--------Reviewer Comments-------- Reviewer 1: In this work a heralded single photon is generated by 4-wave mixing in a Rb cloud, and is used to excite a single atom. The excitation probability and transmitted amplitude are studied vs BW of the photon. The motivation is the need for deterministic interactions between single photons and single quantum emitters for quantum information processing. The experiment and its results are of high quality and well presented, and the subject is important, as bandwidth issues are often ignored or not considered thoroughly and realistically enough. I therefore recommend publication in Optics Express. I have two remarks, which the authors can choose to address: Regarding the experiment - it is indeed unfortunate that it explores only photons with BW larger than the natural BW of Rb, exploring only one side of the curve BW>Gamma_0. Additionally, in these experimental parameters, as the authors indeed mention, there is no difference between a coherent state with mean n=1 and their single photon source because of small spatial overlap, and it is certainly not clear, even if there was a measurable difference, why not just use a weak coherent state (n< < 1) and post select on a 'click' (which will project the state to mostly 1 with negligible probability for 2 photons or more). Regarding the motivation - the temporal/BW aspect is indeed very important for single photon < --> single quantum emitter interactions, yet two level systems are not enough for quantum information processing, and storage/processing is done with two ground states of 3-level systems or more. Accordingly, deterministic coupling with such systems does not involve just a single transition, thereby avoiding this BW issue. Again, in my view this is nonetheless an interesting and high-quality work on an important subject, and I recommend accepting it for publications. Reviewer 2: The paper “Photon bandwidth dependence of light-matter interaction” by M. Steiner reports experimental results on the influence of the bandwidth of a photon onto the absorption of the photon by a single atom, finding a strong dependence of the atom’s excitation on the photon bandwidth. The experimental findings are in very good agreement with calculations also presented in the paper. The photons are generated in pairs in a cloud of cold atoms by four-wave mixing, with one photon being used as herald and the other one being focused onto the target atom by means of an high NA objective. This way of producing the photons is strongly underlining the technological relevance of the paper, since such a scenario with different quantum systems may easily occur in quantum technologies involving hybrid systems, as also the authors emphasize in the introduction of the paper. The paper is written in a very clear manner, all material is presented in a convincing and scientifically sound way. I can hardly find anything to criticize, thus I recommend the paper for publication with only minor changes, for which I do not need to see the manuscript again. Suggestions for minor changes: 1) Between Eqs. (1) and (2) the authors introduce the ‘scattering probability \epsilon’. They should define the term ‘scattering probability’ more clearly as the probability to scatter a photon out of the mode of the incident light and highlight its relation to the extinction of the incident light. Otherwise, readers not working in the same field might have problems to understand the meaning of this parameter. For the same reasons: The overlap parameter \Lambda in Eq. (2) combines the mode structure of the focused light as well as the solid angle used for focusing [12,13]. Since the authors detect the transmitted photons via focusing onto a single mode fiber, and I assume the used lens and fiber are of the same type as used for guiding the signal photons to the single atom setup, the authors project the detected photons onto the same mode as incident onto the atom. This circumstance should be highlighted already here and not only later when describing the setup, because without projection onto the incident mode, e.g. by focusing onto a detector directly, the (1-\Lambda) term in Eq. (2) would have to be modified. 2) page 3 bottom, beginning of experimental section: I fully appreciate the balanced and comprehensive way the authors relate to the work of others. However, to my best knowledge Refs. [31] and [32] of the manuscript do not report on a measurement of the transient excitation of an atom. I suggest to cite only Ref. [13,33] here. 3) on page 4, bottom: The authors should clarify the mean photon number of the coherent state pulse used in the experiments. --------Pre-Production Review-------- [x] Authors: Move commas after the author name but before the superscripts in your author listing. [x] OCIS codes: Please include OCIS codes below the copyright section. [x] References: You can view the guide for reference format here: http://www.opticsinfobase.org/oe/submit/style/jrnls_style.cfm#refs Journal titles Correct your journal titles to the standard journal abbreviations. Be sure to include all necessary periods and other punctuation when abbreviating your journal titles. [x] Main text: Citations such as "In Ref. 10" should not be used. It should be "In [10], Smith et al...." In-text citations—equations: Include parentheses around the equation number in the text: Eq. (2), or Eqs. (6)--(8). Do not enclose your figure numbers in parentheses. Parentheses are reserved for parts of a figure [Fig. 2(a)] and equations [Eq. (4)]. Please confirm that all of your funding sources have been added into your Prism submission in the Fees and Funding step.