A novel state of thorium opens the possibility for a nuclear clock

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Why are there atomic clocks but no nuclear clocks? After all, an atom's nucleus is typically surrounded by many electrons, so in principle it should be less susceptible to outside noise (in the form of light). A nucleus, for high-atomic number atoms, contains more particles than does the element's electrons. It holds nearly the entire mass of the atom while taking up only about 1/100,000th of the atom's space. While the first atomic clock was invented in 1949, no nuclear clock has yet been feasible.

The simple reason is that it takes much more energy to excite a nucleus into a higher energy state than it does an atom. Atomic clocks typically excite cesium atoms with photons of energy 4 x 10^-5 electronvolts. The most promising nucleus for a potential nuclear clock is currently thought to be thorium-229, with nuclear excitation states that require photons of about 8 eV, over 200,000 times higher. That's microwaves versus ultraviolet. Furthermore, the interaction between light and the nucleus can be weak.

Now scientists from China have discovered an interaction between light and a nucleus that is much stronger and more efficient—more than 10% of the nuclei of highly ionized thorium-229 can be excited with a single laser pulse. Thorium usually has 90 electrons around its nucleus (its atomic number), and the group removed all but one of them to produce hydrogen-like thorium, with an electronic charge of +89 from all the protons in the nucleus minus the one electron. Their work is published in Physical Review Letters.

Existing atomic clocks work by utilizing the resonant frequencies of atoms. Using a group of atoms that can be in one of two energy states, the lower energy group is radiated with light from a laser of just the right energy to pump as many atoms as possible to the higher energy level.

The more precise the radiation's frequency, the more atoms that jump to the higher state. The different types of states are separated, and the high energy atoms decay to the low state, emitting light of the same characteristic frequency, which for cesium-133 atoms is precisely 9,192,631,770 Hertz. The incoming light then pumps the atom up to the higher energy level again, with subsequent decay, etc.

With enough adjustment of the incoming light's frequency, a maximum of lower state atoms resonantly transition to the higher state again. And so on. In this way, the atom can be used as an oscillator, which is the basis of all clocks.

Lead author Hanxu Zhang of the China Academy of Engineering Physics in Beijing, with colleagues, showed that currently available intense lasers and hydrogen-like thorium atoms ²²⁹Th⁸⁹⁺ may be able to achieve the resonance required for a nuclear analog of an atomic clock. An isomer of this nucleus—a metastable state of the nucleus—can be excited with a probability of 10% by using intense laser pulses of 10²¹ watts/cm².

When transitioning back to a lower energy state, these highly ionic thorium atoms emit multiple wavelengths of light that are harmonics (integer multiples of a frequency) of the isomer transition frequency, in about 0.01 seconds. (The transition time for the bare thorium nucleus ²²⁹Th⁹⁰⁺ is roughly a thousand seconds.)

This gives a new opportunity for nucleus-based coherent light emission—having the same frequency but a constant phase difference between the light from the different transitions, similar to a laser.

The transition probability of 10% is a highly nonlinear change from typical energy transitions of the isomer, with the nuclear hyperfine mixing induced by the magnetic field of the single 1s electron on thorium⁸⁹⁺. (The electron's magnetic dipole moment is about 1,000 times larger than the magnetic dipole moments of the nuclear states.)

That strong magnetic field finely alters ("splits") the nuclear energy levels from the isotope with no electrons, Th⁹⁰⁺, while significantly reducing the upper states' lifetime by a factor of about 100,000, per the numbers above. This resonance could open the path to a nuclear optical clock.

The team found that increasing the laser's energy intensity by four orders of magnitude changed the probability of excitation (to the isomer state thorium⁸⁹⁺) by a single laser pulse from a linear variation with energy to a highly nonlinear variation with an increase of 14 orders of magnitude (see figure above). After that, it does not increase further with higher energy intensity.

In this way, the probability of a nuclear energy transition increases from about 10^-15 to 10^-1 (10%). Together with the resonant frequency, this vast increase opens the way to a possible nuclear clock.

"These results open up a new frontier of light-matter interaction," the group writes, "offering exciting prospects for manipulating atomic nuclei with light. The discovery of a novel mechanism for nuclear coherent light emission carries broader implications across diverse fields of study."

They note that their results could be readily implemented with experimental setups that exist today, "underscoring their practical relevance and immediate applicability."

More information: Hanxu Zhang et al, Highly Nonlinear Light-Nucleus Interaction, Physical Review Letters (2024). DOI: 10.1103/PhysRevLett.133.152503

Journal information: Physical Review Letters

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