Selectively tunable optical Stark effect of anisotropic excitons in atomically thin ReS2

The optical Stark effect is a coherent light–matter interaction describing the modification of quantum states by non-resonant light illumination in atoms, solids and nanostructures. Researchers have strived to utilize this effect to control exciton states, aiming to realize ultra-high-speed optical switches and modulators. However, most studies have focused on the optical Stark effect of only the lowest exciton state due to lack of energy selectivity, resulting in low degree-of-freedom devices. Here, by applying a linearly polarized laser pulse to few-layer ReS2, where reduced symmetry leads to strong in-plane anisotropy of excitons, we control the optical Stark shift of two energetically separated exciton states. Especially, we selectively tune the Stark effect of an individual state with varying light polarization. This is possible because each state has a completely distinct dependence on light polarization due to different excitonic transition dipole moments. Our finding provides a methodology for energy-selective control of exciton states.

The authors report an observation of optical Stark effect in atomically thin ReS2. Prominent two excitonic resonances in ReS2 have distinct dipole selection rules which sensitively depend on linear polarization of light. Authors use polarization-resolved optical pump-probe spectroscopy to demonstrate that optical Stark effect can selectively induce resonance energy shift with the control of pump pulse polarization. The presentation of their manuscript is clear and their main conclusion of the work is sound and mostly justified. Although the claimed application would be a little speculative and far-stretched, this work can potentially lead to further interesting physics and applications. I would recommend for a publication in Nature Communication.
However, I suggest to check one thing before the publication. I am concerned about their explanation on residual energy shift even when pump polarization is completely orthogonal to the resonance (Figure 3c). Could this be simply because two exciton resonances share either the same conduction band or valence band which forms the exciton states? If this is the case, it will simply explain their observation without introducing coherent coupling.
Reviewer #2 (Remarks to the Author): The authors report the observation of a polarization-dependent optical stark effect in ReS2. This arises due to the anisotropic formation of excitons in this material. The observations were made using ultrafast optical pump-probe techniques, which is the same technique used in previous observations of the optical stark effect. The observation of a polarization dependent optical stark effect is new, the data and analysis is convincing, and the paper is well written. I think it is highly suitable for publication in Nature Communications. I would only suggest adding some words on how this anisotropic optical stark effect affects things in the two valleys at K and K'. This would be useful information since the previous publications on this subject have focused on the valley selectivity of the effect in this material class.
Reviewer #3 (Remarks to the Author): The authors performed an optical Stark effect experiment on bilayer ReS2. They claim that two different states can exhibit relatively different energy shifts depending on the laser polarization. They show additional fluence and time dependence measurements to support the above conclusion.
I have read carefully the main text and the supplementary, and below is my review concerning (i) the novelty, (ii) the quality/clarity, and (iii) the impact of this work, which are the criteria to maintain the high-standard journal of Nature Communications.
Regarding the novelty of this work, it is natural to make a comparison with the existing related works on the optical Stark effect found in the literature: Note that the optical Stark effect is already known for many years in atoms and in solids (References 1-11). Selectively tunable optical Stark effect has also been shown in transition-metal dichalcogenides (TMDs, and in lead-halide perovskites (Science Advances, DOI: 10.1126/sciadv.1600477), where two different exciton states can exhibit different energy shifts depending on the laser polarization. This is basically the same phenomenon that is claimed by the present author, and simply using linear instead of circular light polarization into a slightly different material is not sufficient to claim this as a new finding. In addition to bilayer ReS2, there are many other materials that exhibit anisotropic electronic and optical properties such as carbon nanotubes and black phosphorus, from which anisotropic optical Stark effect is expected. In this perspective, the present manuscript is too similar with existing works, and it lacks the novelty required for Nature Communications.
