SciPost Submission Page
Absence of quantum features in sideband asymmetry
by J.D.P. Machado, Ya.M. Blanter
This is not the current version.
|As Contributors:||João Machado|
|Date submitted:||2019-09-07 02:00|
|Submitted by:||Machado, João|
|Submitted to:||SciPost Physics|
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.
Submission & Refereeing History
- Comment by Prof. Davis on 2020-04-16
- Comment by Anonymous on 2020-04-20
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Reports on this Submission
Anonymous Report 2 on 2019-12-22 (Invited Report)
1 - Inappropriate language
2 - Unclear on subtle aspects of calculations, while asserting that other work is unclear/incorrect
3 - Unconvincing conclusions
Sideband asymmetry in optomechanical systems has been observed in a number of experiments. The origin of this sideband asymmetry has been discussed by a number of authors, and is somewhat subtle, being dependent on the method of detection of scattered radiation. It 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, though in a manner which is rather unconvincing and much less clear than prior work on the subject. Here the asymmetry appears to be attributed to “coincidental” variations in intrinsic system parameters, in a manner which is unlikely to be reproducible across multiple experiments and would be experimentally testable, should anybody be sufficiently motivated.
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.
While I have not attempted to reproduce the authors’ calculations myself, I am skeptical as to their correctness.
Some specific comments follow:
- The authors claim, using melodramatic and inappropriate language, that the sideband asymmetry has solely been attributed to the mechanical zero-point fluctuations. The authors will find that this is not the case after a quick perusal of the relevant literature; alternative interpretations have been discussed at length.
- 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. The full sideband spectrum of an optomechanical system has been calculated in other places, though this is not it.
- 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 crux of this work is their assertion that the calculations in Ref 6 are incorrect. Given this claim, they should directly compare their results with that work and point out the supposed flaw in Ref 6. As it stands, and without having reproduced either calculation in full myself, I find Ref 6 much more clear and convincing.
Anonymous Report 1 on 2019-11-4 (Invited Report)
Quite generally, I think this manuscript could be a valuable contribution to the field of quantum optomechanics. Indeed, with regards to experiments showing sideband asymmetry, the authors have convinced me that the question of operator ordering has not been given an appropriate level of attention. I found the paper fairly well written, with relevant examples that are placed in the context of prominent experiments. These comparisons are very pointed and will certainly aid in initiating further discussions on this topic.
As the paper currently stands, I see two minor weaknesses. Both of which could be easily resolved.
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 susceptibilty. I suspect a more concise version would actually have a stronger impact (with the details moved into the supplemental material).
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.
As a broad field of research, cavity optomechanics has been around for many decades. However, many early experiments where limited to the classical regime since reaching/measuring the quantum level was (and still is) experimentally challenging. As a result, the community identified certain experimental signatures that could be used to distinguish quantum behaviour from classical behaviour. One such signature is the observation of asymmetry in the displacement noise power spectral density.
In the manuscript presented here, the authors present an argument against this convention, claiming that this particular experimental signature (sideband asymmetry) is an artifact of the decision to use a particular operator ordering. Indeed, I agree with the authors claim that, in contrasting quantum from classical behaviour, one needs to carefully consider the form of measurement being performed (in addition to the physical system itself).
If this paper is published it would hopefully initiate further discussions. Those discussions may, or may not, fall in favour of the claims made here; eitherway I think it's conversation worth having.
I recommend its publication in SciPost
As per earlier suggestions;
1-Condense theoretical section.
2-Add discussion on photon counting experiments.