be in practice to apply the construction in section 3.2 to the sort of general 2D case implied by the diagram in figure 2? Second, I had some questions about the element of random fluctuations in figure 7. Is there any particular reason for the size of fluctuations being considered? Since only a small number of realisations were used, am I to understand that this was enough to determine that any fluctuations of this size have a negligible effect on the results? Was each realisation of the fluctuations fixed as $\varphi$ is varied or was it randomised separately at each value of $\varphi$? Does the author have any estimate or intuition for how large these fluctuations would need to be to disrupt the effect?

Overall, I think that this work has an important place in its field, particularly as a tool to assist in the design of future theoretical and experimental studies of these systems, and am happy to recommend it for publication in SciPost Physics Core, provided that certain necessary corrections to the presentation can be implemented.

1- Different quantities labelled $H$ (with or without factor of $\hbar$) need to be properly distinguished from each other around line 79 and again around line 191.
2- The size or arrangement of figure 3 should be adjusted to that the caption does not overlap the page number.
3- Caption of figure 3 refers to "white arrows" which are now actually black arrows. In my opinion, figure 1 might also be improved by adding similar arrows to more strongly indicate the driven sites.
4- While it is fairly clear what is meant by "hopping matrix", it might be even better if $V$ introduced in section 3.2 is defined unambiguously in terms of the original model in equation 1.
5- I think the quantity $D(\omega)$ in equation 27 is improperly defined in line 303 below. Is it not supposed to be the determinant of the matrix being multiplied by $1/D(\omega)$, not of the the whole of $\tilde{G}$ including that factor? If so can the definition or equation 27 be adjusted to clarify this.
6- The x-axis labels of figure 5 b) & d), as well as the bottom y-axis label of figure 6 refer to a parameter $t$ which I assume is supposed to be $J$.
7- The way panels b) & d) of figure 6 are plotted could be adjusted so that the data for sites 1 & 2 is more easy to distinguish.

Ask for minor revision