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Peer Review File
REVIEWER COMMENTS
Reviewer #1 (Remarks to the Author):
I have read the authors' response to my earlier comments, as well as the revised manuscript. The
authors have responded to all comments in a satisfactory way. I believe that the manuscript has
significantly improved, with the work now put in proper context and the main points of novelty made
more specific and clear. I believe the manuscript presents great work and is definitely suitable for
publication in Nature Communications.
Reviewer #2 (Remarks to the Author):
In the manuscript ′′Topological phonon transport in an optomechanical system′′, Ren, Shah and co-
authors report on the experimental observation of topologically protected
∼
0.3 GHz phononic modes
travelling along a phononic crystal interface. Each unit cell embeds a lower-scale photonic crystal
cavity enabling optomechanical sensitive spatial readout of the thermally excited phonon states all
along the interface. The demonstration of topological protection is convincing, based on theoretical
calculations and Finite-Element Simulations. The measurements are also compared between different
designs, topological and trivial.
These results are very interesting and there is no doubt that it constitutes a significant advance at the
crossroads of the fields of topological matter, phononics and optomechanics. I would therefore
recommend publication In Nature Communications after the following minor points are addressed:
- While the topological protection should be robust to some level of disorder, higher disorder will
unavoidably modify the band structure up to a point where the topological protection is no more
present. Can the authors provide information on the tolerance of their design to disorder, regarding
the topological protection?
- The experiment is realized at room temperature, but this information does not appear in the main
text. I strongly suggest emphasizing this point early in the manuscript.
- In the SI, (SI-78), the authors provide information on the estimated displacement amplitude (≈10
fm) but what is the displacement sensitivity of the measurement setup?
- line 132-135, the authors write ′′we focus here on the vibrational modes that couple to light, the in-
plane modes which are even under the mirror operator Mz (z
→
-z).′′ Does this imply that the Comsol
simulations use a symmetric condition or were the odd modes also simulated? For example, in Fig.S-2,
are all the modes represented?
- Please precise the optical power launched to the cavity, in the experiments, i.e. after the polarization
controller.
- It seems that the data shown in the schematic of the spectrum analyzer, Fig2.c, are not used in the
discussion. Please remove if so.
Authors’ Response NCOMMS-21-23583-T
January 12, 2022
Authors’ Response:
We thank all the reviewers for their careful and detailed review of our manuscript. We are happy
that all of them acknowledge the high quality of our work and praise it as impressive. The reviewers’
points are marked in
black
while our responses are marked in
blue
.
A list of changes is given below. We hope that with these replies and the changes and additions
implemented here, our manuscript is ready to be published in Nature Communications.
With best regards,
Hengjiang Ren, Tirth Shah, Hannes Pfeifer, Christian Brendel, Vittorio Peano, Florian Mar-
quardt, Oskar Painter
Brief summary of changes
Based on the reviewers’ feedback we have made the following changes in the revised version of our
manuscript and the Supplemental Information:
•
We have modified section 7 of the Supplementary Information to include the details about
the sensitivity of the measurement setup (see reply to Referee 2).
•
We have modified a paragraph in the main text and the section 11 of the Supplementary
Information to highlight the robustness of the topologically protected edge state with respect
to the fabrication disorder, based on new simulations (see reply to Referee 2).
Reviewer #1:
I have read the authors’ response to my earlier comments, as well as the revised
manuscript. The authors have responded to all comments in a satisfactory way. I believe
that the manuscript has significantly improved, with the work now put in proper context
and the main points of novelty made more specific and clear. I believe the manuscript
presents great work and is definitely suitable for publication in Nature Communications.
[Authors’ Response]: We are happy that the referee is satisfied with our responses and the improve-
ments in the manuscript.
1
Reviewer #2:
In the manuscript Topological phonon transport in an optomechanical system, Ren,
Shah and co-authors report on the experimental observation of topologically protected
0.3 GHz phononic modes travelling along a phononic crystal interface. Each unit cell
embeds a lower-scale photonic crystal cavity enabling optomechanical sensitive spatial
readout of the thermally excited phonon states all along the interface. The demon-
stration of topological protection is convincing, based on theoretical calculations and
Finite-Element Simulations. The measurements are also compared between different
designs, topological and trivial.
