Recently, a research team composed of Pan Jianwei, Chen Yuao, Dai Hanning, etc., from the Institute of Quantum Information and Quantum Technology Innovation of the Chinese Academy of Sciences at the University of Science and Technology of China, has successfully developed a strontium atomic optical lattice clock with stability and uncertainty better than 5E-18 in 10,000 seconds, which has become the optical clock system with the best indicators in China. The results were published in the international academic journal Metrologia on January 12. This work is about how we define time in the future, and even compare time on a larger spatial scale, its important value and significance, and listen to Mo Xiaomeow slowly.
From microwave to optics,
It is people's pursuit of higher time accuracy
The unit of "time" is one of the seven basic units, and its position is extremely important, so people have always demanded more precision than other basic units. The accuracy standard of time has important applications in many fields, and if we count from the realization of the cesium beam atomic clock in 1955, the unremitting pursuit of it has lasted for more than half a century.
Based on Rabbin's vision, the cesium beam atomic clock became the first atomic clock to be realized, and it has developed rapidly. Now we define "second" as the duration of the two ultrafine energy levels of the ground state of the 133Cs atom at sea level for 9192631770 cycles corresponding to the transition radiation in the zero magnetic field. However, its transition frequency is in the microwave band, and after the relative uncertainty has reached about 1×10-16, it is difficult to increase it again.
If scientists want to reduce uncertainty, they need to look for higher transition frequencies. The transition frequency of optical atomic clocks is above 1014Hz, which is more than 4 orders of magnitude for microwave clocks, and has great development potential.
As early as 1973, it was proposed to adopt an optical frequency standard, but due to technical limitations, it failed to fully meet the requirements of the scheme. With the development of technologies such as cooling atoms or ions and high-precision detection of optical frequencies, around 2000, optical clocks officially ushered in an era of vigorous development.
离子VS Atom
The optical atomic clocks we mentioned mainly include ion optical atomic clocks and optical lattice atomic clocks.
As early as 2019, the system uncertainty of the 27Al+ optical clock developed by NIST has reached 9.4×10-19. However, in the quantum world, it is inevitable that atoms or ions will randomly collapse into other ground states or excited states, which will introduce quantum projection noise. The stability of single-ion optical clocks is limited by quantum projection noise, and it is difficult to improve it after reaching the order of 10-15τ-0.5 (τ is the integral measurement time). Of course, there are also proposals for excessive ionic optical atomic clocks, but the question of how to eliminate the effects of ion-to-ion interactions and how the potential wells of trapped ions affect the transition frequencies remains to be studied.
Comparatively speaking, optical lattice atomic clocks based on neutral atoms can contain a large number of neutral atoms, and the quantum projection noise is greatly compressed, and the stability is better.
Thus, H. Professor Katori, Professor Ye Jun of the Joint Laboratory for Astronomical Physics (JILA) and other research teams have focused their efforts on optical lattice atomic clocks. In 2002, Professor H. Katori proposed the realization of a high-performance optical lattice atomic clock at the 6th Symposium on Frequency Standards and Metrology, and in 2005, he realized the 87Sr optical lattice atomic clock for the first time. IMMEDIATELY AFTERWARDS, ONLY A YEAR LATER, THE YE JUN GROUP OF THE AMERICAN JOINT ASTROPHYSICAL LABORATORY (JILA) AND THE EXPERIMENTAL GROUP OF THE PARIS OBSERVATORY (LNE-SYRT) IN FRANCE SUCCESSIVELY REALIZED THE 87Sr OPTICAL LATTICE ATOMIC CLOCK, AND THE RESULTS OF THE TWO CORROBORATED EACH OTHER. Professor Katori has made improvements to his optical lattice atomic clock.
▲ In September 2023, in the "Mozi Salon" event, Jun Ye (Jun Ye) brought a wonderful popular science report as a guest.
In a short period of time, research institutes such as the Joint Laboratory for Astronomical Physics (JILA), the National Bureau of Standards (NIST) and the Paris Observatory (LNE-SYRTE) have appeared one after another, and breakthroughs have been made in related technologies, and the competition is in full swing. Among them, the Chinese-American scientist Ye Jun is a leader in this field, and for more than ten years, his 87Sr optical clock, stability and accuracy have always been at the forefront of the world. According to the published papers, the uncertainty of his team's 87Sr optical lattice atomic clock system has also reached 2×10-18 or even lower, and the stability has reached 4.8×10-17τ-0.5.
So, what does the uncertainty and stability of the optical clock mean, and how complex is it to optimize them?
