Parameter Optimization of Josephson Parametric Amplifiers Using a Heuristic Search Algorithm for Axion Haloscope Search
, Junu Jeong 1,†, Sungwoo Youn 1,*, Sungjae Bae 1,2, Arjan F. van Loo 3,4, Yasunobu Nakamura 3,4, Sergey Uchaikin 1 and Yannis K. Semertzidis 1,2
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThis paper focuses on the interesting topic of exploiting the Josephson effect to detect dark matter.
I have read this article carefully and find it rather interesting. However, I have comments and conceptual issues that prevent me from recommending this manuscript for publication
1) The text of the article gives the impression that the 5.3 GHz frequency is some sort of universal constant for detecting dark matter. I would like to see in the text of the paper calculations and formulas that could clearly show how axion characteristics affect JPA parameters?
2) A technical question. What types of Josephson junctions are used dc SQUID, SNS, SFS, Sc(constriction)S, SIS? Does the junction type have some sort of effect on the characteristics of JPA?
3) I recommend that the authors take a deeper look at the literature on this subject. In particular, mention the following similar works
https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.231801
https://iopscience.iop.org/article/10.1088/1475-7516/2009/08/011/meta
(none of those papers are mine)
Author Response
This paper focuses on the interesting topic of exploiting the Josephson effect to detect dark matter.
I have read this article carefully and find it rather interesting.
=> Thank you very much for the referee’s interest.
However, I have comments and conceptual issues that prevent me from recommending this manuscript for publication
=> Please find below for our responses.
1) The text of the article gives the impression that the 5.3 GHz frequency is some sort of universal constant for detecting dark matter. I would like to see in the text of the paper calculations and formulas that could clearly show how axion characteristics affect JPA parameters?
=> The frequency 5.3 GHz is not relevant to any universal constants for detecting dark matter. As indicated in the sentence ‘Since the axion mass (equivalently frequency with ma ≃ ωa = 2πfa) is unknown a priori, …’, the frequency of axion dark matter is unknown and thus the entire possible frequency spectrum needs to be scanned. The choice of the frequency region around 5.3 GHz in this study stems from the utilization of the JPA for an experimental search around that frequency. This is stated in the sentence ‘Our study is limited to the frequency range between 5.24 and 5.35 GHz, over which the JPA was utilized in an axion search experiment [22]’.
The target search frequency determines the JPA pump frequency with the relationship of fp = fs + fi due to the three-wave mixing process, as stated in the manuscript.
2) A technical question. What types of Josephson junctions are used dc SQUID, SNS, SFS, Sc(constriction)S, SIS? Does the junction type have some sort of effect on the characteristics of JPA?
=> The junctions in our JPA are Al/AlOx/Al, which is an SIS type junction. One of the advantages of SIS junctions is that when looking at the junction using the RSCJ model, where a single junction is replaced by the parallel combination of an ideal junction, a resistor and a capacitor, the resistance value is considered to be infinite, so there is no resistive path for currents available. The specific materials are standard materials used in both quantum amplifiers and quantum computing, because Al/AlOx/Al junctions can be flexibly fabricated to allow for a huge range of critical currents. As far as I know they are still the best known Josephson junction when it comes to device quality.
We add the following sentence for the reader’s information: “The Josephson junction of our JPA is a type of superconductor/insulator/superconductor fabricated from Al/AlOx/Al, known for its flexible manufacturing process and wide critical current range.”
3) I recommend that the authors take a deeper look at the literature on this subject. In particular, mention the following similar works
https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.231801
https://iopscience.iop.org/article/10.1088/1475-7516/2009/08/011/meta
(none of those papers are mine)
=> The works cited by the referee utilize the Josephson junction directly for detecting dark matter or dark energy. In contrast, the JPA employed in our study functions as an amplifier utilizing the nonlinear characteristics of Josephson junctions to achieve parametric amplification. In our application, the JPA is employed to amplify pre-generated photon signals with minimal noise, thereby enhancing the experimental Signal-to-Noise Ratio (SNR). Therefore, the two ways to use Josephson junctions are very different.
Reviewer 2 Report
Comments and Suggestions for AuthorsComments for author File: 
Comments.pdf
Author Response
General comments:
The paper presents an interesting new methodology to optimize the parameter space for the use of JPAs. The manuscript is well written, and I suggest the publication in MDPI Electronics.
=> We thank the referee very much for recommending the manuscript for publication!
Minor points:
The only suggestion I have is to add a quantitative comparison table between the method presented in the manuscript and the other methods currently used to tune the parameter space of a JPA.
=> Without knowing the great details of how to characterize JPA using different methods by the individual groups (Refs. 24, 25, 26, 34 and 36 in the revised manuscript), it would be difficult to make a quantitative comparison. Instead, we provide a qualitative comparison table as follows:
“Table 1. Comparison of the JPA characterization methods for axion search experiments. The characterization times are approximate estimates based on the information provided in the corresponding references.”
|
Method |
Pros |
Cons |
Char. time [s] |
|
Pre-scanned |
Comprehensive |
Unreliable in changing environments |
O(104) |
|
Target gain |
In-situ, time efficient |
Not optimal solutions |
O(100-1) |
|
Nelder-Mead |
In-situ, optimal solutions |
Heuristic |
O(101-2) |
Reviewer 3 Report
Comments and Suggestions for AuthorsThe paper has relevant information about very low noise amplifiers based on nonlinear Josephson junctions.
