$J=0$ metastable state of $\mathrm{Th}^{2+}$ for a hyperfine-free nuclear clock

This paper reports the laser population and detection of a metastable $J=0$ state in $\mathrm{Th}^{2+}$, characterizing its isotope shift and collision-limited lifetime to establish its potential as a hyperfine-free nuclear clock for probing the low-energy $^{229}$Th nuclear resonance.

The Gist

The Big Idea: A Super-Stable Atomic Clock

Imagine you want to build the most perfect clock in the universe. Usually, clocks use the swinging of a pendulum or the vibration of a quartz crystal. But scientists are trying to build a clock based on the "heartbeat" of an atomic nucleus.

The paper focuses on a specific atom: Thorium. Inside a Thorium nucleus, there is a transition (a jump between energy levels) that happens at a very low energy. This makes it a perfect candidate for a clock because it's very sensitive and precise.

However, there's a problem. The nucleus is surrounded by an "electron shell" (a cloud of electrons). These electrons act like a noisy crowd around a quiet speaker. They interact with the nucleus and mess up the clock's ticking, especially if there are magnetic or electric fields nearby. This is called hyperfine interaction.

The scientists in this paper found a way to quiet that crowd. They looked at a specific version of the Thorium ion (Th²⁺) where the electrons are arranged in a special, symmetrical way (called a J=0 state). In this state, the electrons are like a perfectly balanced, silent sphere. They don't "talk" to the nucleus as much as usual, making the nucleus much more isolated and the clock much more accurate.

The Challenge: Finding the "Hidden Room"

The problem with this special, silent state is that it's a metastable state. Think of it like a hidden room in a house that has no door leading directly to the outside.

• The Ground Floor: The atom usually sits in its lowest energy state (the ground floor).
• The Hidden Room: The special "J=0" state is high up, but there is no direct elevator (radiative decay) to get back down to the ground floor. Once you get in, you are stuck there for a long time.
• The Goal: The team needed to figure out how to get the atoms into this room and how to know they are actually inside.

How They Did It: The "Laser Elevator"

Since there is no direct door, the scientists built a temporary "laser elevator."

1. Loading the Elevator: They started with Thorium ions that were sitting on the "ground floor" (a specific low-energy state).
2. The First Jump: They fired a laser at 484 nm (a specific color of light). This acted like a boost, kicking the atoms up to a high-energy "landing pad" (an excited state).
3. The Drop: The atoms naturally fell from that landing pad. Most fell back to the ground, but some accidentally dropped into the "Hidden Room" (the J=0 metastable state).
4. Checking the Room: To see if the atoms were actually in the room, they used a second laser (at 724 nm) to try to pull them out. If the atoms were there, they would glow (fluoresce), confirming their presence.

What They Discovered

Once they successfully got the atoms into the room and confirmed they were there, they measured two important things:

1. The "Isotope Shift" (The Weight Difference)
They compared two versions of Thorium: the common kind (Thorium-232) and the rare kind used for the clock (Thorium-229).

• Analogy: Imagine two identical-looking suitcases, but one is slightly heavier because it has a different internal structure.
• Result: They measured how much the "frequency" of the laser needed to change to hit the heavy suitcase versus the light one. They found the difference was very small (0.6 GHz). This small difference is actually good news! It means the electrons in this special state are barely noticing the difference in the nucleus's charge, which is exactly what you want for a clock that ignores external noise.

2. The "Lifetime" (How Long They Stay)
They wanted to know how long an atom could stay in this "Hidden Room" before being kicked out.

• The Problem: In their experiment, the room wasn't perfectly empty. There was a "buffer gas" (like Argon or Helium) floating around to cool the atoms down.
• The Collision: Occasionally, a gas molecule would bump into the Thorium atom. This collision was like a rude guest kicking the atom out of the hidden room and shoving it into a different room (a nearby state called 5f6d 3G3) where it could easily escape.
• The Result: Because of these collisions, the atoms only stayed in the room for a tiny fraction of a second (about 225 microseconds).
• The Promise: The scientists calculated that if they could remove the gas entirely (creating a perfect vacuum), the atom would stay in that room for about 95 seconds. That is a very long time for an atom, giving the clock plenty of time to take a precise measurement.

The Future Plan

The paper concludes by proposing a blueprint for a Hyperfine-Free Nuclear Clock.

• The Setup: Instead of just letting the atoms bump into gas, they propose trapping the Thorium ions in a vacuum and cooling them down using other, easier-to-cool ions (like a "nanny" ion that cools the Thorium without touching it).
• The Benefit: In this perfect vacuum, the "rude guests" (collisions) are gone. The Thorium atom would stay in its silent, symmetrical state for nearly 2 minutes.
• The Outcome: This would allow scientists to listen to the nucleus's "heartbeat" for a long time without the electron cloud interfering, potentially creating the most accurate clock humanity has ever built.

Summary

The paper is a successful "proof of concept." The scientists showed they can:

1. Find the special, quiet state in Thorium.
2. Get atoms into that state using lasers.
3. Detect them when they are there.
4. Prove that the state is very stable, provided you can stop gas molecules from bumping into it.

They haven't built the final clock yet, but they have built the key components and shown that the "engine" works.