Difficult and difficult light clock
The working principle of an optical clock does not sound complicated. Strontium metal is heated up in the "furnace" and converted into gaseous atoms, and scientists "grab" these atoms at a temperature of several hundred degrees Celsius for laser cooling, and when the temperature is reduced by nine orders of magnitude, to about micro-opening, the cold atoms can be "loaded" into the optical lattice and start working. In practice, it is much more complicated, scientists first have to prepare the atomic state - for example, use the pumping method to make the atoms basically at a certain required energy level, and then use the "bell laser" to excite the atoms to make them jump. It is conceivable that the more consistent the laser and the transition frequency, the greater the probability of the transition, and the more the laser frequency deviates from the transition frequency, the less likely it is to jump. Therefore, scientists also need to build a frequency servo feedback system, which can adjust the frequency of the laser to achieve the maximum resonance with the atom transition - that is, to reach the highest point of the transition peak on the spectrum, so as to obtain a stable system and make the optical atomic clock enter the closed-loop operation. And this laser frequency is exactly the output frequency of the optical clock that scientists need to probe for. Of course, the optical frequency comb is then used to convert the optical frequency down-conversion to the wavelength band required for our usual application.
From the above process, we have a general understanding of the two important metrics that determine the quality of optical clocks: stability and uncertainty.
Stability describes the jitter of the output frequency on the time axis, while uncertainty describes the accuracy of the frequency shift correction when the clock transition frequency changes.
If we use the metaphor of the two indicators of the optical clock, uncertainty refers to the accuracy of measuring the distance between the obtained result and the real bull's-eye, while stability describes the concentration of the results of multiple "targeting".
Among them, the stability indicator is a bit complicated. As we mentioned earlier, stability describes the jitter of the output frequency, and if we describe the jitter in the time domain using certain noise analysis methods, we will find that, in general, the stability is proportional to the -0.5 power of time τ, which is why stability is sometimes expressed by multiplying the constant by τ-0.5. But for each specific experiment, we actually need to consider the ability to stabilize in a short time (e.g., 1 second) and stability for a long time (e.g., 10,000 seconds). The short-term stability demonstrates the fast measurement capability of the optical clock system, and the long-term stability represents the measurement accuracy limit of the optical clock system. In some experiments, the ability to stabilize for a long time is relatively lacking, while the shortcoming of some systems (such as ion clocks) lies in the stability of a short time (such as 1 second).
In experiments, the factor that has the greatest impact on stability is Dick noise. The root cause of Dick noise is that the noise of the bell laser is not fully sampled. The ideal bell laser is a sharp, clean spectral line, but the actual clock laser will inevitably have jitter and noise. If we can sample the entire cycle, we can make the mean value of the white noise tend to zero, and then correct the laser frequency through the servo. However, there are some "dead times" in the clock cycle, (such as when preparing atomic states), and the laser is not sampled in the dead time, and the servo system cannot be effectively corrected, and the stability will deteriorate.
In order to reduce the influence of Dick noise, it is necessary to reduce the noise of the clock laser as much as possible, which requires technology to avoid the jitter and noise of the clock laser, so that its transition line frequency is stable and the noise is small. Therefore, scientists need to increase the proportion of the clock detection time in the whole clock cycle, that is, reduce the preparation time of the atom, increase the action time of the bell laser and the atom, and even further design a dead-time sampling scheme, for example, two quantum reference systems can be used, through which the frequency noise of the same clock laser can be sampled alternately, so that the sampling covers the entire clock cycle.
In addition, quantum projection noise will also have a certain impact on the neutral atomic optical clock, scientists deal with it by increasing the number of atoms, and other technical noises, such as the electronic noise of the electronic system, the photon shot noise of the photoelectric detection device, the change of environmental factors such as magnetic field, electric field, light field jitter, temperature, vacuum degree, etc., will also affect the stability. In addition, the linear drift rate of the superstable cavity needs to be well compensated for by the grounding of the main cavity.
Solving the stability problem, let's look at the uncertainty side. We know that there are many factors that can cause the transition frequency of an atomic system to change, and in order to ensure that different clocks output the same result at different times and places, this frequency shift must be evaluated and corrected at all times. The accuracy of evaluation and correction is the system uncertainty of the optical clock. The smaller the uncertainty, the more "accurate" the optical clock.
There are many factors that affect the uncertainty of the system, the most significant of which is the blackbody radiation frequency shift. The blackbody radiation photons are diffused around the atoms, and if the frequency of the blackbody radiation is close to the transition frequency of the atoms of the system, it will shift the clock transition frequency. Its effects are related to the difference in polarizability between the upper and lower energy levels of the atomic clock transition and the uncertainty of the ambient temperature. The uncertainty of the polarizability difference is difficult to optimize, so the main purpose of accurately measuring the blackbody radiation shift is to accurately measure the temperature near the atom and control the temperature field to make it evenly distributed.