More fundamentally, note that the two states investigated in this study are already different in energy by 50 meV. Hence, any attempt to further shift their relative energies by merely 1 meV has only little significance for fundamental science and applications. This situation is different from the selective energy shift in TMDs and perovskites above because the two states are originally identical in energy and protected by a certain symmetry. Hence, shifting their relative energies is of significant interest in fundamental science and applications, which is not the case for bilayer ReS2.
Regarding the quality of this work, I think the measured DT spectra (Fig 2c, Fig 2e, Fig 3a) can still benefit from (i) improving the signal-to-noise ratio and from (ii) acquiring finer interval data points, as compared to the better data quality in the earlier works mentioned above. Besides, these DT spectra do not show a straightforward interpretation of an energy shift, where a simple derivative-like curve should be expected. This is because the two states are not well separated in energy, with energy separation that is comparable to their peak widths. I have no doubt that the optical contribution from the optical Stark effect does exist, as the authors have provided their best efforts to show it in their analysis. But again the compromising data quality makes it difficult to disentangle the contributions from possible coherent spectral oscillations (Phys. Rev. Lett. 59, 2588(1987, Optics Letters 13, 276 (1988)) or from other long-lived dissipative processes. This also makes difficult to accurately determine the magnitude of the energy shift that, as of now, can be too sensitive to the input fitting parameters. I am afraid that the lack of clarity in the data may be confusing for some readers from interdisciplinary background.
The authors emphasize on the word "selectivity" in this work, but according to Figure 3c the selectivity is only up to a factor of 1.75-to-0.50. This is a rather poor contrast as compared to other existing works, and it is rather impractical for applications, in contrast to the authors' claim.
Regarding the impact of this work, "Science-wise" the anisotropic property of this material is already known and the polarization-selective optical Stark effect is already demonstrated in previous works, "Applications-wise" it is a little difficult to say because the observed effect (1 meV) is much smaller than the linewidth and the thermal energy at room temperature. I think currently it is rather important to study the equilibrium phenomena of this material more rigorously. For example, the equilibrium electronic structure of ReS2 still suffers from controversial reports on whether the lowest energy gap corresponds to a direct or an indirect transition (References 18 and 23), or whether the interlayer coupling is really insignificant (References 18 andNano Lett. 16, 1404 (2016) etc.). This controversy could affect the data interpretation of the present work. This is extremely important especially considering the high standard Nature Communications that maintains the novelty, the high data quality, and the correct interpretation. Therefore, I cannot recommend the publication of this work in Nature Communications. But I think the authors can still consider submitting their works in a more specialized journals, possibly in the ACS or AIP journals. Also, it would be good to use less excessive phrase in the revised manuscript: -The phrase "multiple energy levels" is mentioned several times (Line 30,58,82,150), while only two energy levels are relevant in this work. This can be potentially confusing because the readers would expect a multiple number of energy levels like 5 or more. -Line 46, 57, 82, "So far there has been no strategy for accessing multiple energy levels of excitons in a selective manner." However, selective tuning of two different excitons has been demonstrated in TMDs and perovskites above. Also, manipulating different energy levels can also be done simply by tuning the excitation photon energy.
In particular, the following sentences in the current manuscript are stretching too far into pseudoapplications because the observed effect is too small: -Line 37, 163, 169, "... we finally reveal a new applicability of ReS2 for modulating optical transmittance in the real-time domain." Note that the 1 meV shift is much smaller than the linewidth, and much smaller than the thermal energy at room temperature, thus rendering this effect impractical for the functionalities mentioned in the conclusions.
The authors report an observation of optical Stark effect in atomically thin ReS2. Prominent two excitonic resonances in ReS2 have distinct dipole selection rules which sensitively depend on linear polarization of light. Authors use polarization-resolved optical pump-probe spectroscopy to demonstrate that optical Stark effect can selectively induce resonance energy shift with the control of pump pulse polarization. The presentation of their manuscript is clear and their main conclusion of the work is sound and mostly justified. Although the claimed application would be a little speculative and far-stretched, this work can potentially lead to further interesting physics and applications. I would recommend for a publication in Nature Communication.

