Absence of quantum features in sideband asymmetry

The referee presents unsubstantiated and rather vague criticism of our manuscript, which is largely based on arguments against statements not present in our manuscript and seemingly personal bias. We urge the referee to read the manuscript thoroughly and elaborate a report that reflects higher scientific standards. Particularly, the referee should pay attention to two major issues: the real goal of the manuscript, which is to show that backaction is responsible for sideband asymmetry; and careless attacks on the validity of the present work.

Regarding the latter, the referee states that "While I have not attempted to reproduce the authors’ calculations myself, I am skeptical as to their correctness.", " As it stands, and without having reproduced either calculation in full myself, I find Ref 6 much more clear and convincing." and "The authors undertake some calculations which appear reasonably standard, though I have not followed them through in detail. I expect they are mostly correct, though am suspicious of them in more subtle points where the authors are unclear.".

The referee repeatedly dismisses our findings, and yet is unable to point to any precise instance where the referee believes that we are wrong or unclear. We find that such statements lack any scientific basis and preclude all healthy scientific discussion. Further, the statements made by the referee that the referee has not attempted to reproduce nor follow our work in detail while judging it as unsound, constitutes a poor scientific practice. If the referee has spotted any mistake or flaw in our work, the referee should point what and where exactly the error is, for which we would be considerably grateful. The same holds for the points where the referee believes to be unclear.

Regarding the purpose of the article, this is repeatedly stated throughout the manuscript:

» abstract-'we find that the asymmetry arises from the backaction caused by the probe and the cooling lasers';

» introduction, end of page 2: 'we show that ZPM does not contribute to the asymmetry and that SA naturally arises from the backaction between the cavity and the mechanical oscillator';

» end of subsection 3.1, page 7: 'As backaction already occurs at the classical level, Eq.(23) shows a classical origin for SA.';

» end of subsection 3.2, page 8: '... backaction leads to an asymmetry in the spectrum.";

» conclusion, beginning of page 9: ' we have shown that SA arises from the backaction caused by the laser drive, and that no ZPM contributes to the asymmetry';

» conclusion, end of page 9: 'We stress once more that there are no quantum features in SA. For a linear system, the noise response function is identical in both classical and quantum descriptions, and as Stokes and anti-Stokes processes provide different amplitudes for the sidebands, an asymmetry naturally emerges.'


Nevertheless, the referee insists on contradictory views about our manuscript, none of which has any solid anchoring in our manuscript:

"The crux of this work is their assertion that the calculations in Ref 6 are incorrect." - The purpose of our manuscript was not to assert that Ref.6 was wrong. We believe that Ref.6 contains a mistake, and we mention it once in the body of the manuscript. Nevertheless, the emphasis given by the referee on Ref.6 does not reflect its importance to our present manuscript, nor does Ref. 6 stand out from the other references. We thus find that the insistence of the referee with Ref.6 is not due to any scientific reason.

"Sideband asymmetry ... has been attributed to zero-point fluctuations of the mechanical or electromagnetic modes, or due to correlation between backaction noise and the imprecision noise of the detector.
The present paper appears to support the latter interpretation" - There is no statement present in the paper that supports such interpretation.



Reply to the referee's remaining concerns:

"The spectral densities are defined in an unclear manner, presenting a spurious distinction between the time and frequency domain, where in fact they can be related in a well-defined manner if one is sufficiently careful. This has been done in a number of other places." - There are 2 issues to be addressed here:

»1st: we do not understand what precisely is unclear to the referee. None of the spectral densities present in the article are new, and they have been defined before elsewhere. Further, we always work in the frequency domain, so we do not understand what exactly the referee means with " spurious distinction between the time and frequency domain". We ask the referee to point to specific equations or sentences which the referee believes to be unclear, so that we can provide a proper answer.

»2nd: the referee seems to suggest that defining spectral densities in a quantum context is a matter of meticulosity. This is simply not true, and the issues associated with defining quantum spectral densities are already known from the literature (for a good review on the subject, see J.D. Cresser, Phys. Rep. 94, 47 (1983))


Related to this later issue, the referee states:
"The authors assert that Eq (1) is simply asserted to be true, where in fact this expression appears to me to be just an expression proportional to the Fourier transform of the position correlation function of the undamped quantum harmonic oscillator, easily calculated."

Our reply: The referee seems to have overlooked an entire section (Section 2) discussing the issues with the aforementioned spectral density (pages 3 & 4 of our manuscript). Further, the "easily calculated Fourier transform of the position correlation function of the undamped quantum harmonic oscillator" is not as well-defined as the referee seems to believe (once again, see J.D. Cresser, Phys. Rep. 94, 47 (1983)).


And at last, the referee states:
"The authors claim ... that the sideband asymmetry has solely been attributed to the mechanical zero-point fluctuations."

Our reply: We do not make such claim. Once the referee reads our manuscript carefully, the referee will find that we discuss other interpretations of sideband asymmetry as well:

»'Alternative interpretations and explanations such as interference between different noise channels [6,15] and laser phase noise [16] have been discovered': page 2 of our manuscript

»'The interpretation of SA differs for different operator orders (arising from different detector models' - page 2 of our manuscript

Further, the referee's comments about Ref.6 answered above contradict the referee's own statement.

We thank referee 1 for his valuable feedback.

The referee says "First, the details of the calculations in Sec. 3 detract from the overarching message. For example, the list of Fourier components in Sec. 3.1 (Eq. 9-15) does not, in my opinion, provide any additional insight beyond what is said elsewhere. This is also true for Sec. 3.2 (Eq.28-31), which finds a result similar to that obtained in Sec. 3.1 but with a modified susceptibility. I suspect a more concise version would actually have a stronger impact (with the details moved into the supplemental material)."

Our reply: We fully agree with the referee and we have implemented his suggestions. For a description of the new structure of the manuscript, see the list of changes.


The referee says "Second, there is no reference to recent optomechanical experiments that use single photon detection, such as those performed in the laboratories of Oskar Painter and Simon Groblacher. I understand this is an different measurement technique to homodyne and heterodyne, and not necessarily the target of the claims made in this paper. However, that sub-community has borrowed the term "sideband asymmetry" to denote the difference in click rates between the upper and lower sidebands. Furthermore, they reference many of the papers under discussion in this manuscript. I think it would be valuable to broaden the context and directly comment on these experiments."

Our reply: We agree with the referee that the aforementioned single photon detection experiments should be mentioned. However, as the referee is aware, these experiments are not equivalent to the homo-/heterodyne detection considered in our manuscript, and we fear that an extended discussion of single-photon detection is beyond the scope of our manuscript and that it would harm the conciseness and focus we intended to achieve. We have thus briefly discuss them in the manuscript and enlightened the differences. For the additional discussion, see the list of changes.