Tag: thorium-229m

• A laser worthy of a nuclear clock

  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.

  2026.02.14

• Clocks on the cusp of a nuclear age

  You need three things to build a clock: an energy source, a resonator, and a counter. In an analog wrist watch, for example, a small battery is the energy source that sends a small electric signal to a quartz crystal, which, in response, oscillates at a specific frequency (piezoelectric effect). If the amount of energy in each signal is enough to cause the crystal to oscillate at its resonant frequency, the crystal becomes the resonator. The counter tracks the crystal’s oscillation and converts it to seconds using predetermined rules.

  Notice how the clock’s proper function depends on the relationship between the battery and the quartz crystal and the crystal’s response. The signals from the battery have to have the right amount of energy to excite the crystal to its resonant frequency and the crystal’s oscillation in response has to happen at a fixed frequency as long as it receives those signals. To make better clocks, physicists have been able to fine-tune these two parameters to an extreme degree.

  Today, as a result, we have clocks that don’t lose more than one second of time every 30 billion years. These are the optical atomic clocks: the energy source is a laser, the resonator is an atom, and the counter is a particle detector.

  An atomic clock’s identity depends on its resonator. For example, many of the world’s countries use caesium atomic clocks to define their respective national “frequency standards”. (One such clock at the National Physical Laboratory in New Delhi maintains Indian Standard Time.) A laser imparts a precise amount of energy to excite a caesium-133 atom to a particular higher energy state. The atom soon after drops from this state to its lower ground state by emitting light of frequency exactly 9,192,631,770 Hz. When a particle detector receives this light and counts out 9,192,631,770 waves, it will report one second has passed.

  Caesium atomic clocks are highly stable, losing no more than a second in 20 million years. In fact, scientists used to define a second in terms of the time Earth took to orbit the Sun once; they switched to the caesium atomic clock because “it was more stable than Earth’s orbit” (source).

  But there is also room for improvement. The higher the frequency of the emitted radiation, the more stable an atomic clock will be. The emission of a caesium atomic clock has a frequency of 9.19 GHz whereas that in a strontium clock is 429.22 THz and in a ytterbium-ion clock is 642.12 THz — in both cases five orders of magnitude higher. (9.19 GHz is in the microwave frequency range whereas the other two are in the optical range, thus the name “optical” atomic clock.)

  Optical atomic clocks also have a narrower linewidth, which is the range of frequencies that can prompt the atom to jump to the higher energy level: the narrower the linewidth, the more precisely the jump can be orchestrated. So physicists today are trying to build and perfect the next generation of atomic clocks with these resonators. Some researchers have said they could replace the caesium frequency standard later this decade.

  But yet other physicists have also already developed an idea to build the subsequent generation of clocks, which are expected to be at least 10-times more accurate than optical atomic clocks. Enter: the nuclear clock.

  When an atom, like that of caesium, jumps between two energy states, the particles gaining and losing the energy are the atom’s electrons. These electrons are arranged in energy shells surrounding the nucleus and interact with the external environment. For a September 2020 article in The Wire Science, IISER Pune associate professor and a member of a team building India’s first strontium atomic clock Umakant Rapol said the resonator needs to be “immune to stray magnetic fields, electric fields, the temperature of the background, etc.” Optical atomic clocks achieve this by, say, isolating the resonator atoms within oscillating electric fields. A nuclear clock offers to get rid of this problem by using an atom’s nucleus as the resonator instead.

  Unlike electrons, the nucleus of an atom is safely ensconced further in, where it is also quite small, making up only around 0.01% of the atom’s volume. The trick here is to find an atomic nucleus that’s stable and whose resonant frequency is accessible with a laser.

  In 1976, physicists studying the decay of uranium-233 nuclei reported some properties of the thorium-229 nucleus, including estimating that the lowest higher-energy level to which it could jump required less than 100 eV of energy. Another study in 1990 estimated the requirement to be under 10 eV. In 1994, two physicists estimated it to be around 3.5 eV. The higher energy state of a nucleus is called its isomer and is denoted with the suffix ‘m’. For example, the isomer of the thorium-229 nucleus is denoted thorium-229m.

