Superconducting Sub-Terahertz Oscillator with Continuous Frequency Tuning

Round 1

Reviewer 1 Report

Flux-flow emission in underdamped Josephson junctions is strongly affected by geometrical (Fiske) resonances. Generally, such resonances are very beneficial for the emission. However, they lead to a discontinuous emission spectrum with maxima at the cavity mode frequencies.  In this work the authors aim to develop FFO with a continuous spectrum. Their strategy is to dampen the resonances by shunting the junctions. I think this is an interesting development of the FFO device, which deserves a publication. However, significant changes would be needed before publication.

Detailed critics.

1.      Fiske steps are describes as foes of the FFO, so that the problem is fixed by removing them. This is misleading. Fiske steps are very beneficial for FFO and removing them greatly deteriorates FFO performance.  Therefore, this is a tradeoff problem. This has to be clearly articulated and the effect of deterioration explicitly discussed.

2.      In the last sentence of conclusion it is stated: ”This geometry will help to improve the suppression even further without significant change in losses compared with the standard FFO geometry.” The statement is confusing. A significant damping has to be introduced to suppress Fiske steps. I assume that Rn should have dropped a lot after shunting. Please provide all the necessary data before and after, including Rn and IcRn. Substantiate the claim, if correct. Remove otherwise.

3.      Concerning peaks in Rd of unshunted junctions in Fig. 2 (c). I assume that this is largely an artifact of numerical derivation using several points in the IV. The actual IV is jumping between the steps. Therefore, the numerical Rd would be strongly dependent on the number of points used in the derivation.

4.      What is the connection between the frequency and voltage? How well in the ac-Josephson relation satisfied? This is not granted for a system with a resonance.  Is voltage vs frequency in Figs. 9,11 exactly linear?

5.      References. I counted > 41% of selfcitations. Many of them are redundant and do not provide significant new information. Josephson oscillators developed by many other groups are not mentioned (especially for stacked junctions and junction arrays). This is not good and certainly not fair to my taste.

6.      Suppression of Fiske steps is a rather well studied issue. Apart from the straightforward damping, there is another way – by selecting a special junction shape [see e.g. Physica C 249, 12 (1995)]. Why is this method worse?

Author Response

Dear reviewer,

We kindly appreciate your attention and detailed critics of our work. Your suggestions and remarks definitely helped to improve the paper; also some unobvious and unclear moments were revealed and rewritten. Though, the strategy is not to shunt the junction, but to introduce the layers of normal metal in idle region, which have an electric contact only with the top electrode.

Detailed critics.

1. Fiske steps are describes as foes of the FFO, so that the problem is fixed by removing them. This is misleading. Fiske steps are very beneficial for FFO and removing them greatly deteriorates FFO performance.  Therefore, this is a tradeoff problem. This has to be clearly articulated and the effect of deterioration explicitly discussed.

      Indeed, Fiske steps are very beneficial for FFO operation, at the same time continuous frequency tuning is impossible in this regime. We agree that is a trade-off problem; thank you for the suggestion. We added some additional information to the text to stress the trade-off between the linewidth and damping (see the end of Chapter 1, page 4)

      “The linewidth of the oscillator is proportional to the square of the differential resistance R_d of the FFO at the operating point [32–34]; this, in turn, imposes restrictions on the value of R_d required to implement the PLL regime, and therefore special attention should be paid to this problem as R_d is increased for the geometry with the suppression.”

      Importance of low Rd (and consequently low linewidth) and trade-off between tuning and linewidth are also discussed on page 5:  “For the successful operation of the superconducting oscillator as a local oscillator (LO) in the integrated receiver [10,11], continuous tuning of the FFO frequency in the entire available frequency range of the device is necessary; in addition, to implement the PLL mode, the linewidth of the FFO emission should not exceed 10–15 MHz. The linewidth of the Josephson junction is determined by the combination of thermal and shot noise in the tunnel junction, which translates into frequency fluctuations at the tunnel junction by the square of differential resistance R_d;”

      In addition, the trade-off between the radiated power and damping is also discussed in Chapter 3.2 (page 7, 8):

“The location of the resistive layers along the FFO on its sides (Figure 3b) does not provide complete suppression of geometric resonances. There are still weakly expressed regions with a characteristic stepped structure on the IVC in the resonant mode. The inclusion of additional resistors on both edges of the generator and along the FFO (Figure 3c) allows for the suppression of the resonances completely, but leads to strong losses, since only part of the power generated by the FFO reaches the mixer (especially at high frequencies). The location of the resistors only at the non-radiating edge where the fluxons enter the FFO (Figure 3d) results in good suppression of resonances and does not lead to considerable additional power losses.”