Some comments:
In section 2.3 "Measurement setup and calibration", there is a description of Figure 2 (measurement setup), but in such Figure doesn't appear the described components: Dilution refrigerator (DR), Noise Source (NS) or mixing-chamber plate (MXC). What is the 50 Ohm block on the left? Is it the "Noise Source"? What kind of component is the connected between JPA and central circulator? Is it a directional coupler? Please, clarify it.
Author Response
The paper has relevant information about very low noise amplifiers based on nonlinear Josephson junctions.
Some comments:
In section 2.3 "Measurement setup and calibration", there is a description of Figure 2 (measurement setup), but in such Figure doesn't appear the described components: Dilution refrigerator (DR), Noise Source (NS) or mixing-chamber plate (MXC). What is the 50 Ohm block on the left? Is it the "Noise Source"? What kind of component is the connected between JPA and central circulator? Is it a directional coupler? Please, clarify it.
=> We clarify all the components in the figure. Yes, the 50 Ohm is the noise source. We add the following sentence to the caption: “The directional coupler is positioned between the JPA and the central circulator to facilitate JPA gain measurement using the network analyzer.”
Reviewer 4 Report
Comments and Suggestions for AuthorsThe paper provides a well written account of the improved optimisation of a Josephson amplifier. It achieves this by using the Nelder-Mead technique to quickly establish the optimal parameters of the amplifier obtaining a significant gain in the required time. My main query is the attribution of the two features in Figure 8. The authors claim that they are due to an impedance mismatch and the maximum resonance frequency. Especially, the impedance mismatch occurs in the middle of the studied frequency window and could therefore be problematic. However, within the paper there is no mention of identifying the root cause of these artefacts?
Some further comments/ questions; On page 2 at the end of the paragraph below equation 2, the authors make the claim that JPAs are used in various applications. While a statement like that is fine, the expectation is that references are provided to back up this claim.
In figure 6 the authors fit the data with two equations. For the first they state in the caption that this equation is described in the text, but in the text they are simply referring to another paper. I would suggest that this equation is provided and explained in a bit more detail. The second equation is a 5th order polynomial function. This equation is used without any further indication why this is appropriate and indeed correct.
Author Response
The paper provides a well written account of the improved optimisation of a Josephson amplifier. It achieves this by using the Nelder-Mead technique to quickly establish the optimal parameters of the amplifier obtaining a significant gain in the required time.
=> We thank the referee for the positive statement.
My main query is the attribution of the two features in Figure 8. The authors claim that they are due to an impedance mismatch and the maximum resonance frequency. Especially, the impedance mismatch occurs in the middle of the studied frequency window and could therefore be problematic. However, within the paper there is no mention of identifying the root cause of these artefacts?
=> The regions where impedance mismatches occur are omitted from the search, thereby limiting our search range. Usually, these regions are covered by employing a different JPA or adjusting the configuration. The cause of these artifacts remains unclear; however, empirical observations indicate a possible link to impedance mismatch, as stated in the manuscript: “It was observed that slight variations in configuration, such as using different circulators or adjusting line lengths, resulted in shifts of these regions to different frequencies. This suggests that such regions are presumably caused by impedance mismatch.” An additional statement suggesting a separate study is included in the original manuscript “Further investigation will be necessary to gain a clear understanding of the underlying cause.”
Some further comments/ questions; On page 2 at the end of the paragraph below equation 2, the authors make the claim that JPAs are used in various applications. While a statement like that is fine, the expectation is that references are provided to back up this claim.
=> We add several references to support this claim.
In figure 6 the authors fit the data with two equations. For the first they state in the caption that this equation is described in the text, but in the text they are simply referring to another paper. I would suggest that this equation is provided and explained in a bit more detail. The second equation is a 5th order polynomial function. This equation is used without any further indication why this is appropriate and indeed correct.
=> We add the following equation we have derived from Ref. [43]:
ωJPA ≈ (LeCe+LJCe/cos[πΦ/Φ0])-0.5,
where Le and Ce are the effective inductance and capacitance for the equivalent circuit, LJ is the Josephson inductance of the SQUID, and Φ/Φ0 is the magnetic flux generated by the bias current, measured in units of the flux quantum Φ0.
We also replace the phrase in the caption “described in the text” with “derived from Ref. [43]”.
The pump power profile does not show a certain feature that can be described using a known function. We chose a 5th order polynomial function to approximate the profile. While this function may not precisely capture all nuances of the profile, the fitting results serve as the initial seeds for the simplex in the Nelder-Mead algorithm, which is designed to find the final solution through a series of iterations. Therefore, the function does not need to perfectly describe the profile.
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsI recommend this manuscript for publication