Technical Summary

Technical Summary: $J=0$ Metastable State of Th$^{2+}$ for a Hyperfine-Free Nuclear Clock

Problem and Motivation
The exceptionally low-energy nuclear transition in $^{229}$Th (approximately 8.4 eV) offers a unique opportunity for realizing a nuclear optical clock. While solid-state approaches using doped crystals have resolved the transition frequency, trapped ion systems offer the potential for higher accuracy by isolating the ion from environmental perturbations. However, in most charge states, the sensitivity of the nuclear transition frequency to external fields is mediated by hyperfine coupling between the nucleus and valence electrons. To minimize this sensitivity, states with specific angular momentum properties are required: either $J=0$ or $J=1/2$ electronic states, or stretched states with maximum total angular momentum $F$.

While $^{229}$Th$^{3+}$ has been proposed for nuclear clocks due to its simple level structure and laser-cooling capabilities, its metastable $s$-state ($J=1/2$) has a lifetime of only $\sim$600 ms. Conversely, $^{229}$Th$^{4+}$ possesses a $J=0$ ground state but lacks resonance lines for laser cooling or state detection in common wavelength ranges. This work investigates $^{229}$Th$^{2+}$, specifically a metastable electronic level with total angular momentum $J=0$ (configuration $6d^2$ $^3P_0$ at 5090 cm$^{-1}$). This state is attractive because it possesses no dipole-allowed radiative decay channels and is connected to the ground state only via an electric quadrupole transition, theoretically offering a hyperfine-free environment largely immune to field-induced frequency shifts.

Methodology
The experiments were conducted using a radio-frequency ion trap at the Physikalisch-Technische Bundesanstalt (PTB). The experimental sequence involved:

1. Ion Production: Th$^+$ ions were generated via laser ablation from $^{232}$Th and $^{229}$Th targets. These were subsequently ionized to Th$^{2+}$ via a three-photon process (402 nm and 269 nm photons).
2. State Preparation: Ions were cooled to near room temperature using buffer gases (Argon or Helium). To populate the metastable $J=0$ state ($5090_0$), a 484 nm laser pulse (150 $\mu$s duration) drove the transition from the thermally populated $63_2$ state to the $20711_1$ level. Subsequent spontaneous decay populated the $5090_0$ state.
3. Detection: Population in the metastable state was detected via laser-induced fluorescence using a two-photon excitation scheme ($5090_0 \to 20711_1 \to 29300_1$). The 1164 nm laser was stabilized to the $20711_1 \to 29300_1$ transition, while a tunable 640 nm laser scanned the $5090_0 \to 20711_1$ transition.
4. Lifetime Measurement: The lifetime of the $5090_0$ state was determined by monitoring the population of the nearby $5060_3$ state (which decays via an electric dipole transition) through collisional mixing. Fluorescence at 545 nm was recorded following the 484 nm excitation pulse.

Key Results

• State Identification and Isotope Shift: The $J=0$ state was successfully populated and detected in both $^{232}$Th$^{2+}$ and $^{229}$Th$^{2+}$. The isotope shift for the forbidden transition $63_2 \to 5090_0$ was determined to be 0.6(3) GHz. This value is an order of magnitude smaller than isotope shifts reported for other transitions in Th$^{2+}$, indicating that the $5090_0$ state has minimal interaction with the nuclear charge distribution and a field shift coefficient nearly identical to the $63_2$ ground state.
• Hyperfine Structure: For $^{229}$Th$^{2+}$ ($I=5/2$), the hyperfine structure of the intermediate $J=1$ state ($20711_1$) was resolved, revealing three $F$ levels. The measured transition wavelengths and frequency separations were consistent with theoretical expectations and previous data.
• Lifetime Measurements: In the presence of buffer gas, the lifetime of the $5090_0$ state is limited by collisional mixing with the nearby $5060_3$ state.
  • With Argon buffer gas, the lifetime was measured at 225 $\mu$s at a pressure of $3.2 \times 10^{-3}$ Pa.
  • With Helium, the lifetime was slightly shorter due to faster collisional mixing dynamics.
  • The observed lifetimes are significantly shorter than the calculated radiative lifetime of 95.5 s (for the electric quadrupole decay to the $63_2$ state at 1989 nm), confirming that collisional mixing is the dominant decay mechanism in the current setup.

Significance and Claims
The paper establishes that the $6d^2$ $^3P_0$ state in Th$^{2+}$ is a viable candidate for a hyperfine-free nuclear clock. The primary significance lies in the demonstration of efficient laser population and detection of this specific $J=0$ state. The authors claim that, unlike the $J=1/2$ state in Th$^{3+}$, the $J=0$ state in Th$^{2+}$ offers a system where leading hyperfine interactions are minimized, potentially allowing for longer interrogation times (limited only by the radiative lifetime of $\sim$95 s in ultrahigh vacuum).

The authors propose a future experimental scheme where sympathetically cooled Th$^{2+}$ ions are prepared in the $5090_0$ state using a stimulated Raman process (utilizing 484 nm and 640 nm lasers). In such a setup, the nuclear transition could be driven at 148 nm. The authors note that because no electronic levels exist near the 9.0 eV excitation energy, this approach minimizes the risk of parasitic electronic excitation. The detection of nuclear excitation could be performed via quantum logic spectroscopy using co-trapped laser-cooled ions (e.g., Sr$^+$ or In$^+$).

The work concludes that while the current setup is limited by collisional mixing, the $J=0$ state in Th$^{2+}$ represents a promising pathway toward a nuclear clock with reduced sensitivity to external field perturbations, provided the ions can be maintained in an ultrahigh vacuum environment.