Response:
We appreciate the time that Reviewer 1 took to read our paper. We are quite pleased that reviewer 1 found our work is sound and interesting. We are also very grateful for his/her thoughtful comments on the light-polarization dependence of the observed excitonic optical Stark shifts. This has been very helpful for us in improving the quality of our manuscript. Below we present our response to the reviewer 1's comments.

Comments 1-1:
However, I suggest to check one thing before the publication. I am concerned about their explanation on residual energy shift even when pump polarization is completely orthogonal to the resonance ( Figure 3c). Could this be simply because two exciton resonances share either the same conduction band or valence band which forms the exciton states? If this is the case, it will simply explain their observation without introducing coherent coupling.

Response 1-1:
We thank the reviewer for her/his very important comments. In the measurement of the polarization-dependent optical Stark effect, we observed that the excitonic blue-shift takes place even when the polarization of the pump is perpendicular to the excitonic transition, as shown in Fig. 3c of the original manuscript. We attributed this to the coherent coupling of Stark shifts, based on the phenomenological similarity of our result to a prior study (Donovan et al., Phys. Rev. Lett. 87, 237402 (2002)). However, we fully agree with Reviewer 1 that the shared conduction or valence band of the two excitonic transitions (labeled by X 1 and X 2 ) explains the observed results much better, because such interpretation have been successfully figured out, showing similar results in many previous studies (e.g., Joffre et al., Phys. Rev. Lett. 62, 74 (1988); Gupta et al., Science 292, 2458(2001Choi et al., Phys. Rev. B 65, 155206 (2002)). Moreover, introducing coherence generally requires more rigorous proof. For these reasons, we have revised our manuscript, as shown in Table.   Regarding this issue, please note that we have inserted the revised sentence in Table. R1-1 into the section 5 of the Supplementary Information because we have transferred all original data to the Supplementary Information. In the revision process, we have re-measured full data sets with a thicker sample at low temperature (78 K) to improve the data quality (in the original manuscript, the sample was bilayer and all experiments were performed in room temperature). In the original work, we also used a circularly-polarized probe to simultaneously measure the shifts of X 1 and X 2 . Consequently, both excitons were influenced on differential transmission (DT), resulting in somewhat complex shapes of spectra ( Fig. 3a and 3b in the original manuscript). This invoked many free parameters in the fitting procedure. In such a situation, the fitting procedure is generally non-intuitive rendering the estimation of the exciton shift (E) to be overly sensitive to input parameters. For this reason, We can see that the pump-polarization dependence of the remeasured data ( Fig. R1-1b) is almost identical to that of the original ones ( Fig. R1-1a). We of c

General remarks of Reviewer 2:
The authors report the observation of a polarization-dependent optical stark effect in ReS2. This arises due to the anisotropic formation of excitons in this material. The observations were made using ultrafast optical pump-probe techniques, which is the same technique used in previous observations of the optical stark effect. The observation of a polarization dependent optical stark effect is new, the data and analysis is convincing, and the paper is well written. I think it is highly suitable for publication in Nature Communications.

Response:
We appreciate the time Reviewer 2 took to read our manuscript and to provide his/her thoughtful opinions. We are pleased that Reviewer 2 found that our work is highly suitable for publication in Nature Communications. His/her comments on the relation of the anisotropy with valley degrees have helped improve our manuscript. We have faithfully considered the comment and revised our manuscript correspondingly. Below we present our response to the Reviewer 2's comment.

Comments 2-1:
I would only suggest adding some words on how this anisotropic optical stark effect affects things in the two valleys at K and K'. This would be useful information since the previous publications on this subject have focused on the valley selectivity of the effect in this material class.

Response 2-1:
We thank the reviewer for her/his important comments.  (2014)). This is because all these studies, including our work, deal with selective optical Stark effect in 2D TMD materials. Although we already discussed differences between our work and previous studies in the original manuscript (line 52-58), we agree with Reviewer 2 that additional comments can be very useful for readers.
As discussed in the original manuscript, while ReS 2 is a group-VII TMD with in-plane anisotropy, materials studied previously are group-VI TMDs (WS 2 and WSe 2 ) which have high in-plane symmetry with a hexagonal structure. Here, the key factor of the valley selectivity is the nontrivial Berry phase at K and K' points, which is characteristic of monolayer group-VI TMDs. However, unlike group VI TMDs, the optical selectivity of ReS 2 in our work stems from linearly anisotropic excitons near  point due to in-plane anisotropy of crystal structure. Thus, it seems somewhat difficult to expect significant connections of the linear anisotropy of ReS 2 with the valley degree of freedoms at K (K') points. Unfortunately, we cannot state the effect of the anisotropic optical Stark effect on valley selectivity for now. We expect that further theoretical study will find valley characteristics an Berry phases at important momentum points in ReS 2 . For this reason, regarding the issue mentioned in the Comment 2-1, the only thing that we can do at this stage is to provide more specific information on the momentum positions of group-VI and group-VII TMDs. We thus have added some phrases to the revised manuscript, as shown in Table. R2-1. We hope reviewer 2 understands that we cannot offer more theoretical background, and thank again for providing her/his thoughtful suggestion.

