Nuclear spin quenching of the $^2S_{1/2}\rightarrow {^2}F_{7/2}$ electric octupole transition in $^{173}$Yb$^+$

This paper reports the coherent excitation of the $^2S_{1/2}\rightarrow {^2}F_{7/2}$ clock transition in $^{173}$Yb$^+$, revealing a nuclear spin-induced quenching effect that significantly shortens the excited state lifetime and enables a 20-fold suppression of the AC Stark shift, thereby facilitating the development of scalable multi-ion optical clocks and quantum computers.

The Gist

Imagine you are trying to build the world's most perfect stopwatch. In the world of physics, these "stopwatches" are called atomic clocks, and they are so precise they wouldn't lose a second over the entire age of the universe.

Usually, scientists use a single atom (like a lone runner) to keep time. But to make an even better clock, they want to use a whole team of atoms (a relay race) running together. The problem? When you shine a laser on a team of atoms to start the race, the laser light itself pushes the atoms around, messing up the timing. It's like trying to time runners while blowing a giant fan at them; the wind (the laser) changes their speed.

This paper is about a clever trick to solve that problem using a specific type of atom: Ytterbium-173.

Here is the story of what they discovered, explained simply:

1. The "Ghostly" Transition

Most atomic clocks work by making an electron jump from a low energy level to a high one, like a frog jumping onto a lily pad. In the Ytterbium ion, there is a specific jump (from a state called $2S$ to $2F$) that is incredibly difficult to make. It's so difficult that the electron would naturally sit on the lily pad for 1.6 years before falling back down.

Because this jump is so rare and slow, the laser needed to force the electron to jump has to be very powerful. But a powerful laser is like a strong wind—it pushes the atoms and ruins the clock's accuracy. This is called the AC Stark shift (or simply, the "laser wind").

2. The Nuclear Spin "Key"

The scientists decided to try a different version of the Ytterbium atom. Most Ytterbium atoms are "smooth" and symmetrical. But the Ytterbium-173 isotope has a wobbly, deformed nucleus with a "nuclear spin" (think of it as a tiny, spinning top inside the atom).

In 2016, theorists predicted that this spinning top would act like a secret key. It would unlock a hidden door, allowing the electron to jump much faster than usual. This is called nuclear spin quenching.

3. The "Super-Shortcut"

When the scientists tested this, they found the prediction was true, but it was even more dramatic than expected.

• The Old Way (Smooth Atom): The electron takes 1.6 years to fall back down. You need a huge laser to push it up.
• The New Way (Spinning Atom): For certain "teams" of atoms (specifically those with a total spin of 4), the electron falls back down in just 49 days.

Because the electron falls back down so much faster, the atom is ready for the next jump much sooner. This means the scientists can use a much weaker laser to get the same result.

The Analogy:
Imagine you are trying to push a heavy boulder up a hill.

• The Old Atom: The boulder is stuck in deep mud. You need a massive truck (high-power laser) to push it. The truck's exhaust fumes (laser wind) blow the boulder off course.
• The New Atom: The spinning nucleus acts like a lubricant. The boulder slides up easily. You only need a gentle push (low-power laser). Since the push is gentle, there is almost no exhaust fumes to blow the boulder off course.

4. The Big Win: A Team of Clocks

Because they could use a weaker laser, they finally solved the "laser wind" problem. They were able to trap three atoms in a crystal formation and make them all jump at the exact same time without messing up the timing.

They measured that the "laser wind" effect was reduced by 20 times. This is a massive breakthrough. It means that in the future, we won't just have clocks with one atom; we can have clocks with hundreds of atoms working together.

Why Does This Matter?

• Better Timekeeping: More atoms mean a more stable, accurate clock. This could lead to a new definition of the "second" used by the whole world.
• Quantum Computers: These atoms can act as tiny memory units (qubits). The ability to control them with weak lasers makes building large-scale quantum computers much easier.
• Mapping the Earth: Ultra-precise clocks can detect tiny changes in gravity. By comparing these clocks in different cities, we could map the Earth's interior or detect underground water and oil reserves with incredible precision.