2. In the last sentence of conclusion it is stated: ”This geometry will help to improve the suppression even further without significant change in losses compared with the standard FFO geometry.” The statement is confusing. A significant damping has to be introduced to suppress Fiske steps. I assume that Rn should have dropped a lot after shunting. Please provide all the necessary data before and after, including Rn and IcRn. Substantiate the claim, if correct. Remove otherwise.

      One way to suppress the resonances in the Josephson transmission line is, indeed, to introduce the damping layer. However, the better option is to reduce the reflection from the end of the line. The sentence refers to the geometry#3 from the paragraph 3.3 (see Fig. 6), which is the modification of the traditional FFO with the Chebyshev transformer made of normal metal at the non-radiating end (see Fig. 6). Therefore the attenuation occurs in the transformer out of the JTL, and only minor modifications are made to the junction itself compared to the standard design. However, the operation principle of the FFO is very complex and is affected by the field distribution in it. The analysis of the dynamics of the FFO with the modifications is a subject of further research.

3. Concerning peaks in Rd of unshunted junctions in Fig. 2 (c). I assume that this is largely an artifact of numerical derivation using several points in the IV. The actual IV is jumping between the steps. Therefore, the numerical Rd would be strongly dependent on the number of points used in the derivation.

      Indeed, there are real voltage jumps between Fiske steps, so the Rd is infinite in this voltage ranges. That was confirmed by direct Rd measurements using “traditional” lock-in technique. We agree with your statement. Therefore the dots in the center of the peaks are omitted and the corresponding zones are highlighted with light-yellow color. The recalculation was performed by linear fitting of the IV curve at each voltage value; number of points used in recalculation was 3. This information was added to the description to Figure 2: “c) differential resistance R_d calculated from figure 2b using linear fitting of the IVC over 3 points at each voltage value”

4. What is the connection between the frequency and voltage? How well in the ac-Josephson relation satisfied? This is not granted for a system with a resonance.  Is voltage vs frequency in Figs. 9,11 exactly linear?

      We have carefully checked relation between FFO frequency and voltage both in pure flux-flow and in Fiske step regimes, no deviation from Josephson relation was found. Correctness of the Josephson relation in the Fiske step region was confirmed at direct linewidth measurements [29]. Furthermore, at TELIS flight [18, 19] a specially developed procedure was used to record specific gas lines: program tuned the FFO voltage according to required frequency and after that phase locking of the FFO to stable synthesizer was realized; it was possible since the FFO frequency was already very close to the required value (see Fig 10 as an example). Thus, we can guarantee that the dependence of voltage on frequency in Fig. 9.11 is exactly linear.

5. References. I counted > 41% of selfcitations. Many of them are redundant and do not provide significant new information. Josephson oscillators developed by many other groups are not mentioned (especially for stacked junctions and junction arrays). This is not good and certainly not fair to my taste.

      We agree with your statement about self-citation (although we counted 38%), partially that is because many of the findings in the field of the FFO development were made by our group. To reduce the self-citation rate, we have removed some our references and added a significant number of new papers (partly recommended by another reviewer).

6. Suppression of Fiske steps is a rather well studied issue. Apart from the straightforward damping, there is another way – by selecting a special junction shape [see e.g. Physica C 249, 12 (1995)]. Why is this method worse?

Thank you for this comment; we added this paper to the reference list. Indeed, the FFO shape is rather important; actually we used exactly the same shape for the ends of our FFO (that is possible to see in Fig 3). Due to this shape there are no side-lobs on the dependence of the Ic on magnetic field. Nevertheless, the Fiske steps are still presented in the FFO IVC, although suppression of this steps is rather simple and stable due to “lob-less” Ic(H) dependence – actually that is the main message of the paper by Gijsbertsen et al, where this approach was used for suppression on the Fiske steps in the Josephson junctions for high-resolution X-ray spectroscopy. We used the same shape for the ends of the FFO (see Fig. 3); although in the range of magnetic fields required for the FFO operation the Fiske steps were still presented on the FFO IVCs..

