Optical Measurements of Binary Buffer-Gas Partial Pressures for Vapor-Cell Atomic Clocks

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This is a very respectable and important manuscript for researchers working with alkali and buffer gas filled vapour cells. Imprecise buffer gas mixtures can have a major impact on the atomic clock performance and production viability/variability. Whilst I cannot claim the proposed technique is novel, this manuscript will be the first published record of it (to the best of my knowledge) and therefore tremendously valuable to those considering developing vapour cells based for portable atomic clocks/other atom sensors (even those that do not use buffer gases, this technique could be useful to to check for impurities and MTBF measurements). Here are some suggested improvements:

Line 47 – For completeness, in the intro sections it might be useful to point out the relative benefit of improving the cell temp insensitivity problem relative to other, perhaps more dominant, forces, e.g. AC stark shifts, RIN, helium, Rb-density changes, etc. I appreciate it is difficult to quantify this here, but perhaps can mention that there are other causes of long-term drift. It may also be useful to quantify (if possible) the level of partial pressure ratio error that is deemed “tolerable” over a certain temp control range; For example, with optimised partial pressures – one can achieve XXX stability with sub-10mK thermal control, but if there is an error is 60% in the partial pressure calculation, a 10mK change in temp can lead to XXX frequency stability.

Line 58 – Similar to the volume problem, another potential source of error in using pre-mixed volumes is that the temperature at which that volume was mixed and sealed off is not often the same temperature as the vapour cell filling rig, which can cause subtle but appreciable changes to the partial pressures.

Line 74 – Don’t agree that little work has been done to measure buffer gas partial pressures. I believe little has been published in this area – so this paper is useful for those who do not have a suitable method in place to determine partial and total pressure accuracy.

Line 89 – The setup for performing linear absorption spectroscopy can be easily designed in such a way that it can also be used the clock frequency measurement setup.

Line 94 – Its quite common to use a pure Rb cell as a reference, rather than a UTC derived frequency. Perhaps some people use a UTC calibrated frequency source but seems impractical.

Line 110 – It may be worth clarifying that one will need to drive the suitably narrow-linewidth single longitudinal mode VCSEL (<100 GHz?) with a suitably low noise current source (few nA rms up to a few MHz?) to reduce noise on the averaged traces; otherwise will need to wait a long time to average out the relevant features – process time is critical in volume manufacturing.

Line 116 – Temp at 40degC – typical operating temp in commercial Rb atomic clocks is >80degC. Not sure this detracts from the main messaging or experiment. Can see other temps referenced later in the article at ~60degC, etc. These are fine for lab-table bound research clocks but too low for commercial Rb clocks.

Line 150 – A note that there are a range of values for gamma and delta in different literature sources, and using different values from different literature can yield appreciable differences in the result. [15] seems ok here. This probably doesn’t matter so long as one uses the same values. The calculations performed to estimate coefficients seem reasonable but the large uncertainty in ΔP, ΔPAr = −(0.5 ± 2.4)% and ΔPN2 = (6.5 ± 4.1)% may cause large error bars in ones estimations? Also a large error presented in the measured partial pressures which the authors have noted (line 205).

Line 242 – There is a ~10% error in the prediction vs the measured hyperfine shift – this is notable. It would be useful to get the views of the authors as to what the cause(s) of this discrepancy and how might one reduce this.

Line 251 – Completely impossible because…? presumably the Rb atoms will fully saturated and absorb all the light at or near the resonance. Worth clarifying for completeness.

Author Response

We want to thank this Reviewer for their very detailed feedback, and we have taken many of the Reviewers' suggestions.

• The Reviewer asked us to include other sources of long-term frequency instability and to perhaps point out how significant an error in the filling might be.  We now write in the Introduction

Though the temperature dependence of the buffer-gas shift is only one potential source of long-term frequency instability for a clock (along with the AC Stark shift [8], microwave power variations [9], and spin-exchange [10] to name just a few) it can be a dominant contributor to long-term frequency instability. As an example, consider an ⁸⁷Rb vapor cell supposedly filled with an Ar/N₂ buffer-gas mixture at a total pressure of 20 Torr, and which is supposed to zero d[Δν_hfs]/dT at 60 ^oC: P(Ar)/P(N₂) = 1.625 [7]. However, if the ratio were just a few percent off, then [Δν_hfs]/dT would be ~ -5´10^-11/^oC at 60 ^oC implying a necessity to hold the vapor cell temperature to better than milliKevin levels in order to get the long-term frequency stability into the 10^-14 to 10^-15 range [11].     

