Recently, Ye Jun's team at the University of Colorado United States successfully measured the thorium-229 nuclear transition frequency, which is expected to bring ultra-precision nuclear clocks into a new era.
Written by | Li Huadong
Perhaps, apart from physicists, no one is so obsessed with defining "one second".
On September 4, 2024, the journal Nature published a cover paper titled "The nuclear transition of the thorium−229m isomer to the frequency ratio of the strontium−87 atomic clock".
On the same day, a review article was published on the official website of Science magazine, saying that the achievement "is expected to bring ultra-precision nuclear clocks into a breakthrough in a new era." Some netizens claimed that the author of this paper, United States Ye Jun's team at the University of Colorado, is expected to win the Nobel Prize in Physics in the future.
So, what kind of research can make the two top journals of Nature and Science recommend together? What difference does this "nuclear clock" make to the definition of "one second"?
Defining "one second": 1/86,400 of a day?
In the eyes of the public, "one second" is the time when the second hand on the clock passes through the "one square". It walked 60 blocks, and a minute passed; After 3600 squares, an hour passed; After 86,400 squares, a day has passed......
Everything seems so natural, because that's how the Earth rotates and revolves. When the day passes, the sun will be in the same place again – 86,400 seconds is that long.
Since the Earth is orbiting the Sun, the place A where the Sun is directly shining on that day, after the Earth has made one rotation (23:56, a sidereal day), it has to wait for the Earth to turn at a certain angle (4 minutes) before it can be directly exposed to the Sun again, which takes a total of 24 hours (a solar day). 丨Image source: Renaissance Universal
The problem is that changes in the Earth's rotation and orbital cycle, although small, do occur due to factors such as tidal action, changes in the mass of the Sun, and the gravitational pull of other celestial bodies.
People rely on "days" to define "how long is a second", and it doesn't always seem that long.
Thus, in the 20th century, physicists moved from macroscopic to microscopic, from classical physics to the quantum world, and found that there was a super "clock" in nature, which was far more stable than the motion of celestial bodies.
It defines one second as 9 192 631 770 times the period of the electromagnetic wave radiated during the transition between the two hyperfine energy levels of the ground state of the cesium−133 atom. Although this may be difficult for ordinary people to understand, it has become a powerful tool for physicists to study the properties of space-time.
After all, who wouldn't want to be able to measure the gravitational redshift caused by the Earth within easy reach?
Reading Tip: Gravitational redshift
Gravitational redshift refers to the phenomenon that due to the existence of the gravitational field, the frequency of light or other electromagnetic radiation emitted from the gravitational field decreases when it is far away from the gravitational field, and the wavelength becomes longer, thus moving towards the red end of the spectrum, which is one of the phenomena predicted by Einstein's general theory of relativity. If the gravitational redshift can be observed, it is a powerful verification of the general theory of relativity.
And because the Earth's gravitational field is relatively weak, the redshift effect is very small at hand. Under laboratory conditions, it is difficult to detect such small changes even with very precise instruments. Therefore, this is also a problem that many scientists are trying to solve.
Atomic clocks and light clocks are more accurate! But...... Is it the most precise?
2022年2月17日，《自然》杂志封面论文《Resolving the gravitational redshift across a millimetre-scale atomic sample》表示，即便高度只相差1毫米，时间流逝的不同也能被测量出来。
The authors of the paper, Ye Jun's team at the University of Colorado, measured the transition frequencies of a 1-millimeter-thick strontium-87 cluster (about 100,000 atoms) and found that there was a difference of about 1 in 100 billion between the top and bottom atoms.
This means that after 300 billion years, the atom in the uppermost layer will experience one second more time than the lowest atom. This is the first time that the gravitational redshift effect predicted by the general theory of relativity has been verified on the millimeter scale.
The higher the position of the atom, the more obvious the gravitational redshift effect will be, and the longer it will elapse. 丨Image source: Wikipedia
The premise of all this is that the definition of a unit of time (i.e., "one second") is precise enough that we can discern the slightest difference in time.
