by Zhang Zhiqiang, Kyle J. Arnold, Rattakorn Kaewuam et al.
Applied Phyics
Science Advances | 3 May 2023 | Vol 9, Issue 18
Discussion
In summary, we have used correlation spectroscopy to compare two 176Lu+ atomic references with an inaccuracy at the low 10−18 level. This has provided a high accuracy assessment of the quadratic Zeeman shift, which is the leading systematic for the 176Lu+ 1S0 ↔ 3D1 clock transition. Hyper-Ramsey spectroscopy is also compatible with HARS and practically eliminates the probe-induced ac-Stark shift as the next leading systematic. This then provides a frequency reference with systematics that are easily controlled to an inaccuracy below 10−18 without the technical challenges faced by other systems.
An accuracy claim for an individual system would require an assessment of the BBR shift. Presumably, the use of simulations and thermal cameras (2, 15) could equally be used here, although it is unclear how to quantify such an assessment for our system. A crude analysis as given in Materials and Methods would bind the temperature to 35(10)βC, which, due to the low BBR shift for the 1S0 ↔ 3D1 transition, corresponds to a BBR shift of just −1.56(27) × 10−18 and gives a total uncertainty for both systems of <8 × 10−19. However, although it is done elsewhere (2, 37), we refrain from making any accuracy claims without a same-species comparison to the appropriate level. Here, stability limits us to the low 10−18, which is primarily limited by a heating problem in Lu-1.
With the lower heating rate and real-time monitoring of EMM, systematics at the mid-10−19 are readily achievable. Correlation spectroscopy with a 10-s interrogation time was demonstrated in our previous work (38), albeit within the same trap. In separate chambers, uncorrelated magnetic field noise may be a limiting factor. However, at the operating field of 0.1 mT, the maximum magnetic sensitivity of the 848-nm clock states is ⁓0.4 Hz/μT. This is two orders of magnitude smaller than Al+, for example, for which lifetime-limited correlation spectroscopy has been claimed (30). Increasing the interrogation time to an anticipated 10 s would make comparisons below 10−18 achievable on the time scale of a few days.
The relative ease at which a comparison at this level can be achieved with this system should not be underrated. Comparisons between clock systems claiming this level of accuracy (39, 40) have variations of the measured ratios that cannot be explained by the error budgets of the individual systems, which is compelling evidence that large systematic shifts are not being controlled to the levels claimed. Such problems are unlikely to occur for systems such as lutetium or thullium (41) for the simple fact that systematics are not large enough to cause such variations. The total shift and any single contribution given in Table 2 is, at most, at the level of the current measurement precision. Moreover, it is self-evident that systems having such low systematics have substantial room for improvement if current state-of-the-art technologies were used to take advantage of this potential. This is particularly noteworthy for lutetium as the magnetic field sensitivity of the clock states is the lowest of any atomic system that we are aware of and the lifetime is practically indefinite. Consequently, interrogation times will not be limited by lutetium in any foreseeable future.
Analysing 'Discussion'
Consider these moves when analysing 'Discussion':
Restate the researchg question, hypothesis or objective.
Summarise the central results.
Make a tentative interpretation.
Link these findings ro other available resarch.
Reflect on the limitations of the present study.
State the broader social, political, ethical, medical, etc. implications of these findings.
Suggest further (follow-up) research which is now necessary.
Based on Macgilchrist 2014
Examples of opening lines in Discussion sections:
The main results of our (survey, etc.) ....
In the research reported here, we investigated how ...
Previous studies have shown that ...
We suggested that ... may affet ...
Based on Macgilchrist 2014
Miscellaneous: Academic style
Depending on the discipline, genre, audience, and purpose, academic texts can range from formal to quite informal in style. Certain disciplines, particularly law, are associated with a higher level of formality. In most disciplines however, academic texts are neither very formal nor very informal. In fact, in some more popular academic textbooks, the style can be slightly more informal, less 'academic', or more literary.
(A) Formal style: «Notwithstanding these benefits, these research ...»
(B) Informal style: «Despite this development of tags, it is doubtfull ...»
Source: de Chazal 2014
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