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Deterministic nuclear spin squeezing and squeezing by continuous measurement using vector and tensor light shifts
by Alice Sinatra, Ali Moshiri
Submission summary
| Authors (as registered SciPost users): | Ali Moshiri |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202508_00007v1 (pdf) |
| Date submitted: | Aug. 3, 2025, 11:50 a.m. |
| Submitted by: | Moshiri, Ali |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We study the joint effects of vector and tensor light shifts in a set of large spin atoms, prepared in a polarized state and interacting with light. Depending on the ratio $\epsilon$ between tensor and vector coupling and a measurement rate $\Gamma$, we identify a regime of quantum non-demolition measurement squeezing for times shorter than $(\sqrt{\epsilon}\Gamma)^{-1}$, and a deterministic squeezing regime for times longer than $(\epsilon \Gamma)^{-1}$. We apply our results to fermionic isotopes of strontium, ytterbium, and helium, which are atoms with purely nuclear spin in their ground state, benefiting from very low decoherence. For ytterbium 173, with a cavity such as that of \cite{Thompson2021}, it would be possible to achieve an atomic spin variance reduction of $0.03$ in $\simeq 50 \rm ms$.
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- Present a breakthrough on a previously-identified and long-standing research stumbling block
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Report
The paper is about the evaluation of how the tensor component of the interaction Hamiltonian of nuclear spins (alkali atoms) and a detuned light field affects the squeezing of the spins. The authors identify two regimes of squeezing, a quasi-QND and a deterministic one. They consider the so-called Holstein-Primakoff approximation to obtain a model Hamiltonian for the system. Then, they solve a two-mode master equation where they also take into account decoherence for the atomic mode and photon loss in the cavity. From this they obtain the expectation values of the quadrature of the atomic mode. They apply these results to ytterbium 173, strontium 87, and also, He 3. In doing so, the authors consider cavities from real experiments. As far as I understood, the main result is that considering the tensor term, “better squeezing” can be achieved in the deterministic regime. I believe the results are important as due to their long coherence times, these atoms are frequently used in quantum metrology and quantum information processing.
The paper is well-written; the formulas and derivations seem correct. It is rather technical for a reader without sufficient background, but the provided appendices and referenced literature definitely help with grasping the main ideas and derivations. In my opinion, the paper has the potential to be useful for future squeezing experiments with alkaline earth atoms.
Therefore, I recommend its publication in SciPost Physics after the authors do some minor revisions on the manuscript so that it is more accessible to an even broader audience.
I have the following comments, questions:
• The authors could also mention entanglement detection as an application of squeezing in the Introduction part.
• Can the authors explain briefly somewhere (maybe already in the Introduction) what is the main difference between the two squeezing regimes (quasi-QND and deterministic) intuitively? What advantage has one compared to the other? And why is this missing in the f=1/2 case?
• Also, is there a simple, intuitive explanation why does the tensor term introduce this new regime or one just has to look at Section 3.1 and understand through the formulas?
• The authors say that „In experimental works, those terms [tensor type terms] are either neglected for a large detuning, or else neutralized by dynamic decoupling.” Why is this neutralized if it can in principle provide advantage?
• In the Introduction it would be good to briefly mention the main results beyond “For each regime, we quantify analytically the metrological gain as a function of the atomic parameters, including decoherence.” Especially, what is the advantage of considering the tensor part of the interaction?
• It would be nice to have a brief description of the subsequent Sections’ content at the end of the Introduction.
• I would explicitly state near Eq. (1) that Appendix A explains where does Eq. (1) come from to help the reader.
• Would it be possible to change the first plots (for \epsilon) for Yb and Sr (in Fig 3 and Fig 4) so that they are both logarithmic or non-logarithmic? If it is possible, in my opinion it would look better if these plots were unified.
• Are there experiments where they did squeezing without the tensor term? It would be great to see a table (if there are enough experiments) with how the squeezing can be improved by considering the tensor terms in „real life” situations.
• In Section 3.2. what is needed for the alpha^t to cancel? (only the detuning is needed?) It would be nice to remind the reader of the physical content of these parameters from time to time. This goes for other parameters as well, as there are many of them (for example in Figs 3-5).
• In Section 3.2, is it true that the higher the detuning is, the better squeezing we have? Are there drawbacks of having a very high detuning? It would be nice to have some comments on this.
• Many equations have „avec” in them (e.g. Eq. (32)). It would be better to write it in English.
• Regarding helium 3 the authors say that the previous theory holds with minor modifications. Can the authors elaborate what are these minor modifications?
• What is the main conclusion of the paper? Is it that a better squeezing can be achieved with considering the tensor part? It should be emphasized more both in the Introduction and Conclusion.
The paper is well-written; the formulas and derivations seem correct. It is rather technical for a reader without sufficient background, but the provided appendices and referenced literature definitely help with grasping the main ideas and derivations. In my opinion, the paper has the potential to be useful for future squeezing experiments with alkaline earth atoms.
Therefore, I recommend its publication in SciPost Physics after the authors do some minor revisions on the manuscript so that it is more accessible to an even broader audience.
I have the following comments, questions:
• The authors could also mention entanglement detection as an application of squeezing in the Introduction part.
• Can the authors explain briefly somewhere (maybe already in the Introduction) what is the main difference between the two squeezing regimes (quasi-QND and deterministic) intuitively? What advantage has one compared to the other? And why is this missing in the f=1/2 case?
• Also, is there a simple, intuitive explanation why does the tensor term introduce this new regime or one just has to look at Section 3.1 and understand through the formulas?
• The authors say that „In experimental works, those terms [tensor type terms] are either neglected for a large detuning, or else neutralized by dynamic decoupling.” Why is this neutralized if it can in principle provide advantage?
• In the Introduction it would be good to briefly mention the main results beyond “For each regime, we quantify analytically the metrological gain as a function of the atomic parameters, including decoherence.” Especially, what is the advantage of considering the tensor part of the interaction?
• It would be nice to have a brief description of the subsequent Sections’ content at the end of the Introduction.
• I would explicitly state near Eq. (1) that Appendix A explains where does Eq. (1) come from to help the reader.
• Would it be possible to change the first plots (for \epsilon) for Yb and Sr (in Fig 3 and Fig 4) so that they are both logarithmic or non-logarithmic? If it is possible, in my opinion it would look better if these plots were unified.
• Are there experiments where they did squeezing without the tensor term? It would be great to see a table (if there are enough experiments) with how the squeezing can be improved by considering the tensor terms in „real life” situations.
• In Section 3.2. what is needed for the alpha^t to cancel? (only the detuning is needed?) It would be nice to remind the reader of the physical content of these parameters from time to time. This goes for other parameters as well, as there are many of them (for example in Figs 3-5).
• In Section 3.2, is it true that the higher the detuning is, the better squeezing we have? Are there drawbacks of having a very high detuning? It would be nice to have some comments on this.
• Many equations have „avec” in them (e.g. Eq. (32)). It would be better to write it in English.
• Regarding helium 3 the authors say that the previous theory holds with minor modifications. Can the authors elaborate what are these minor modifications?
• What is the main conclusion of the paper? Is it that a better squeezing can be achieved with considering the tensor part? It should be emphasized more both in the Introduction and Conclusion.
Recommendation
Ask for minor revision