The nucleus of the thorium-229 isotope has a special property: it has an excited state that’s incredibly close in energy to its ground state. The existence of such an isomer is remarkable because when nuclei normally get excited, they need enormous amounts of energy — hundreds of thousands or even millions of electron volts (eV). But the Th-229 nucleus’s excited state is only about 8.4 eV above its ground state. This is really small by nuclear standards and, importantly, it means light can excite the nucleus into this energy level.
This in turn matters because scientists have developed very precise atomic clocks over the last few decades that work by using lasers to excite electrons in atoms and measure the frequency of the light required to do this. These clocks are so accurate that they’re used for GPS, keeping time on the internet, and in fundamental physics experiments. But they also have a limitation: electrons are relatively easy to disturb, so a stray external electric or magnetic field can shift their energy levels slightly but enough to make the entire clock less stable.
Nuclei on the other hand are much smaller and are buried deep inside the atom, shielded by the electron cloud from the world beyond. So a nuclear clock based on a nuclear transition would potentially be much more stable and accurate than even the best atomic clocks.
The Th-229 isomer is the only nuclear transition that’s low enough in energy for scientists to realistically build a laser to make happen. In fact they have been trying to make a nuclear clock based on this transition for years now. Recently, two research groups finally managed to create this transition using lasers and they determined that the wavelength of light needed is 148.4 nm. This is in the vacuum ultraviolet range — i.e. ultraviolet light with a very short wavelength. Such light gets absorbed by air so they need to operate in a vacuum. Thus the name.
But here’s the catch: the laser sources that these research groups used to excite the transition were pulsed lasers, which means they only produced light in very short bursts, lasting just a few nanoseconds each.
When you have such short pulses, the light inherently has a broad range of frequencies mixed together. Scientists say the linewidth is several gigahertz wide. But the natural linewidth of the Th-229 isomer transition is very narrow, only about 60 microhertz. That’s a difference of several orders of magnitude. It’s like trying to measure something with a 1-m-long stick when you need precision down to the width of a single atom. Nuclear clocks demand a much more stable laser with a really narrow linewidth — ideally continuous rather than pulsed.
In a paper published in Physical Review Applied on February 11, researchers from Tsinghua University and the Chinese Academy of Sciences have proposed a way to generate a continuous-wave vacuum ultraviolet laser light at exactly 148.4 nm, with a very narrow linewidth, using a process called four-wave mixing.
Four-wave mixing is a nonlinear optical process. Normally, when light passes through a material, it just passes through without the different colours of light affecting each other. But if you have intense enough light and the right kind of material, you can get nonlinear effects, i.e. where multiple photons of light interact with atoms in the material to create new photons at other frequencies.
In four-wave mixing, you take three laser beams and send them through such a special medium. If everything is set up just right, they will combine to create a fourth beam at a new frequency. And the frequency of this new beam will be the sum of the frequencies of the three input beams.
The authors have proposed using cadmium vapour as the mixing medium. Cadmium because it has many properties that make it perfect for this job. First, it has electronic transitions that can be exploited to make the nonlinear process very efficient. Specifically, the team plans to use a two-photon resonance, meaning two of the input laser beams will have frequencies that, when added together, will exactly match the energy needed to excite cadmium atoms to a particular excited state. This resonance will greatly enhance the efficiency of the process. Second, the wavelengths of the lasers required to produce the desired output are readily available (of wavelengths 375 nm and 710 nm).
The two previous studies also used four-wave mixing but ended up with pulsed laser light because they used xenon as the mixing medium. Xenon is a generic choice because it results in light of a wide range of wavelengths. If researchers are exploring and don’t know exactly what wavelength they need or if they do want to use light of different wavelengths, xenon is great. On the flip side, it isn’t particularly suited to generating 148.4 nm light. Rather, it can if researchers can supply the input light at enormous power.
Pulsed lasers help with this requirement using a trick. Imagine you’ve a water hose: if water flows out continuously at a steady rate, you might get a gentle stream, but if you put your thumb over the end and suddenly release it, you get a powerful jet that can spray much farther even when the total amount of water per minute is the same. Pulsed lasers work like this: at the brief moment when the laser emits light, the intensity is very high even though the average power is low. And four-wave mixing is much more efficient with this intense light — enough to generate enough vacuum ultraviolet light to detect the nuclear transition.
To this end, the paper went into considerable technical detail about calculating how efficient using cadmium vapour would be, including assessing the element’s atomic structure. The authors also calculated something called the nonlinear susceptibility, which said how strongly the cadmium atoms would respond to the light.
They also had to worry about phase-matching. For the four-wave mixing process to work efficiently, the different light waves need to stay synchronised as they travel through the medium. This is tricky because different wavelengths of light travel at slightly different speeds through cadmium vapour (a phenomenon called dispersion). However, the authors showed that carefully controlling the temperature of the vapour and tightly focusing the laser beams could result in good phase-matching.
Overall, their calculations suggested that with input laser powers of 3 W at 375 nm and 6 W at 710 nm — both very achievable using current technology — they could generate more than 30 µW of vacuum ultraviolet light at 148.4 nm. While 30 µW may not sound like much, it’s actually a lot for spectroscopy experiments. More importantly, because this is a continuous-wave process rather than a pulsed process, and because it’s essentially just a frequency multiplication of stable input lasers, the output light should have a very narrow linewidth. The team estimated it could be below 1 kHz, which is orders of magnitude better than the pulsed sources currently in use.
A narrow linewidth is so important because then scientists can observe something called Rabi oscillations in the nuclear transition. This is when you can coherently drive the nucleus back and forth between its ground state and excited state, which is essential to build a nuclear clock. The researchers showed that with their proposed laser system, the linewidth would be narrow enough to observe these oscillations, opening the door to much more precise measurements of the Th-229 transition and eventually to building an actual working nuclear clock.
Such a clock could have applications beyond just timekeeping. The Th-229 transition is particularly sensitive to changes in fundamental constants of nature, so it could be used to test whether these constants actually stay constant over time; scientists could also use it to search for certain types of dark matter. The proposed laser system thus represents a crucial technological step towards all these applications.