Original Revised
Since the valley excitons in these studies are energetically indistinguishable (line 56-57, Since the valley excitons at K (K') point in these studies are energetically indistinguishable (line 58-59, page 3) The absorption peaks, labeled as X1 and X2, arise from the two lowest, energetically nondegenerate direct exciton states (line 66-68, The absorption peaks, labeled as X 1 and X 2 , arise from the two lowest, energetically nondegenerate direct exciton states near  point 27 (line 70-71, page 3) In addition to the issue raised by Reviewer 2, we have made important changes in the manuscript. We have re-measured all data sets using a few-layer ReS 2 sample at 78 K in order to improve the data quality. In addition, while we have used circularly-polarized probe in our original work, in the revised manuscript, we used linearly polarized light to detect more direct signals for the selective optical Stark effect . As a result, we have obtained more intuitive data sets, but, the main conclusion (i.e., selective anisotropic optical Stark effect) has not been changed. Please refer to the revised main text and Supplementary Information.

General remarks of Reviewer 3:
The authors performed an optical Stark effect experiment on bilayer ReS2. They claim that two different states can exhibit relatively different energy shifts depending on the laser polarization. They show additional fluence and time dependence measurements to support the above conclusion.
I have read carefully the main text and the supplementary, and below is my review concerning (i) the novelty, (ii) the quality/clarity, and (iii) the impact of this work, which are the criteria to maintain the high-standard journal of Nature Communications.

Response:
We appreciate the time Reviewer 3 took to read our manuscript. Her/his thoughtful comments on the novelty, the data quality and the impact of our work have helped us to significantly improve our manuscript with high completeness. In order to obtain high quality data, we have performed all measurements under changed experimental conditions. We also have rewritten a considerable portion of the manuscript. Below we present our point-by-point response to Reviewer 3's comments.

Comments 3-1:
Regarding the novelty of this work, it is natural to make a comparison with the existing related works on the optical Stark effect found in the literature: Note that the optical Stark effect is already known for many years in atoms and in solids (References 1-11). Selectively tunable optical Stark effect has also been shown in transition-metal dichalcogenides (TMDs, References 12-13) and in lead-halide perovskites (Science Advances, DOI: 10.1126/sciadv.1600477), where two different exciton states can exhibit different energy shifts depending on the laser polarization. This is basically the same phenomenon that is claimed by the present author, and simply using linear instead of circular light polarization into a slightly different material is not sufficient to claim this as a new finding. In addition to bilayer ReS2, there are many other materials that exhibit anisotropic electronic and optical properties such as carbon nanotubes and black phosphorus, from which anisotropic optical Stark effect is expected. In this perspective, the present manuscript is too similar with existing works, and it lacks the novelty required for Nature Communications.