These results are very interesting and there is no doubt that it constitutes a significant
advance at the crossroads of the fields of topological matter, phononics and optome-
chanics. I would therefore recommend publication In Nature Communications after the
following minor points are addressed:
[Authors’ Response]: We are happy that the referee thinks that our results are significant for the
mentioned scientific communities. Indeed, we believe that to establish a firm connection between
them is one of the main achievements of our work.
While the topological protection should be robust to some level of disorder, higher
disorder will unavoidably modify the band structure up to a point where the topological
protection is no more present. Can the authors provide information on the tolerance of
their design to disorder, regarding the topological protection?
[Authors’ Response]: The referee raises an important point about the effect of the fabrication-
induced disorder on the topological protection of the edge state. Indeed, more detailed information
about the disorder would be important to assess the design concept of multiscale optomechanical
crystals.
Inspired by the referee’s question, we have now carried out new simulations and discussed their
results in a new section 11 in the revised Supplementary Information to answer this particular
question by the referee, setting up a new full tight-binding simulation of the entire setup and
connecting its disorder level to the underlying microscopic disorder level.
In summary, our estimates show that introducing a standard deviation of 10 nm, for geometrical
parameters of both the snowflake and cylindrical holes, the round trip reflection probability
|
r
rt
|
2
in the triangular mechanical cavity (Fig. 2 of the main-text) is around 1% - thus still quite small.
We now mention this new result also in the main body of the paper.
The experiment is realized at room temperature, but this information does not appear
in the main text. I strongly suggest emphasizing this point early in the manuscript.
[Authors’ Response]: Thank you for pointing this out. We have modified the main text and
emphasized that the experiment is realised at room temperature.
In the SI, (SI-78), the authors provide information on the estimated displacement am-
plitude (10 fm) but what is the displacement sensitivity of the measurement setup?
[Authors’ Response]: The displacement sensitivity of the measurement setup turns out to be
S
xx
≈
8
×
10
−
17
m
/
√
Hz (
√
Γ
S
xx
≈
90 fm). Thus, in a single-shot measurement (not carried out
2
in the present work), we would be able to determine the position (quadrature) of the mechanical
oscillator up to a precision of 90 fm in a measurement time Γ
−
1
(corresponding to the decay time
of the mechanical vibrations). The procedure to estimate the sensitivity is now described in the
revised Supplementary Information section 7.
line 132-135, the authors write ’we focus here on the vibrational modes that couple
to light, the in-plane modes which are even under the mirror operator Mz (
z
7→ −
z
).’
Does this imply that the Comsol simulations use a symmetric condition or were the odd
modes also simulated? For example, in Fig.S-2, are all the modes represented?
[Authors’ Response]: Yes, the Comsol simulations use an even mirror-symmetric condition in Fig.S-
2. We thank the referee for pointing this out. We have now updated the caption of Fig.S-2 to
describe this important point. Given the good match between theory and experiment, we conclude
that any potential disorder-induced coupling between the symmetric mechanical modes of interest
and antisymmetric modes turns out to be negligible (also note that the antisymmetric modes do
not couple to the light).
Please precise the optical power launched to the cavity, in the experiments, i.e. after
the polarization controller.
[Authors’ Response]: The optical power after the polarization controller, before the dimpled fiber
taper, is 240
μ
W. The optical power after the dimpled fiber taper is 60
.
3
μ
W. We assume the ef-
ficiencies for both sides of the dimpled fiber taper are the same, and the optical power launched
to the cavity is 120
.
6
μ
W. We have now added this information to the Supplementary Information,
section 2.
It seems that the data shown in the schematic of the spectrum analyzer, Fig2.c, are not
used in the discussion. Please remove if so.
[Authors’ Response]: Thank you for your suggestion. The data shown in the schematic of the spec-
trum analyzer are not discussed in the main text, which represents the uncalibrated raw data for
Fig2.f. We have now updated Fig2.c and removed the data in the schematic of spectrum analyzer.
3
REVIEWERS' COMMENTS
Reviewer #2 (Remarks to the Author):
The authors have convincingly addressed all my comments and questions, and modified their
manuscript accordingly. I believe this work is suitable for publication in Nature Communication.