# The influence of spacetime curvature on quantum emission in optical analogues to gravity

### Submission summary

 As Contributors: Maxime Jacquet · Friedrich Koenig Arxiv Link: https://arxiv.org/abs/2001.05807v2 (pdf) Date accepted: 2020-07-31 Date submitted: 2020-06-04 02:00 Submitted by: Jacquet, Maxime Submitted to: SciPost Physics Academic field: Physics Specialties: Atomic, Molecular and Optical Physics - Theory Condensed Matter Physics - Theory Gravitation, Cosmology and Astroparticle Physics Quantum Physics Approach: Theoretical

### Abstract

Quantum fluctuations on curved spacetimes cause the emission of pairs of particles from the quantum vacuum, as in the Hawking effect from black holes. We use an optical analogue to gravity to investigate the influence of the curvature on quantum emission. Due to dispersion, the spacetime curvature varies with frequency here. We analytically calculate for all frequencies the particle flux, correlations and entanglement. We find that horizons increase the flux with a characteristic spectral shape. The photon number correlations transition from multi- to two-mode, with close to maximal entanglement. The quantum state is a diagnostic for the mode conversion in laboratory tests of quantum field theory on curved spacetimes.

Published as SciPost Phys. Core 3, 005 (2020)

We have considered the referee reports and implemented major revisions to our manuscript as described by our replies to the referees.

### List of changes

Abstract: amend final sentence to "The quantum state is a diagnostic for the mode conversion in laboratory tests of
quantum field theory on curved spacetimes."

After Eq.1, insert sentence "The refractive index of most dielectrics is sufficiently well described by 3 resonances."

Final paragraph of section 2, modify $S_\omega$ to $S(\omega)$

After Eq. 3, insert sentence "In (3) the notation is omitting dependencies on $\omega$."

In paragraph discussing Fig. 3 b and d, insert correlation strengths.

New paragraph discussing Fig.3 a, c and e "The correlation structure is very different when there are no horizons. In the low frequency interval (Fig.3 a), significant correlations exist between three mode pairs simultaneously: C(N(nuL),N(uL))=0.56, C(N(noL),N(uoL))=0.97 and C(N(nlL),N(lL))=0.68. In the middle frequency interval (Fig.3 c), significant correlations exist between five modes pairs: C(N(nuL),N(uL))=0.43, C(N(noL),N(uoL))=0.71, C(N(noL),N(moR))=0.67, C(N(nlL),N(loL))=0.47 and C(N(nlL),N(lL))=0.43. In the high frequency interval (Fig.3 e), significant correlations exist between four mode pairs: C(N(nuL),N(uL))=0.83, C(N(noL),N(uL))=0.52, C(N(nlL),N(loL))=0.80, and C(N(nlL),N(lL))=0.50. Without horizons, strong correlations exist albeit with more than two modes."

New penultimate paragraph of Section 3: "In addition to the observations above, we note that strong correlations are possible without horizons (e.g. in Fig.3 a). Therefore, horizons lead to strong correlations but the converse is not true. Clearly, if we considered a two-mode system without horizons, any emission would be in correlated pairs with unit correlation coefficient."

First paragraph of section 4: append ", and coupling to modes outside the optical branch is responsible for this." to final sentence.

Fig 7 is now Fig 6, plot with Log-Log scale.

Discussion of (new) Fig 6 is now at the end of section 4 (content moved from App. B), with the following modification: insert "Furthermore, we remark firstly that for a finite correlation coefficient the degree of entanglement is limited below unity. Secondly, correlations close to unity indicate close to maximal entanglement. The degree of entanglement obtained for C<0.5 varies largely, whereas for C>0.5 the degree of entanglement can be reliably inferred from the correlations. Lastly, even small correlation coefficients indicate some entanglement. Further investigations of the relation between J and C beyond this particular analogue are needed." before final sentence of paragraph.

Appendix A: modify penultimate paragraph to "If one focuses the analysis on the kinematics of modes u|out' and d2|out' at low k, the dispersion is approximately linear and the flow velocity is subsonic in the left region and supersonic in the right region. The mode analysis above shows, when input and output modes are taken into account, that two-way motion is possible in both regions of the BEC.".

Appendix A: insert "in particular" in first sentence of final paragraph.

### Submission & Refereeing History

Resubmission 2001.05807v2 on 4 June 2020
Submission 2001.05807v1 on 17 January 2020

## Reports on this Submission

### Anonymous Report 2 on 2020-7-6 (Invited Report)

• Cite as: Anonymous, Report on arXiv:2001.05807v2, delivered 2020-07-06, doi: 10.21468/SciPost.Report.1812

### Report

I am surprised by the little care the authors have dedicated to the improvement of their work. Although some of the obvious flaws of the presentation of the first version have been cured, others have been introduced, as the renaming of the axis label of Fig. 6, which makes it more difficult to connect this figure with the quantities defined in the text. Is it ln(I) plotted as a function of ln(C) ?

But my main concern is about secs. 3 and 4. The authors didn't try to improve their very concise presentation. I find the suggestion of the first report of the other referee quite relevant: it would make sense to merge this work with "1908.02060 into a single and comprehensive long paper".

Of course, the author should decide themselves of the publishing policy of their own work. But, as far as the revue is concerned, I do not think that the level of clarity of this manuscript matches the editorial criteria of a journal of the quality of SciPost Physics.

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

### Anonymous Report 1 on 2020-7-1 (Invited Report)

• Cite as: Anonymous, Report on arXiv:2001.05807v2, delivered 2020-07-01, doi: 10.21468/SciPost.Report.1796

### Report

The authors have performed only minor changes to the manuscript in response of my and the other Referee's remarks. Most of my objections still apply to the revised version. From this, I conclude that the authors are not willing to make any serious effort to reinforce the manuscript according to the review reports. This is a bit of a pity as the subject is very interesting and I have the feeling there is a lot of exciting physics remains to be explored at a relatively weak effort. As it is now, the paper reports the finding of an interesting link between different quantities, but does not really illuminate the readers on the underlying mechanisms. Moreover, it is a bit annoying that important details of the section on new results are postponed (see footnote 4) to a forthcoming publication: according to the journal's policy, it should be as self-contained as possible.

Anyway, even though I am not really happy with the manuscript, I have no objections against its publication.

• validity: good
• significance: ok
• originality: ok
• clarity: low
• formatting: good
• grammar: good