  After a 2005 study further refined the energy requirement to 5.5 eV, a 2007 study provided a major breakthrough. With help from state-of-the-art instruments at NASA, researchers in the US worked out the thorium-229 to thorium-229m jump required 7.6 eV. This was significant. Energy is related to frequency by the Planck equation: E = hf, where h is Planck’s constant. To deliver 3.5 eV of energy, then, a laser would have to operate in the optical or near-ultraviolet range. But if the demand was 7.6 eV, the laser would have to operate in the vacuum ultraviolet range.

  Further refinement by more researchers followed but they were limited by one issue: since they still didn’t have a sufficiently precise value of the isomeric energy, they couldn’t use lasers to excite the thorium-229 nucleus and find out. Instead, they examined thorium-229m nuclei formed by the decay of other elements. So when on April 29 this year a team of researchers from Germany and Austria finally reported using a laser to excite thorium-229 nuclei to the thorium-229m state, their findings sent frissons of excitement through the community of clock-makers.

  The researchers’ setup had two parts. In the first, they drew inspiration from an idea a different group had proposed in 2010: to study thorium-229 by placing these atoms inside a larger crystal. The European group grew two calcium fluoride (CaF2) crystals in the lab doped heavily with thorium-229 atoms, with different doping concentrations. In a study published a year earlier, different researchers had reported observing for the first time thorium-229m decaying back to its ground state while within calcium fluoride and magnesium fluoride (MgF2) crystals. Ahead of the test, the European team cooled the crystals to under -93º C in a vacuum.

  In the second part, the researchers built a laser with output in the vacuum ultraviolet range, corresponding to a wavelength of around 148 nm, for which off-the-shelf options don’t exist at the moment. They achieved the output instead by remixing the outputs of multiple lasers.

  The researchers conducted 20 experiments: in each one, they increased the laser’s wavelength from 148.2 nm to 150.3 nm in 50 equally spaced steps. They also maintained a control crystal doped with thorium-232 atoms. Based on these attempts, they reported their laser elicited a distinct emission from the two test crystals when the laser’s wavelength was 148.3821 nm. The same wavelength when aimed at the CaF2 crystal doped with thorium-232 didn’t elicit an emission. This in turn implied an isomeric transition energy requirement of 8.35574 eV. The researchers also worked out based on these details that a thorium-229m nucleus would have a half-life of around 29 minutes in vacuum — meaning it is quite stable.

  Physicists finally had their long-sought prize: the information required to build a nuclear clock by taking advantage of the thorium-229m isomer. In this setup, then, the energy source could be a laser of wavelength 148.3821 nm; the resonator could be thorium-229 atoms; and the counter could look out for emissions of frequency 2,020 THz (plugging 8.355 eV into the Planck equation).

  Other researchers have already started building on this work as part of the necessary refinement process and have generated useful insights as well. For example, on July 2, University of California, Los Angeles, researchers reported the results of a similar experiment using lithium strontium hexafluoroaluminate (LiSrAlF6) crystals, including a more precise estimate of the isomeric energy gap: 8.355733 eV.

  About a week earlier, on June 26, a team from Austria, Germany, and the US reported using a frequency comb to link the frequency of emissions from thorium-229 nuclei to that from a strontium resonator in an optical atomic clock at the University of Colorado. A frequency comb is a laser whose output is in multiple, evenly spaced frequencies. It works like a gear that translates the higher frequency output of a laser to a lower frequency, just like the lasers in a nuclear and an optical atomic clock. Linking the clocks up in this way allows physicists to understand properties of the thorium clock in terms of the better-understood properties of the strontium clock.

  Atomic clocks moving into the era of nuclear resonators isn’t just one more step up on the Himalayan mountain of precision timekeeping. Because nuclear clocks depend on how well we’re able to exploit the properties of atomic nuclei, they also create a powerful incentive and valuable opportunities to probe nuclear properties.

  In a 2006 paper, a physicist named VV Flambaum suggested that if the values of the fine structure constant and/or the strong interaction parameter change even a little, their effects on the thorium-229 isomeric transition would be very pronounced. The fine structure constant is a fundamental constant that specifies the strength of the electromagnetic force between charged particles. The strong interaction parameter specifies this vis-à-vis the strong nuclear force, the strongest force in nature and the thing that holds protons and neutrons together in a nucleus.

  Probing the ‘stability’ of these numbers in this way opens the door to new kinds of experiments to answer open questions in particle physics — helped along by physicists’ pursuit of a new nuclear frequency standard.

  Featured image: A view of an ytterbium atomic clock at the US NIST, October 16, 2014. Credit: N. Phillips/NIST.

  2024.07.06