In addition, the Stark shift and density shift of lattice optical AC are also two factors that have a great impact on the uncertainty of the system.
The lattice light AC Stark shift is caused by the standing wave field formed by the lattice light. Although the Doppler and photon recoil shifts are solved, the existence of lattice potential wells will cause the energy levels of the ground state and excited states corresponding to the bell transition to shift, resulting in the frequency shift of the bell transition, which is the optical lattice AC Stark shift (optical lattice AC Stark shift). H. Katori discovered the magic wavelength, and the scientists placed the optical lattice near the so-called magic frequency, so that the difference in polarizability between the ground state and the excited state was almost zero, so that the magnitude of the AC Stark shift depended on the accuracy of the "magic wavelength" measurement.
▲ In September 2023, at the 2023 International Conference on Emerging Quantum Technologies in Hefei, Katori, as the winner of the "Micius Quantum Prize", delivered a wonderful on-site award-winning report.
However, with the deepening of research, the uncertainty of the optical clock is getting smaller and smaller, and at this time, the influence of the higher-order Stark shift can not be ignored, and the higher-order Stark shift, which is related to the atomic thermal distribution in the crystal lattice, the electric quadrupole/magnetic dipole transition and the superpolarizability, cannot find a "magic wavelength". For example, Katori's group uses a microscopic model to calculate the optical frequency shift under the given radial temperature and axial mode layout, and some studies have pointed out that the frequency and well depth of the lattice can be appropriately selected to cancel out the first-order term and the higher-order term. Therefore, the accuracy of this means may become a new limiting factor for the AC Stark frequency shift.
Density frequency shift, also known as cold collision frequency shift, is caused by various interactions between atoms in the lattice point in the process of approaching or colliding, and the more atoms in the same lattice point, the greater the density frequency shift. For 3D optical lattice clocks, we can find ways to "blow away" the excess atoms in the same lattice point, and in the case of 1D optical lattice clocks, scientists also have a set of methods to control and evaluate the impact of such collisions. The more accurate the evaluation, the less uncertainty there is due to density frequency shifts.
Of course, there are many other factors that affect the uncertainty of the system, such as the DC Stark effect due to electrostatic fields, the Zeeman effect due to magnetic fields, etc., which need to be evaluated and sought to be as accurate as possible.
There are a number of other factors that affect uncertainty, some of which can be measured more accurately or can be estimated by theoretical models, but the frequency shifts they bring are so much lower than these factors that they are negligible.
The Chinese team is at the forefront of the world
In this report, the Chinese team also uses the 87Sr atomic system. The team also addressed the factors that we mentioned earlier that affect stability and uncertainty.
Using the high-beam integrated strontium atomic source designed and built by the team, the vacuum integration design scheme of atomic furnace, Zeeman reducer, transverse cooling module and atomic deflector is adopted, and after generating high-beam hot strontium atomic gas, it is shot at a deflection angle of 20 degrees after being cooled laterally by Zeeman reducer. The reason for this design is to ensure that the "heat" of the furnace does not affect the "cold" in the main chamber. The strontium atomic source produces a beam of cold 87Sr atoms up to 2×108 atoms per second. When our atoms are loaded into a one-dimensional optical lattice and ready to work, the second-order deflection on the source side of the atom can be quickly turned off to ensure that atoms that are not bound by the lattice do not come in and "mess around". In addition, the coordination of the differential division can effectively ensure the ultra-high vacuum of the main cavity and achieve the atomic life of the lattice of 20s, and also solve the problem of blackbody radiation frequency shift caused by the atomic furnace. The results of this atomic source were published in Review of Scientific Instruments in 2023.
On the one hand, the PDH frequency stabilization technology is used to quickly lock the laser frequency to the high-precision and high-stability F-P optical reference cavity, so as to output ultra-narrow linewidth, On the other hand, by suppressing the magnetic field noise in the main cavity and precisely compensating the background magnetic field, the clock pulse is extended to 1.4s, and the subhertz atomic transition spectral line is obtained, which further reduces the dead time, and at the same time, according to the frequency noise peak of the unique environment where the experiment is located, the preparation time of the atom and the action time of the clock laser and the atom are appropriately selected, which weakens the influence of the noise peak and suppresses the Dick effect to 4.5×10-16τ-0.5.