As mentioned earlier, 9 192 631 770 times the period of electromagnetic waves (microwaves) radiated by the transition between the two ultrafine energy levels of the ground state of the cesium-133 atom is "one second", and the transition frequency of cesium-133 can also be defined by the strontium-87 used by Ye Jun's team:
The time of 429 228 004 229 873.4 times the period of electromagnetic waves (visible light) radiated by the strontium−87 atom during the transition between the 5s2 1S0 and 5s5p 3P0 energy levels is "one second".
This may seem complicated, but there is no need to dwell too much, just know that the electrons in an atom will release electromagnetic waves when they transition between different energy levels, and the frequency of electromagnetic waves is only related to the energy level of the transition to the initial and final states, because it is extremely stable, so it has become the first choice for physicists to keep time.
When electrons transition in front of different energy levels, they release electromagnetic waves of a certain frequency (energy). 丨Image source: Wikipedia
When the electromagnetic waves emitted by the atoms used in the timing device during the transition are in the microwave band, it is an atomic clock. When the electromagnetic wave emitted by the transition is in the visible light band, it is called the optical clock.
Theoretically, optical clocks are more accurate than atomic clocks because they emit electromagnetic waves with higher frequencies and narrower line widths.
High frequency means that more cycles can be measured per unit of time, which can be used to determine the time of a single cycle more accurately; Narrow linewidths mean less uncertainty at the frequency, which further improves the accuracy of the defined time.
周期（Period）、频率（Frequency）、线宽（Bandwidth）的示意
In this way, even if the clock is on the same quantum scale, there are different performances, not to mention that external factors such as magnetic fields, temperature, and vibration will amplify this difference.
So, is there a more stable, less sensitive tool that can define "one second" more precisely?
Yes! That's the nuclear clock.
What is the principle of a nuclear clock?
As early as 1996, Russia physicist Eugene V. Taklya proposed the idea of "nuclear excitation" as a highly stable light source for timing.
The so-called "nuclear excitation" is similar to the process by which electrons outside the nucleus jump to a higher energy level after absorbing energy, leaving the atom in an excited state. It is also possible that the nucleus itself is in a state of higher energy after absorbing a specific amount of energy.
Extranuclear electron stimulation transition process丨Image source: University of Rochester
Similarly, the nucleus of an atom will also emit electromagnetic waves of a certain energy during the excited transition.
Since the stimulated radiation of atoms can be used as atomic clocks and optical clocks, why can't the stimulated radiation of atomic nuclei be used as "nuclear clocks"?
Based on this idea, scientists studied the feasibility of a nuclear clock. Slowly, they discovered that, unlike the cesium-133 and strontium-87 commonly used in atomic and optical clocks, only thorium-229 nuclei were currently feasible for nuclear clocks.
Because the transition energy of other nuclei between different energy levels is too high, the frequency of the electromagnetic waves radiated is too high to be measured for timekeeping.
The "thorium-229m isomer" mentioned at the beginning of this paper and in the paper of Ye Jun's team is an excited state of the thorium-229 nucleus, and the energy level difference between it and the ground state is about 8.3557 eV, and the corresponding electromagnetic wave radiated is in the ultraviolet band.
钍−229原子核的最低能级差丨图片来源：Physics
This is more frequent than radiated electromagnetic waves within atomic clocks and optical clocks, but fortunately within the range that can be measured by the instrument. Therefore, theoretically, if you use it for timekeeping, you can achieve higher accuracy.
In addition, compared with the electrons outside the nucleus in the atom, the nucleus itself is less disturbed by external factors such as magnetic field and thermal radiation, which is like a person holding an umbrella on a stormy day, when a gust of wind blows (external disturbance), the degree of shaking of the umbrella (electron) must be greater than that of a person (atomic nucleus).
