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.