Response 3-1:
We thank Reviewer 3 for providing her/his thoughtful comments on the novelty of our work.
In the manuscript, we demonstrated that the excitonic Stark effect in ReS 2 can be selectively tuned by manipulating the polarization angle of linearly polarized light. This was possible  (2002)). As summarized in Fig. R3-1, these early studies showed that the optical Stark shift can efficiently occur only when the polarizations of pump and probe beams share the same circular polarization, whereas the effect is significantly weakened in the counter-polarized configuration. Such polarizationselectivity stems from the light-polarization-dependent optical selection rules. Considering only the phenomenological results, main results in the early studies are almost the same as the recent papers that Reviewer 3 mentioned. Similar to the early works, excitonic optical Stark shift in monolayer group VI TMDs and 2D provskites also take place only when the pump and probe are co-polarized due to the light-polarization-dependent optical selection rules. Of course, there is a small phenomenological difference; unlike early papers, the Stark shift in the recent works can be almost completely suppressed in counter-polarized pump-probe configuration, owing to their non-shared electronic or hole states in excitonic transitions. Such a difference is simply related to the efficiency of the polarization selectivity, but, it cannot be a critical liability for the novelty of the recent works.
If we follow Reviewer 3's opinion, it seems that the recently reported optical Stark effect in group VI 2D TMD should also significantly lose their novelty since the basic physics is exactly the same as the early works. However, there is no doubt that these papers have a great novelty, confirmed by the fact that both of them were published in top journals (Nature Nanotechnology and Science). As far as we understand, the key novelty of these works lies not in the polarization selectivity of the Stark effect, but in the selective optical control of "valley" states which are newly emerged quantum degrees of freedom in the monolayer group VI TMDs. In other words, the phenomenological similarity cannot reduce the novelty of the associated studies. Viewed in this way, our work definitely has novelty. As described in the original manuscript, the two lowest excitons in ReS 2 are linearly polarized due to its reduced in-plane structural symmetry, and, more importantly, their optical selection rules manifest completely different light-polarization dependence. The fundamental physics of such unique excitonic characteristics are obviously different from other materials in previous works, such as valley-selective optical transition in monolayer group VI TMDs (determined by the nontrivial Berry phase at K (K') valleys and angular momentum of atomic orbitals) and spin-selective optical selection rules in conventional semiconductors of early studies. Moreover, there have been no reported studies on the optical Stark effect of linearly anisotropic excitons with distinct optical selection rules.  (2015)). After thorough literature searches, no single literature exists reporting the optical Stark effect in BPs. If one says that the experimental result is not novel simply because it is "expected", then the argument went too far from reality, and there are virtually no novel scientific experiments other than the theoretical expectation. Thus, among other anisotropic materials that Reviewer 3 mentioned, our observation is (arguably) very original, and ReS 2 itself is an interesting material platform for testing the polarization-dependent exciton selective control of optical Stark effect.
Regarding this issue, we have added following sentences in the revised main text.
-Added sentences in the revised manuscript (Discussion section) Of course, group VII TMDs are not the only material family exhibiting anisotropic property of excitons; there are several systems possessing anisotropic excitonic properties (such as carbon nanotubes (CNTs) and black phosphorus (BP)) 12,30-32 . However, both of them lack polarization-dependent exciton selectivity so that energy-selective optical Stark effect cannot be expected. For CNTs, since the anisotropy of excitonic transition arises simply from the geometrical alignment, all excitonic transitions should have same polarization dependence 12 . For BP, there is only one prominent excitonic transition with distinct anisotropy 30 . Thus, group VII TMDs are ideals material platforms for testing the energy selective control of the excitonic optical Stark effect.
Additionally, one paper mentioned by Reviewer 3 (Giovanni et al., Sci. Adv. 2, e1600477 (2016)) was published just after we have summited our manuscript to Nature Communications. We even did not notice whether this paper was already submitted or not. Thus, it is inappropriate to compare our work with the paper mentioned when discussing novelty; this paper was published just before we received the Reviewers' reports, giving us no chance in telling how novel the work is compared to our work. However, even if the comparison is acceptable, we want to emphasize that our work still has novelty because the background physics is completely different, as discussed above. We have added this paper to the reference list in the revised main text.

Comments 3-2:
More fundamentally, note that the two states investigated in this study are already different in energy by 50 meV. Hence, any attempt to further shift their relative energies by merely 1 meV has only little significance for fundamental science and applications. This situation is different from the selective energy shift in TMDs and perovskites above because the two states are originally identical in energy and protected by a certain symmetry. Hence, shifting their relative energies is of significant interest in fundamental science and applications, which is not the case for bilayer ReS2.