We added the following sentences to the text (page 7): “Special shape of the FFO [64] is beneficial for suppression on the Fiske steps in the Josephson junctions. We used the same shape for the ends of the FFO (see Fig. 3); although in the range of magnetic fields required for the FFO operation the Fiske steps were still presented on the FFO IVCs.”

Reviewer 2 Report

In the current manuscript the authors solve the long-standing problem – how to suppress wave reflections from junction edges that allowed to suppress Fiske steps and perform continuous frequency tuning in Nb long Josephson junctions. While the problem of continuous frequency tuning can be solved with HTSC YBCO Josephson junctions, the Nb counterparts definitely have much larger radiation power, which is important for applications. Another important result is the demonstration that AlN barrier outperforms AlO barrier and allows significant improvement of critical current density. The manuscript is quite interesting and definitely deserves publication. While the authors present detailed introduction and description of the problem, it lacks, however, a number of important citations from 2000-th, which significantly affected the FFO development, see below. Also, it is a pity that the authors do not compare their experimentally measured linewidth with theory. While the detailed analysis can be time-consuming and might delay the publication of the current manuscript, I suggest the authors to write a new paper where this analysis can be presented. Since the authors have managed to defeat a serious problem of load matching, I expect with the current design the authors can achieve an exceptionally low linewidth in comparison with theory. In particular, for a Josephson junctions chain, where multiple IVC steps are observed with chaotic generation, the perfect load matching not only suppresses the chaos, but also leads to really low linewidth Appl. Phys. Lett. 110, 112601 (2017), http://dx.doi.org/10.1063/1.4978514, which seems to be even below the limit of Ref. [33] of the current manuscript. Finally, the manuscript can be accepted for publication with the account of the minor comments below.

Comments:
1. The authors describe the Josephson self-coupling effect, but cite rather old papers [27-29], while this effect has been studied in detail within the FFO context in more recent papers: Phys. Rev. B 2017, 96, 024515 https://doi.org/10.1103/PhysRevB.96.024515 ; J. Low Temp. Phys. 2019, 194, 312 https://doi.org/10.1007/s10909-018-2106-x  and also the preceding paper in Phys. Rev. B, 2007.

2. While some excess noise can appear for high critical density Josephson junctions, see, e.g., Phys. Rev. Lett. 79, 3486 (1997) https://doi.org/10.1103/PhysRevLett.79.3486 and the self-field effect can affect the FFO spectral linewidth, see IEEE Trans. Appl. Supercond. 15, 968 (2005) https://doi.org/10.1109/TASC.2005.850143, significant progress in understanding the broad FFO linewidth has been achieved both in theory and experiment, see. e.g., Physica C 372–376, 316 (2002) https://doi.org/10.1016/S0921-4534(02)00659-7 and the corresponding theoretical papers. Later, using direct computer simulations, it has been shown that even in the absence of excess noise, just starting from the thermal noise of the bias current, significant increase of the spectral linewidth occurs due to the noise self-pumping effect, see Phys. Rev. B 78, 024515 (2008) http://dx.doi.org/10.1103/PhysRevB.78.024515, Fig. 3, where due to this effect the FFO linewidth exceeds the short junction limit by nearly an order of magnitude. Then, it has been demonstrated that both in the travelling wave regime and later in the displaced linear slope regime in Journ. Appl. Phys. 110, 053922 (2011) http://dx.doi.org/10.1063/1.3633231, where giant linewidth due to chaotic generation of a soft soliton chain is possible, this excess linewidth can be decreased in case of good load matching of the junction and suppression of reflections from boundaries, which was perfectly realized in the current manuscript.

Author Response

We kindly appreciate your attention and detailed critics of our work. Your suggestions and remarks definitely helped to improve the paper; also some unobvious and unclear moments were revealed and rewritten. We agree that it would be very interesting and important to compare experimentally measured linewidth with theory, but this out of scope of the present paper. Indeed we looking forward to make comparison with theory in future, it will be topic for a new paper.