• The Reviewer noted that the temperature of the mixing volume when filled can be different from the cell when filled, which is another source of filling error.  We agree but did not include this in the manuscript as we felt that it would be belaboring the point: "Cell filling errors are easy to come by."
• The Reviewer noted that it is unfair to say that "no work has been done" regarding pressure measurements for mixed cells.  We agree.  Manufacturers likely have a number of empirical methods for dealing with this problem.  Nevertheless, as the Reviewer indicates, these are not in the open literature.  Therefore, we have amended the text around line 85.  It now reads

Unfortunately, relatively little work has been documented in the open literature regarding the measurement of buffer-gas partial pressures in sealed vapor-cells.  

• The Reviewer noted that "The setup for performing linear absorption spectroscopy can be easily designed in such a way that it can also be used with the clock frequency measurement setup." We agree, and we now say around line 88,

To date, only one technique has been developed for measuring buffer-gas pressure in atomic clock cells after filling and sealing that is amenable to relatively easy implementation, and this relies on measuring the buffer-gas shift of the hyperfine transition frequency (i.e., Δν_hfs) [12]. [The highlighted text is new.]

• The Reviewer noted that "It's quite common to use a pure Rb cell as a reference, rather than a UTC derived frequency. Perhaps some people use a UTC calibrated frequency source, but this seems impractical." We agree, and we now say around line 113,

Moreover, it requires a calibrated reference frequency to UTC (or a least a good house reference) in order to ensure that a consistent value of Δν_hfs is measured. [Highlighted text is new.]

• The Reviewer asked us to clarify whether or not a low noise current source for the VCSEL laser would be required.  Actually, any commercial laser diode driver should be fine (i.e., low enough current noise.)  Since the dephasing rate of the optical transition is going to be on the order of MHz, it is possible to scan through the resonance very rapidly, allowing many scans to be averaged in a reasonable amount of time.
• The Reviewer noted that our experimental temperature of 40 ^oC is lower than what is typical for Rb atomic clocks.  While we agree, as the Reviewer notes, this is not an important distinction for the technique.
• The Reviewer notes that there are a number of different microwave pressure shift parameters in the literature.  This has been considered by Vanier (Ref. 7), and that is why we employ the parameters from that paper. 
• The Reviewer asks for clarification regarding the 10% error between our measured buffer-gas shift and the predicted buffer gas shift.  In examining the analysis, we realized that we had underestimated our buffer-gas pressure shift uncertainty.  This has been corrected, and our discrepancy is (9.6 +/- 14.1) %.  This is noted in Table 3.
• The Reviewer asked for some clarification on our claim that operating the cell at 206 ^oC was impossible.  This was a fair comment, and we now write near line 275,

... but completely impossible for the actual pressures in the vapor-cell: 206 ^oC, given that at this temperature the vapor would be so optically thick as to allow no resonant light to pass through a vapor of any reasonable length.

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript presents method for rapid determination of correctness of mixed buffer gas ratio in a cells designed for Rb microwave atomic clocks. After production, each cell can be quickly tested whether it should be used for constructing new atomic clock. This approach is important because, according to my knowledge, this technique has not been used before and could potentially improve efficiency of producing new Rb clocks.

The structure of the article is well organized making it easier for readers to understand all key aspects of the research presented.

I suggest minor changes before publication:

1) (line 45) I would suggest adding in Introduction some comment on the typical range of temperatures which are optimal for short term stability of the clock.

2) (line 80) - I would suggest to put full name of the KSK. and (line 94) - the same for UTC.

3) (line 120) - Does the few degrees temperature accuracy is good enough? Are you able to estimate, how much influence it has to the final results?

4) I would recommend to change axis description in plots to commonly accepted form:
"Label / unit" or  "label [unit]" instead of using coma.

5) Is it possible to estimate, how much the long-term stability might be affected if the buffer gas is not well prepared? For example, for the case presented in the manuscript. It would show, how important the problem is for the final result of the clock's stability or accuracy.

Comments on the Quality of English Language

Article is well-written and easy to understand.

Author Response

We want to thank the Reviewer for their careful reading of our manuscript, and have amended the manuscript following the Reviewer's suggestions.

• The Reviewer suggested that we provide the reader with a range of typical vapor-cell operating temperatures.  We now write near line 48,

...T_o must be chosen for optimum SNR (routinely anywhere from about 50 ^oC to 80 ^oC depending primarily on cell length and total buffer-gas pressure).

