# Absence of quantum features in sideband asymmetry

### Submission summary

 As Contributors: João Machado Preprint link: scipost_201909_00003v5 Date submitted: 2020-01-09 Submitted by: Machado, João Submitted to: SciPost Physics Discipline: Physics Subject area: Quantum Physics Approach: Theoretical

### Abstract

Sideband asymmetry in cavity optomechanics has been explained by particle creation and annihilation processes, which bestow an amplitude proportional to 'n+1' and 'n' excitations to each of the respective sidebands. We discuss the issues with this interpretation and why a proper quantum description of the measurement should not display such imbalance. Considering the case of linearly coupled resonators, we find that the asymmetry arises from the backaction caused by the probe and the cooling lasers.

###### Current status:
Editor-in-charge assigned

### List of changes

List of changes:

» The Fourier coefficients of the optical response function in Eq.8 and the optical response for the case where each sideband is driven separately are now displayed in Appendix A.

» The multi-tone case was moved to a separate appendix (App.B)

» Briefly discussed the photon counting detection experiments

- R. Riedinger, S. Hong, R. Norte, J. A. Slater, J. Shang, A. G. Krause, V. Anant, M. Aspelmeyer, and S. Gr\"{o}blacher, {\it Non-classical correlations between single photons and phonons from a mechanical oscillator}, Nature {\bf 530}, 313 (2016), \doi{10.1038/nature16536}

- J. Cohen, S. Meenehan, G. MacCabe, , S. Gr\"{o}blacher, A. H. Safavi-Naeini, F. Marsili, M. D. Shaw, and O. Painter, {\it Phonon counting and intensity interferometry of a nanomechanical resonator}, Nature {\bf 520}, 522 (2015), \doi{10.1038/nature14349}

in section 4 (conclusion). It now reads:

Further, our analysis is focused only on the power spectral density obtained with linear detections methods. There are other methods closely related to SA which also make use of the term sideband asymmetry'', such as the difference between the photon count rates when an optomechanical system is driven with short pulses at the red and blue sidebands [CITATION], that are outside the domain of the present work. Because single photon detection is a method that does not exhibit the operator order issues raised in Sec.2, and because only the instantaneous count rate is measured instead of the frequency spectrum (for weak driving and short enough pulses, the effects of backaction and noise are negligible), our conclusions do not apply to these single photon detection methods. The quantum description of the photon count detection scheme does indeed display a $n/(n+1)$ imbalance and can be used to directly determine the phonon occupancy. Nevertheless, it would be interesting to understand how the two methods are related to each other.

» The new structure of the article was updated in the introduction:

In this article, we start by discussing the problems with the standard interpretation of SA, their connection to how measurements are performed, and the role of ZPM in the spectrum (Sec. 2). We proceed to compute the response function for a system composed by two driven optical modes and a mechanical one (Sec. 3). Considering the symmetric noise power spectral density for both cases, 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. Additional details of the calculations can be found in App. A. For comparison with other measurement methods, we also analyse the case of a system composed by two modes (cavity + mechanical), but driven with multiple tones in App. B. Finally, we present a concise review of previous analyses of SA in App. C.

### Submission & Refereeing History

Resubmission scipost_201909_00003v5 on 9 January 2020
Submission scipost_201909_00003v1 on 7 September 2019

## Reports on this Submission

### Report

Upon resubmission, the authors have made a number of changes to the main text. This includes shifting large sections of text to the supplementary information, and including a brief comment on experiments that leverage single photon detection. I think these changes improve the readability of the paper.

In the previous submission, referee 2 raised a number of criticisms of this work. I can certainly understand his/her perspective on certain aspects, in particular, that the subtle interpretation of sideband asymmetry has been the subject of numerous detailed papers over the last decade. For example, there is the PRA by by Kjetil Børkje (Ref 18) which details the interpretation of sideband asymmetry. There is also the review article by Clerk et. al. (Ref 14) which provides an extremely detailed account of quantum measurement theory. However, without going through the detailed calculations, I can't find any specific errors/contradictions in this manuscript that would negate its claims.

Quite generally, I think this subject is interesting and timely. As a result, I think it should be published in SciPost.

• validity: -
• significance: -
• originality: -
• clarity: -
• formatting: -
• grammar: -

### Strengths

In helping to make the clear the relationship between classical and quantum linear systems, the manuscript makes a valuable contribution to a topic of current interest.

None

### Report

I think the authors have done a good job of improving the manuscript based on the suggestions of the previous referees. I recommend the manuscript for publication.

### Requested changes

none

• validity: top
• significance: good
• originality: good
• clarity: good
• formatting: excellent
• grammar: good