Atomic clocks experience timing errors (frequency changes) when they are subjected to thermal radiation (red beams). (Image source: National Metrology Institute of Germany)
As a result, nuclear clocks are less demanding and more stable than atomic and optical clocks (placed in a vacuum and at ultra-low temperatures near absolute zero).
At this point, we already know the important value of nuclear clocks in the field of precision measurement. So, just how strong is it?
Theoretically, it can achieve an accuracy of 10-19, which is about 10 times more accurate than the best optical clocks available.
What is the concept? 300 billion years is not a second!
Is the nuclear bell finally coming?
In the experiments of Ye Jun's team, thorium-229 was doped into a single crystal of calcium fluoride (CaF2) at a doping concentration of 5×1018/cm3, which means that each cubic centimeter of crystal contains 50 billion thorium-229 atoms.
To excite the thorium−229 atoms, they irradiated the crystal with a vacuum ultraviolet laser (VUV laser), and when there was a fluorescence flicker in it, it meant that the excitation was successful, that is, the thorium−229m state was entered.
Filters (filtering the background light) and photomultiplier tubes are then used to collect the fluorescent photons emitted and measure their frequencies.
Schematic diagram and actual shot of the experimental device丨Image source: Ye Jun's team paper
The entire experiment was controlled at 151 K, or about -122 °C. Obviously, this is much easier to operate than the absolute zero required for atomic and optical clocks, which is about -273°C.
Finally, Ye's team measured the radiation frequency of the thorium-229 nuclear transition—2 020 407 384 335(2) kHz, which is about 4.7 compared to the radiation frequency of the strontium-87 atomic transition.
This means that if the atomic transition frequency of cesium-133 is still used as the benchmark, but the nuclear transition frequency of thorium-229 is defined as one second, then there are:
2 020 407 384 335 000 times the period of the electromagnetic wave (ultraviolet light) radiated by the thorium−229 nucleus during the transition between the thorium−229m and thorium−229 ground states is one second!
Of course, there are still a lot of errors in this result and cannot be used in the official definition. But even so, compared with the past, Ye Jun's team has also improved the accuracy of the nuclear clock by about 6 orders of magnitude, reaching the level of 10-12.
Therefore, although we have not yet reached the end predicted by the theory - as Science magazine said, the results of Ye Jun's team are expected to bring ultra-precision nuclear clocks into a new era, which is "promising", not "already", and whether he can be favored by the Nobel Prize in the future, this is still a big leap forward in the research results!
End
Our home clocks, even if they have an error of 1 second in two days, are completely sufficient; The rubidium atomic clock on the Beidou satellite, with an error of 1 second in 3 million years, is also accurate enough.
For the average person, whether it's a nuclear clock, an optical clock, or an atomic clock, there really isn't any difference between them. Until the earth dies and the galaxy collapses, this "watch" is not short of the goal of "one second", and it seems that it is not important at all in life.
Indeed, from a utilitarian point of view, it is difficult to explain the practical significance of pursuing higher precision timekeeping.
It's like answering the question "What's the point of verifying gravitational redshift on a scale of 1 millimeter?" "What's the point of using the frequency stability of the [future] nuclear clock to find dark matter particles?" A truth.
I don't want to give an answer like "waiting for future applications". Because in my opinion, the greatest significance of studying them, or the study of the basic facts in mathematics and physics, is for the sake of us human beings, for the "evolution" of our cognition.
bibliography
[1]https://www.nature.com/articles/s41586-024-07839-6
[2]https://www.science.org/content/article/breakthrough-promises-new-era-ultraprecise-nuclear-clocks
[3]https://www.nature.com/articles/s41586-021-04349-7
[4]https://en.wikipedia.org/wiki/Atomic_clock#Accuracy
[5]https://en.wikipedia.org/wiki/Nuclear_clock
[6]https://arxiv.org/pdf/2109.12238
[7]https://www.zhihu.com/question/666654065
[8]https://arxiv.org/abs/2407.15924
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