Response 3-2:
We fully agree with Reviewer 3 that lifting of degenerate states using selective energy shift has fundamental significance (Sie et al., Nat. Nanotechnol. 14, 290 (2014); Kim et al., Science 346, 1205 (2014)). However, controlling energy shifts of non-degenerate state also has importance in terms of energy-or frequency-selective modulations. Many literatures have mentioned that the applicability of the excitonic optical Stark effect lies mainly in ultrafast optical modulating, switching and information processing devices. Thus, there is no doubt that relevant optoelectronic devices can have higher functionality and degree-of-freedoms if energy-selective control is possible. So far, however, most relevant studies have focused only on the optical Stark shift of the lowest exciton state (e.g., heavy-hole exciton in GaAs-based quantum wells, A-exciton in group VI TMDs). Although several studies dealt with optical Stark shifts of higher states, no energy-selective control has been reported. This is because there have been no methods in selectively tuning the Stark shift of higher exciton states. In Comment 3-6, Reviewer 3 mentioned that the optical Stark shift of a higher exciton state can be done simply by tuning pump photon energy. However, such a modulation method is not proper in common situations because if we raise the pump photon energy close to the higherlying exciton state over the lower-lying state, it will cause generation of significant magnitude of real excitons and free carriers, which obstruct the observation of the optical Stark effect. For this reason, the maximum photon energy of the pump beam has always been lower than that of the lowest exciton resonance energy in every case, and tuning the pump photon energy has not been utilized in controlling the energy-level-selective optical Stark effect of excitons.
In the revised process, we have obtained very intuitive signals for completely selective shifts of excitons. Although the magnitudes of shifts are about 1 meV, the data clearly shows frequency-selective applicability in modulations or switches. Please refer to response 3-3.  Fig  Fig. 1c  To resolve this issue, unlike the original work, we have selectively measured the optical Stark shift of a certain exciton by using a linearly polarized probe. First, in order to measure the Stark shift of X 1 , the probe polarization angle has been fixed at  = 20, at which X 1 dominates the optical response and X 2 has negligible oscillator strength (see the equilibrium absorption spectrum in the top panel of Fig. R3-7b). Under this condition, we have observed that DT response of a co-linearly polarized pump shows simple absorption-derivative-like shape (middle panel, Fig. 3a) only at the spectral region dominated by X 1 (blue-shaded area), which indicates selective optical Stark effect of X 1 . This result is quite intuitive, and very easy to estimate the magnitude of the shift in the exciton level. The amplitude of Stark signal becomes small when the pump is orthogonally polarized to the probe (bottom panel of Fig.  R3-7b), which indicates reduced blue-shift which agrees well with the original work. In a similar manner, we have selectively measured the optical Stark shift of X 2 at a fixed probe polarization of  = 90 (top panel in Fig. R3-7c). We can clearly see the selective optical Stark shift of X 2 , as shown in the middle panel in Fig. R3-7c. Similar to the X 1 's response, it shows decrease in amplitude in the cross-polarized pump-probe configuration (bottom panel in Fig. R3-7c). Compare to the original work, the re-measured data has higher SNR and spectral resolution.
We have inserted these results into Fig. 3a-3b and the section "Energy-selective optical Stark effect" in the revised main text. We also added a schematic description of derivative-like absorption shape of DT spectrum (Fig. R3-7d) to the revised manuscript (Fig. 2b), in order to help readers from interdisciplinary background understand the measured spectra. Please refer to the revised manuscript.
iv) Although the re-measured DT spectra (Fig. R3-6b and R3-6c) has a simple and intuitive absorption-derivative-like shape, direct estimation of the energy shift (E) is still somewhat inappropriate. This is because the DT response at  = 0 fs is affected by the pump-excited real carriers, generated by two-photon-or phonon-mediated-absorption of pump photons (Knox et al. Phys. Rev. Lett. 62, 1189(1989). Such a mixed response is corroborated in the DT trace in the right panel of Fig. R3-6, where a spike-like peak near  = 0 fs due to the optical Stark effect is followed by long-lasting signals originating from pump-generated carriers. This issue has been a common problem in many relevant studies on the excitonic optical Stark effect in solids (e.g., Von Lehmen et al. Opt. Lett. 11, 609 (1986); Knox et al. Phys. Rev. Lett. 62, 1189(1989; Sie et al. Nature Nanotechnol. 14, 290 (2015)). To resolve this problem, we have fit the transient DT spectra at  = 400 fs (at which no Stark shift is seen) with corresponding fitting parameters to estimate E in the original work ( Supplementary   Information S2). However, such methodology is overly sensitive of the input fitting paramet procedu In this way ter (E). W ation S1.

Comme
The aut selectiv other ex claim.  (Fig. 3c in the original manuscript); the selectivity looks only up to a factor of 1.75-to-0.50, as Reviewer 3 pointed out.