We also agree that chaotic generation is very important issue, although for all presented results we are quite far from the chaotic regime. Actually, we can see such transition at direct linewidth measurements that will be described in another paper. In this paper we will add a few appropriate references

Comments:
1. The authors describe the Josephson self-coupling effect, but cite rather old papers [27-29], while this effect has been studied in detail within the FFO context in more recent papers: Phys. Rev. B 2017, 96, 024515 http://dx.doi.org/10.1103/PhysRevB.96.024515 ; J. Low Temp. Phys. 2019, 194, 312 http://dx.doi.org/10.1007/s10909-018-2106-x  and also the preceding paper in Phys. Rev. B, 2007.

Thank you, recommended by you references are added

2. While some excess noise can appear for high critical density Josephson junctions, see, e.g., Phys. Rev. Lett. 79, 3486 (1997) http://dx.doi.org/10.1103/PhysRevLett.79.3486 

and the self-field effect can affect the FFO spectral linewidth, see IEEE Trans. Appl. Supercond. 15, 968 (2005) http://dx.doi.org/10.1109/TASC.2005.850143, 

significant progress in understanding the broad FFO linewidth has been achieved both in theory and experiment, see. e.g., Physica C 372–376, 316 (2002) http://dx.doi.org/10.1016/S0921-4534(02)00659-7 

and the corresponding theoretical papers. Later, using direct computer simulations, it has been shown that even in the absence of excess noise, just starting from the thermal noise of the bias current, significant increase of the spectral linewidth occurs due to the noise self-pumping effect, see Phys. Rev. B 78, 024515 (2008) http://dx.doi.org/10.1103/PhysRevB.78.024515, Fig. 3, where due to this effect the FFO linewidth exceeds the short junction limit by nearly an order of magnitude.

Then, it has been demonstrated that both in the travelling wave regime and later in the displaced linear slope regime in Journ. Appl. Phys. 110, 053922 (2011) http://dx.doi.org/10.1063/1.3633231, where giant linewidth due to chaotic generation of a soft soliton chain is possible, this excess linewidth can be decreased in case of good load matching of the junction and suppression of reflections from boundaries, which was perfectly realized in the current manuscript.

Thank you again for detailed noise analysis, that will be guideline for next paper. In the present manuscript we add a short description of the noise problem according to your advices, as well as extra references.

“The noise phenomenon observed in Josephson oscillators has been studied since 1980 [57], in addition to the extra noise that can appear for Josephson junctions with high critical current density [58], a significant increase in the spectral linewidth is due to the effect of noise self-pumping [59-61] and transition to the chaotic regime [62,63], a detailed discussion of these effects is beyond the scope of this article.”

Reviewer 3 Report

This manuscript is a well prepared in terms of research quality and writting. 

comments:

1. Page 4, line 140: The reviewer suggests that  a sentence clarifying the motivation of this study should be added at the end of the introduction. For example: Since a small Rd is necessary in phase locking of the FFO, a continous frequency-tuning in the low Rd region is reqired in many applications. The purpose of this study is to fill the tuning gaps in this region. 

2. Page 4, line 149: The aluminum layer does not actually "flat" the surface. It "wets" the surface in spite of its rouphness. 

3. Page 4, line 168: move the defination of Rj/Rn from line 173 to line 168, where it first appears.

4. Page 4, line 178: "calculated"->"designed"

5. Page 5, line 231: "used"->"specific"

6. Page 6, line 241: "make impossible operation"->"make operation impossible"

7. Page 7, line 261: "to detect emitted by the FFO"->"to detect the emittion from the FFO"

8. page 7, Figure 3: In the geometric description of the normal metal obsorbers, the word "edge" is used. To the reviewer, it is slightly misleading because "edge" naturally leads to the image of lateral edges of the long junction instead of the longitudinal deges (ends). It is recommended that the authors should consider rephrasing the description to avoid possible confusing. 

9. page 8, line 283: "Rd(V) dependence"-> Rd dependence on V or Rd-V dependence.

10. page 10, Figure 7: The impedance of the port assigned in the model should be given. |S11| is very close to 1. Why is this significantly mismatched port assigned? The result of #3 configuration is missing in this plot. Is there any reason for dropping #3?