In addition, for the three factors with the greatest uncertainty, namely blackbody radiation, cold collision, and optical lattice AC Stark effect, scientists have established a good evaluation model: for blackbody radiation, the team adopts a similar method as JILA to accurately control the temperature of the main cavity, establish a stable and uniform thermal environment, and combined with the thermal radiation model, it can well monitor and evaluate the blackbody radiation frequency shift, and the blackbody radiation frequency shift uncertainty is assessed to 3.2 ×10−18;For cold collisions, the density frequency shift coefficient is calibrated at different well depths, and the uncertainty of the density frequency shift is evaluated to 1.2×10−18; for the optical lattice AC Stark effect, continental scientists, like NIST laboratory and JILA laboratory, calibrated the optical lattice frequency shift at different lattice frequencies and well depths based on the thermal model method, and evaluated its uncertainty to 2.2×10−18.
In addition, factors such as Zeeman shift, DC Stark shift, background gas collision shift, and servo error shift are also well analyzed and evaluated.
So, how do you verify that the overall performance of this atomic clock is excellent?
The main ways to measure stability are self-comparison, In view of the Dick effect brought by the clock laser, the team adopted a self-comparison method, so that the frequency of the clock laser is alternately locked to the resonance frequency of the bell transition to form two clock rings running alternately in the time domain, and the frequency difference jitter of the two clock rings can reflect the stability, and for the stability of the system as a whole, the team adopts the method of asynchronous comparison of the two clocks, that is, assuming that the stability of the two optical clocks is consistent and independent of each other, so that the two clocks run in two places, and the frequency comparison stability of the two clocks is divided by √2, and the stability of the single clock is obtained。 According to the evaluation, the overall stability of a single set of optical clocks reached 4×10-18 in 10,000 seconds and 2.1×10-18 in 47,000 seconds. The overall reached 5.4×10-16τ-0.5.
As for the uncertainty of the system, the team also evaluated all the influencing factors one by one, and calculated the overall uncertainty of 4.4×10-18 according to the error transfer method, which is equivalent to a deviation of only one second in 7.2 billion years, of which the most influential blackbody radiation frequency shift uncertainty is 3.2×10-18.
Compared with the data given by the world's major optical clock research institutions, our optical clock, the comprehensive index of accuracy and uncertainty is second only to the United States, ranking among the top in the world.
▲Indicators of the world's major optical clock research institutions (among them, the stability given by RIKEN in Japan is synchronous comparison data, which does not reflect the impact of the DICK effect; other institutions are asynchronous comparison data, reflecting the overall stability of optical clocks)
how to define time,
The Chinese fought for a place
At present, the pursuit of the accuracy and stability of atomic clocks, the world's competition can be said to be in full swing, on the one hand, the performance of optical clocks is developing rapidly, on the other hand, the accuracy and stability are also facing some bottlenecks. Related laser technology, optical lattice technology, photoelectric control technology, etc., all aspects have difficulties that need to be overcome.
In terms of application, the most direct and important application of optical atomic clocks is, of course, to provide time-frequency references. Our current definition of "seconds" in atomic time is derived from the resolution of the 26th International Conference on Weights and Measures in 2018 - 133Cs fountain clock. It is foreseeable that when the optical clock is stable and mature enough, we will redefine the "second", and the accuracy of the atomic time will be improved by an order of magnitude. And the current efforts of Chinese scientists are to prepare for a rainy day and gain an important say in the definition of "seconds" in the future. In addition, the importance of optical clocks in scientific research and practicability is also worth paying attention to, and based on the ultra-high frequency measurement accuracy of optical clocks, we can accurately measure those physical quantities that can cause the frequency change of clock transitions. For example, the frequency of an optical clock varies at different heights, which can help us accurately depict the situation of the earth, and for example, a change in the frequency of an atomic clock transition at different times may mean that the fine structure constant is changing, and the fine structure constant is related to the interaction between light and atoms, which means a new physics.
What's even more exciting is that as people's ability to "move" optical atomic clocks becomes stronger and stronger, countries have invariably proposed plans for space science + optical atomic clocks. Combined with high-precision time-frequency transmission technology, a more stable and accurate space-time-frequency system can be established, which not only has great strategic value in the global navigation system, but also is a powerful tool for verifying basic scientific problems such as relativity, gravitational waves, and the search for dark matter. For mainland scientists, the deployment of optical clock research in space has also begun, and as the continent's capabilities in this field gradually match Europe and catch up with the United States, we can expect an experimental satellite like "Mozi" in the future, which will carry a high-performance optical clock developed by the Chinese themselves for the first time to explore the secrets of cosmic time and space.
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