Respon
In the revised manuscript, we have measured the optical Stark shift of each exciton state in a completely selective manner. This was possible since we have used a linearly polarized probe to pre-exclude the response of the unselected exciton, as explained in detail in the Response 3-3. We repeatedly plotted the corresponding results, as shown in Fig. R3-10b (same with the middle panels of the Figs. R3-7b and R3-7c), in order to clearly reveal the improvement. There, obviously we can see that only the selected exciton shows optical Stark effect-induced DT response: when X 1 (X 2 ) is selected, absorption-derivative-like response is observed only at the spectral region of X 1 (X 2 ), as indicated by blue-(red-) shaded area in Fig. R3-10b (Fig.  R3-10c). Thus, these results themselves clearly show the "selectivity" without the necessity to compare magnitudes of their Stark shifts. This interpretation is further supported by the fact that two excitons are well separated in the spectral domain . In this way, energy-selective measurement of excitonic optical Stark effect is possible. Regarding this issue, we added relevant sentences to the revised manuscript as follows.
-Added sentences in the revised manuscript (line 149-158, page 7) These results enlighten us of significant benefits of ReS 2 in terms of selective optical control of excitons. Firstly, as shown in the middle panels of Fig. 3a and 3b, it is possible to measure the shift of a certain exciton state in a completely exclusive manner, indicating high exciton-selectivity. More importantly, the results also reveal energy-selectivity, considering that the two exciton states possess wellseparated energy levels (note that the spectral distance between the two exciton resonances are larger than the sum of their half linewidths, see Supplementary Information S4). In particular, the higher-lying exciton state (X 2 ) can be selectively modulated without being disturbed by the lower-lying exciton (X 1 ) (see Fig. 3b). Such unique functionality is absent in other materials, such as semiconductor quantum wells, carbon nanotubes and group VI TMDs. Schematics in Fig. 1b summarize these findings.
In addition, we of course present the pump-polarization-dependent shifts of excitons in the revised manuscript, as shown in Fig. R3-10d and R3-10e. Note that, unlike the original version ( Fig. R3-10a), we plot the shifts of X 1 (Fig. R3-10d) and X 2 (Fig. R3-10e) in separated figures. This is because the original work had simultaneously measured the shifts of both excitons in the same condition, while different probe polarizations were used in the revised measurements ( = 20 and 90 in Fig. R3-10d

Response 3-5:
First, "Science-wise", we have already provided sufficient ground for the novelty of our work. Please refer to the Response 3-1.
Second, "Application-wise", we agree with Reviewer 3 that the magnitude of the exciton shift (E) is somewhat small compared to the broad linewidth in the original manuscript.
However, in the revised version, the linewidths are significantly reduced at low temperature (right panel of Fig. R3-4), enhancing the efficiency of the Stark effect. In order to evaluate the efficiency of ReS 2 precisely, we have compared the strength of this effect in ReS 2 with that measured in other TMD materials. The strength of the optical Stark effect is defined by  (2009)). In our case, S are ~ 17 D 2 for X 1 and ~ 15 D 2 for X 2 at co-linear pump-probe polarization configurations (where E for X 1 (X 2 ) is 1.4 meV (0.8 meV) as shown in Fig. R3-10d (Fig. R3-10e),  for X 1 (X 2 ) is ~ 90 meV (~ 140 meV), and  is ~ 93 MV/m). These S values are of the same order of magnitude as that of group VI TMD (~45 D 2 , Kim et al. Science 346, 1205Science 346, (2014) at similar experimental temperatures. We have added related sentences to the revised manuscript as follows.
-Added sentences (Line 180-183, page 8) The strengths of the optical Stark effect ( ,14 for X 1 and X 2 are about ~17 D 2 and ~15 D 2 at co-linear pump-probe polarization configurations, respectively. These values are of the same order of magnitude as that of group VI TMD (~45 D 2 ; ref. 14).
In addition to above issues, Reviewer 3 pointed out that study on equilibrium phenomena of ReS 2 should be performed more rigorously before discussing the optical Stark effect. We agree with Reviewer 3 that equilibrium characteristics of ReS 2 have not been fully understood yet. As mentioned in the Comment 3-5, whether the lowest energy gap is direct or indirect is indeed an ongoing debate ( (2016)): while the former study claimed that ReS 2 remains having a direct gap from bulk to monolayer, the latter paper claimed that an emission peak lower than exciton resonance in bulk was assigned to indirect gap transition. However, despite such a discrepancy, there is no doubt that the exciton resonances we measured correspond to direct transitions. Thus, it seems that the occurrence of excitonic Stark shifts and their polarization dependence in our work are not expected to have significant connections with the possible presence of the lower-lying indirect transition. Of course, the lower-lying indirect state can behave as a relaxation channel of photoexcited real carriers in the lowest exciton state, as discussed in the previous study (Aslan et al., ACS Photonics 3, 96 (2016)). However, considering that the optical Stark effect does not originate from pumpgenerated real carriers, it is hard to expect that this issue will be critical in our study. In addition to this issue, another important topic debated in ReS 2 is the presence of strong interlayer coupling and its influence on the layer number-dependent optical characteristics (ref. 18. Tongay et al., Nature Commun. 5, 3252 (2014);He et al., Nano Lett. 16, 1404(2016). However, although it is a very important issue, the layer number dependence of the optical Stark effect is not of interest in our manuscript because the anisotropic excitonic transitions occur regardless of the sample thickness. Indeed, the observed phenomena in our work have been successfully explained without concerning the issues Reviewer 3 mentioned. Thus, it is somewhat hard to accept that there is a significant connection between the debating issues in ReS 2 and the accuracy of our interpretation.

