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Optomechanical damping as the origin of sideband asymmetry

by J. D. P. Machado, Ya. M. Blanter

Submission summary

As Contributors: João Machado
Arxiv Link: (pdf)
Date submitted: 2021-03-22 19:41
Submitted by: Machado, João
Submitted to: SciPost Physics
Academic field: Physics
  • Condensed Matter Physics - Experiment
  • Quantum Physics
Approach: Theoretical


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 as well as other interpretations, such as quantum backaction and noise interference, and show that the asymmetry is due to the optomechanical damping caused by the probe and the cooling lasers instead.

Current status:
Editor-in-charge assigned

Author comments upon resubmission

Dear Editor,

We have carefully analised the comments from the referees and implement the necessary changes to answer to the questions posed. We hope that this new version clarifies the previous questions raised.

List of changes

Title - Optomechanical damping as the origin of sideband asymmetry

The title was changed to state up front what is the origin of sideband asymmetry instead of focusing on what is not.


- We included that we discuss "other interpretations, such as quantum backaction and noise interference" in the abstract.


- Expanded on the historical developments regarding the nature of sideband asymmetry and its connexion with zero-point motion right after Eq.(1), as well as a more detailed discussion of the previous work on sideband asymmetry.

- "Thereafter, the role of ZPM was once again emphasised in the interference between the noise channels, in attempt to reconcile the explanation with the standard result" -> "Thereafter, the quantum nature of SA and the role of ZPM was emphasised in this last interpretation, in attempt to reconcile it with the standard result"

- Moved the discussion on the photon-counting experiments from the conclusion to the introduction.

Section 2

- General cleaning (mostly rephrasing and breaking sentences for clarity)

- "Nevertheless, ZPM plays a role in the variance of $X$, and there is a link between $X(t)$ and the measurement outcome. As $X$ is monitored in time, a definite proof might rest in the theory of quantum continuous measurements." -> " Nevertheless, ZPM could affect the spectrum due to its role in the variance of $X$, and the exact effect of ZPM in the spectrum could be explained with the theory of quantum continuous measurements without the prescription of a spectral density"

Section 3

- "A method to measure SA is to apply a probe beam at $\omega_cav-\Omega$ and measure the red-sideband at $\omega_{cav}$, and then tune the probe frequency to $\omega_{cav}+\Omega$ to measure the blue-sideband at $\omega_{cav}$" -> "A method to measure SA is to apply a probe beam at $\omega_{cav}\mp\Omega$ and measure the red (blue)-sideband at $\omega_{cav}$, and then tune the probe frequency to measure the other sideband"

- The equation for the spectrum was rearranged for increased clarity
- Included a discussion (at the end of the section) on the temperature dependence the quality factor needs to have in order to match the standard result, along with a figure displaying the temperature behaviour, and a comparison with typical experimental values.

- "The standard result given by Eq.(1) predicts a temperature dependence $\zeta=1/\bar{n}_b(T)$ for the asymmetry, and it is observed experimentally that SA becomes more prominent at low temperatures. The asymmetry imbalance in Eq.(11) has a temperature dependence, though indirect. For real physical systems, the bare mechanical quality factor $Q$ varies with the temperature, which makes $\zeta$ temperature dependent. Using Eq. (11) and considering the simplest case of a system probed resonantly ($C= 4g^2 Q /(\kappa \Omega)$) with a single read-out mode, in order to mimic this temperature behaviour, the temperature dependence of $Q$ must be"

Section 4

- Review of the quantum backaction and noise interference interpretations - Previous appendices B and C were merged and rewritten to present a thorough and detailed new section added addressing the issues with the quantum backaction and noise interpretations.


- Adapted the conclusion to include the discussion in the section 4.

Overall - the term "backaction" referring to the source of the asymmetry was replaced by optomechanical damping for better clarity and to avoid confusion with the term "backaction" used to refer to interference between the ZPM of the cavity and the ZPM of the mechanics, as in (Phys. Rev. A86,033840 (2012); Phys. Rev. X4, 041003 (2014)).

Reports on this Submission

Anonymous Report 2 on 2021-4-15 Invited Report


This paper provides a new analysis of sideband asymmetry, something that has been of considerable to the quantum opto-mechanics community, and gives a new interpretation in which this effect is purely classical. The authors have a done an excellent job of comparing their analysis in detail with previous analyses so as to explain the reasons for the differences in interpretation. I think this new version is now appropriate for publication in ScPost Physics.




Acceptance criteria are met.

Requested changes


  • validity: high
  • significance: high
  • originality: high
  • clarity: high
  • formatting: good
  • grammar: reasonable

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