10. page 11, equation (4): there is a phase of pi in the r1 item. It indicates that the port impedance is larger than that of the transmission line. This should be noted as an assumption in the text.

11. page 12, line 409: It is recommended to clarify the size of the junction used to monitor the FFO power.

12. page 13, line 436: "four points marked in Figure 9"->It seems that "two points" is correct.

13. page 14, figure 10(b): It is suggested that the x-axis scale should be made the same as that in (a). 

Author Response

We kindly appreciate your attention and detailed critics of our work. Your suggestions and remarks definitely helped to improve the paper; also some unobvious and unclear moments were revealed and rewritten.

comments:

1. Page 4, line 140: The reviewer suggests that  a sentence clarifying the motivation of this study should be added at the end of the introduction. For example: Since a small Rd is necessary in phase locking of the FFO, a continous frequency-tuning in the low Rd region is reqired in many applications. The purpose of this study is to fill the tuning gaps in this region.

Thank you for the suggestion. The sentence was added to the end of Introduction (page 4):

“The purpose of this paper is a development and systematical study of the continuous frequency tunable FFO with low R_d”

2. Page 4, line 149: The aluminum layer does not actually "flat" the surface. It "wets" the surface in spite of its rouphness.

Thank you for the remark. We changed this place in the paper.

“…a very thin Al layer completely covers the Nb base electrode [35–39], effectively wetting the columnar microstructure of the Nb film and flattening the surface in spite of its roughness [37].

3. Page 4, line 168: move the definition of Rj/Rn from line 173 to line 168, where it first appears.
4. Page 4, line 178: "calculated"->"designed"
5. Page 5, line 231: "used"->"specific"
6. Page 6, line 241: "make impossible operation"->"make operation impossible"
7. Page 7, line 261: "to detect emitted by the FFO"->"to detect the emittion from the FFO"
8. page 8, line 283: "Rd(V) dependence"-> Rd dependence on V or Rd-V dependence.

Thank you. All the places in the text were changed as it was suggested.

8. page 7, Figure 3: In the geometric description of the normal metal obsorbers, the word "edge" is used. To the reviewer, it is slightly misleading because "edge" naturally leads to the image of lateral edges of the long junction instead of the longitudinal deges (ends). It is recommended that the authors should consider rephrasing the description to avoid possible confusing.

We agree with your opinion, in the article "edge" when referring to FFO is replaced by "end".

10. page 10, Figure 7: The impedance of the port assigned in the model should be given. |S11| is very close to 1. Why is this significantly mismatched port assigned? The result of #3 configuration is missing in this plot. Is there any reason for dropping #3?

It is explained in the end of the second paragraph of 3.3

We could assign the port impedance to match the line in order to avoid reflections, but dispersion in the line at high frequencies due to change in London penetration depth and geometrical factor made this task almost impossible. As is shown later, it turned out to be much easier to set the impedance of the excitation port much bigger than the characteristic impedance of the line (impedance of the port was set to 100 Ω and the characteristic impedance of the line was around 0.3 Ω) and then recalculate the data on S11 in order to eliminate the influence of the port.

The reason not to show the geometry #3 on Fig. 7 is that the device with the geometry #3 has not been fabricated yet (compare Fig. 6 and Fig. 3). This geometry is a subject for further research.

10. page 11, equation (4): there is a phase of pi in the r1 item. It indicates that the port impedance is larger than that of the transmission line. This should be noted as an assumption in the text.

Thank you, we added description to the text below the formula:

“  in the first term denotes that the port impedance is larger than that of the line.”

11. page 12, line 409: It is recommended to clarify the size of the junction used to monitor the FFO power.

“The oscillator under study was a part of an integrated microcircuit comprising also a small SIS junction of the area around 1.5 μm² to monitor the radiation of the FFO, and a specially designed matching and tuning elements.”

12. page 13, line 436: "four points marked in Figure 9"->It seems that "two points" is correct.
13. page 14, figure 10(b): It is suggested that the x-axis scale should be made the same as that in (a).

Thank you for the remarks. The changes were done as recommended.

Round 2

Reviewer 1 Report

The modified manuscript is much improved. The authors has replied to my critics in a satisfactory manner. This work presents an important step forward in development of FFO. Therefore, I recommend publication in the present form.