Comments 3-6:
Also, it would be good to use less excessive phrase in the revised manuscript: -The phrase "multiple energy levels" is mentioned several times (Line 30, 58, 82, 150), while only two energy levels are relevant in this work. This can be potentially confusing because the readers would expect a multiple number of energy levels like 5 or more.
-Line 46, 57, 82, "So far there has been no strategy for accessing multiple energy levels of excitons in a selective manner." However, selective tuning of two different excitons has been demonstrated in TMDs and perovskites above. Also, manipulating different energy levels can also be done simply by tuning the excitation photon energy.

Response 3-6:
We agree that the phrase "multiple energy levels" may lead to misunderstanding. Thus, we have revised all sentences including that phrase, as shown in Table. R3-1.

Original Revised
there has been no selectivity in controlling multiple energy levels (line 31, page 2) most studies have focused on the optical Stark effect of only the lowest exciton state due to lack of energy-selectivity (line 30-31, page 2) Our finding provides a novel methodology for selective control of multiple energy states of excitons (line 38-39, page 2) Our finding provides a novel methodology for selective control of multiple energy states of excitons ultrafast energy-selective control of exciton states. (line 37-38, page 2) there has been no strategy for accessing multiple energy levels of excitons in a selective manner (line 46-47, page 2) there has been no strategy for energy-selective control of exciton states. (line 45-46, page 2) it can be said that no experimental approaches for controlling multiple energy states of excitons have been made (line 57-58, page 3) it can be said that no experimental approaches for energy-selective optical Stark effect of excitons have been made. (line 59-61, page 3) The Stark shift for X1 and X2 follow obviously different light-polarization dependence, offering a foundation for selective control of multiple energy levels in excitonic systems (line 81-82, page 4) We gradually tune the Stark shift for X 1 and X 2 , which obviously has different lightpolarization dependence. (line 85-86, page 4) this finding provides a foundation for selective optical control of multiple energy levels in the associated excitonic systems. (line 149-151, page 7) deleted Regarding the selective tuning of exciton states, we have already offered sufficient reasons that explain why the selectivity found in our work is different from those in previous studies. Please refer to the Comment 3-1. In addition, as discussed in the Comment 3-2, tuning photon energy of the pump is not a proper way to manipulate different energy levels because significant excitation of real carriers obstructs the measurement of the Stark shift and lowers the purity of this effect when the pump photon energy is higher than that of the lower-lying state. Of course, excitation with photon energy lower than the lower-lying state also cannot selectively modulate the higher-lying state in conventional materials since shift of the lowerlying exciton will be much larger than that of the higher-lying exciton. Thus, the excitonic optical Stark effect in previous studies definitely lack energy-selectivity. Recent works on 2D TMDs and perovskites also lacks the energy-selectivity because the exciton levels are energetically degenerated. We have stated this point in the revised manuscript as the original one. Please refer to second and third row in Table. R3-1.

Comments 3-7:
In particular, the following sentences in the current manuscript are stretching too far into pseudoapplications because the observed effect is too small: -Line 37, 163, 169, "... we finally reveal a new applicability of ReS2 for modulating optical transmittance in the real-time domain." Note that the 1 meV shift is much smaller than the linewidth, and much smaller than the thermal energy at room temperature, thus rendering this effect impractical for the functionalities mentioned in the conclusions.

Response 3-7:
We agree with Reviewer 3 that the applications regarding modulation transmission in the real-time domain is somewhat far-stretched. In order to focus on the selective optical Stark effect, we have deleted the related sentences in the original manuscript (line 36-38, page 1; line 163-170, page 7 in the original main text).
However, for the applicability of our findings, we have achieved significant improvement in the linewidth by decreasing experimental temperature (right panel of Fig. R3-4), which makes two exciton state well-separated (Fig. R3-5). It also has enabled completely selective measurements of excitons in the frequency domain via detection using a linearly polarized probe (Fig. R3-7b and Fig. R3-7c). Moreover, as discussed in Response 3-5, we have shown that the strength of the optical Stark effect in ReS 2 is of the same order of magnitude as that of group VI TMD. Base on such improvements, we believe that ReS 2 has a potential applicability for ultrafast frequency-selective optical modulators or switches.