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In a recent report on experiments with a sample of ultracold ${\rm {}^{87} Sr}$ atoms, T. Bothwell et al. (physics.atom-ph:2109.12238), the abstract ends and culminates in the following punchline:

"This heralds a new regime of clock operation necessitating intra-sample corrections for gravitational perturbations."

(Unfortunately, the suggested "corrections" are not further specified, or even only mentioned, anywhere in the article; and I haven't had the opportunity to check the extensive list of references for clues. Has some particular method of "correcting atomic clocks for gravitational perturbations" been explicitly described elsewhere already ?)

However, I also have a general question on the purpose of applying a "correction"; or in other words, on deciding whether (and in how far) certain evaluations constitute "a correction" to a given clock:

Considering that it has been argued, for instance here, that "a clock is supposed to measure the arclength of its path through spacetime", is likewise (or perhaps even more strictly) a corrected clock supposed to measure (ratios of) arc lengths of its path segments more correctly than an uncorrected clock (on the same spacetime path) ?

user12262
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The measurements shown in this paper are made by shining a tightly focused laser beam onto a cloud of Sr atoms, where the cloud has a vertical size of about 1 mm. This allows comparing the frequency of the clock transition between different parts of the cloud. Figure 3 shows a plot of the measured frequency shift over the vertical extent of the atom sample. From this, it can be seen that after subtracting all known errors from effects other than gravity, a finite slope remains: the clock frequency depends on position. Hence, measuring the average clock frequency in the entire atomic cloud (for example, to get better signal-to-noise ratio) would yield a transition shape broadened by the gradient of the gravitational field.

Simply said: the clock's size is finite, therefore its top follows a different path through spacetime than its bottom. You could fix this by:

  • Making the the clock smaller. This will be difficult at some point, because using fewer atoms or higher atomic densities will cause other errors to grow.
  • Moving the clock into weaker gravitational fields. Probably there are already people working on this, but bringing an atomic lattice clock so far away from earth is certainly expensive.
  • Calculating the expected differential shift and compensate it in data processing. This latter method seems to be what the abstract is pointing to.
Roman
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  • Roman: "the clock's size is finite, therefore its top follows a different path through spacetime than its bottom." Right, but: Does this fact by itself in need of correction ?? In other words: In the OP I've asked a specific "Yes-or-No"-question, and I'm missing a specific "Yes-or-No"-answer in your response (apart from elaborations). "Figure 3 shows [...] a finite slope remains [...] compensate it in data processing" -- What's the correct way of "compensating slope" (if at all) ? – user12262 Nov 02 '21 at 21:09
  • Which "yes-or-no question" are you referring to? Including the title, I can see three questions, none of them strictly "yes-or-no". Concerning the question in the comment: You would model the distribution of atom number density versus gravitational shift. Then you deconvolve the measured frequency response with this distribution, resulting in a narrower peak. – Roman Nov 02 '21 at 21:41
  • Roman: "Which "yes-or-no question" are you referring to?" -- "[Is] a corrected clock supposed to measure (ratios of) arc lengths of its path segments more correctly than an uncorrected clock (on the same spacetime path) ?". "Concerning the question in the comment: You would model the distribution of atom number density versus gravitational shift. Then you deconvolve the measured frequency response with this distribution, resulting in a narrower peak." -- Does this procedure correctly fix the mean value of the resulting narrower peak ? – user12262 Nov 02 '21 at 22:13
  • I'm still having a hard time understanding what you're after. Could you give an example of a way in which the procedure I've described might fail to correctly fix the mean value? – Roman Nov 06 '21 at 09:09
  • Roman: "Could you give an example of a way in which the procedure I've described might fail to correctly fix the mean value?" -- In order to construct a concrete example it'd certainly be helpful and even necessary for you to describe your suggested procedure more explicitly; and we'd have to review exactly how Fig. 3 of https://arxiv.org/abs/2109.12238 was obtained. There appear values $z~{\rm [mm]}$, for instance ... Also, I'm worried whether and how the geometry of the connection (red line on bottom of Fig. 1a) between "optical lattice" and "Si cavity" might enter ... – user12262 Nov 06 '21 at 09:56
  • I've edited my answer to hopefully make more clear what Figure 3 shows. I'm not aware of any effect of the geometry of the path of the light between the atoms and the cavity. The only thing that matters is the relative position of the cavity and the atom sample in the gravitational field. Wich path the light takes in between is irrelevant as far as I know. – Roman Nov 06 '21 at 11:07
  • Roman: "The only thing that matters is the relative position of the cavity and the atom sample in the gravitational field." -- Right!, that's what I thought, too. So: Explicitly how would this matter in the "correction procedure" you're proposing ?? And: Is it even documented (with "mm accuracy") ?? "Which path the light takes in between is irrelevant as far as I know." -- Even a couple of cm/s difference in speed (wrt. a suitable non-rotating reference system) might be relevant as well ... – user12262 Nov 07 '21 at 23:55