• The Reviewer asked us to spell out UTC, which we have done (line 115).  The Reviewer also asked us to spell out KSK.  However, this wouldn't really add anything to the manuscript, and the reader will be better informed looking at the referenced paper [Ref. 12].
• The Reviewer asked about the few degrees uncertainty in our vapor.  This only affects our estimate of the Doppler width, which is affected by temperature via the atomic velocities.  For a three-degree uncertainty in temperature, there will be a 1% uncertainty in the atomic velocity and hence the Doppler width.  This is insignificant.
• The Reviewer asked us to change the axes labels in our figures.  We will defer to the Editor regarding how they want the axes to be presented.
• The Reviewer asked us to estimate "how much the long-term stability might be affected if the buffer gas were not well prepared.  We now write near line 55,

As an example, consider an ⁸⁷Rb vapor cell supposedly filled with an Ar/N₂ buffer-gas mixture at a total pressure of 20 Torr, and which is supposed to zero d[Δν_hfs]/dT at 60 ^oC: P(Ar)/P(N₂) = 1.625 [7]. However, if the ratio were just a few percent off, then [Δν_hfs]/dT would be ~ -5´10^-11/^oC at 60 ^oC implying a necessity to hold the vapor cell temperature to better than milliKevin levels in order to get the long-term frequency stability into the 10^-14 to 10^-15 range [11].

 

Reviewer 3 Report

Comments and Suggestions for Authors

The authors provide an interesting and viable technique for an all-optical estimation of the partial pressures of buffer-gas in a vapor cell filled with alkali metal and a binary mixture of inert gases.

The manuscript is clear and well written. The topic is of interest from a scientific and also from a clock manufacturer’s point of view. I have very few comments or observations that I ask the authors to address before publication:

1) Line 29: Albeit the cited reviews (Ref. 1-4) are very useful, I encourage the authors to add a few more citations about state-of-the art GNSS-grade clocks, possibly avoiding self-citations.

2) Lines 154-155: it is not very clear if both the shift (S) and the broadening (B) are expected to have the same scaling with temperature and if also broadening coefficients B have been rescaled to the operational temperature with the same formula.

3) Line 192: Can the shift be determined again from the fit of the convolution of the two Voigt profiles, without recurring to the isoclinic point? Is there an intrinsic advantage in using the isoclinic point as second variable (either in accuracy of the method, correlation in the two parameters, etc.)?

Also, is there a preferred range of buffer-gas pressures for which this method applies? Is it applicable as well at higher BG pressure than the one considered here, for example 100 Torr-300 Torr , when the isoclinic point might not be resolved?

Maybe the authors can clarify or add a comment to this points (necessity of the isoclinic point, i.e. working with the D1 line, and range of pressures detectable with reasonable accuracy with the proposed method).

Author Response

We want to thank the Reviewer for their careful reading of our manuscript and have made the following revisions based on the Reviewer's comments.

• The Reviewer asked us to provide some additional references regarding space clocks.  We have now added Ref. [2], "GNSS-grade space atomic frequency standards: Current status and ongoing developments."  Neither of the present authors is an author of this manuscript.
• The Reviewer felt that our discussion of the temperature dependence of the broadening and shift coefficients was not quite clear.  We now write near line 174

For Ar we use the expected power-law temperature-scaling parameter k [9,21]: S(T) = S(T_r)(T/T_r)^k where T_r is the temperature corresponding to the line-shift coefficient’s measurement. However, given the lack of both theoretical and experimental estimates for nitrogen’s temperature-scaling parameter we use k = 0.3, which is the expectation when the alkali/buffer-gas interaction potential has a R^-6 form [9]. For the temperature dependence of the broadening coefficients, we used the theoretical values tabulated by Keilkopf [21].

• The Reviewer asked if the shift could be determined from the Voigt fit without recourse to the isoclinic point.  Yes it could, but the isoclinic point provides a more accurate and reliable measure.  Moreover, one does not require the isoclinic point to be a "dip" in the excited state hyperfine spectra (i.e., low enough pressures so that the excited state hyperfine splitting is resolved).  Even if the excited state hyperfine splitting is not resolved, the unresolved resonances will have a combined peak that is temperature independent (hence an isoclinic point), since the ground-to-excited state matrix elements for the two resonances are still equal.  We now write near line 158,

We employ the isoclinic point for a measurement of the shift, since it is less susceptible to the errors that occur when attempting to extract a center-of-gravity shift from a 10 GHz alkali first-resonance Voigt spectrum.