The Bottom Line

The scientists found a way to use the "wobbly" nature of a specific atom's nucleus to create a shortcut. This shortcut lets them use a gentle laser instead of a sledgehammer, allowing them to build clocks with many atoms working in perfect harmony. It's a small change in the atom that could lead to a giant leap in how we measure time and explore the universe.

Technical Summary

1. Problem Statement

Trapped ion optical clocks, particularly those based on the highly forbidden electric octupole (E3) transition in Ytterbium ions ($^{171}\text{Yb}^+$), offer exceptional accuracy and sensitivity to new physics. However, scaling these systems to multi-ion configurations is hindered by the AC Stark shift (light shift) induced by the clock laser.

• The Challenge: The E3 transition in $^{171}\text{Yb}^+$ has an extremely long natural lifetime (~1.6 years), resulting in a very narrow linewidth. To achieve sufficient excitation rates (Rabi frequencies) for coherent control, high laser power is required. This high intensity causes significant AC Stark shifts, which limit the precision and scalability of multi-ion clocks.
• The Proposed Solution: The odd isotope $^{173}\text{Yb}^+$ possesses a nuclear spin ($I=5/2$) and a large nuclear electric quadrupole moment. Theoretical predictions suggested that hyperfine interactions could mix the metastable $^2F_{7/2}$ state with intermediate states, inducing an electric dipole (E1) component to the otherwise forbidden E3 transition. This "nuclear spin quenching" would shorten the lifetime of specific hyperfine states, allowing for faster excitation with lower laser power, thereby reducing the AC Stark shift.

2. Methodology

The authors employed a trapped-ion experimental setup to investigate the hyperfine structure and transition dynamics of $^{173}\text{Yb}^+$.

• Experimental Setup:

  • A single $^{173}\text{Yb}^+$ ion was confined in a radiofrequency (RF) Paul trap with a defined quantization axis ($B = 0.2$ mT).
  • Cooling & Detection: Doppler cooling and state detection were performed using 370 nm, 935 nm, and 760 nm lasers.
  • Clock Laser: An ultra-stable 467 nm laser (stabilized to a cryogenic silicon cavity) was used to probe the $^2S_{1/2} \to {}^2F_{7/2}$ transition.
  • Reference: Absolute frequencies were measured relative to the well-characterized E3 transition in $^{172}\text{Yb}^+$ (known to 11 Hz uncertainty).

• Measurement Techniques:

  • Rapid Adiabatic Passage (RAP): Used to efficiently scan and identify previously unobserved hyperfine transitions despite decoherence.
  • Rabi Oscillation Measurements: Coherent excitation of specific hyperfine transitions ($F_g=3 \to F_e=2, 4, 6$) was performed to extract Rabi frequencies ($\Omega$).
  • Decoherence Modeling: Experimental Rabi oscillations were fitted using a combined Jaynes-Cummings (JC) model (for thermal dephasing) and an exponential decay model (for magnetic/laser noise) to accurately extract Rabi frequencies and decoherence times.
  • Multi-Ion Demonstration: A 3-ion Coulomb crystal was used to compare the AC Stark shifts of the "quenched" transition ($F_e=4$) versus the "unquenched" reference ($F_e=6$).

3. Key Contributions

• First Observation of Nuclear Spin Quenching: The paper provides the first experimental confirmation that the hyperfine structure in $^{173}\text{Yb}^+$ induces a strong electric dipole (HFE1) contribution to the E3 clock transition, significantly enhancing the decay rate for specific hyperfine states.
• Absolute Frequency Determination: The authors determined the absolute frequency of the unquenched reference transition ($|2S_{1/2}, F_g=3\rangle \to |2F_{7/2}, F_e=6\rangle$) with high precision.
• Quantification of HFE1 Rates: By measuring Rabi frequencies, the team quantified the effective E1 transition rates, demonstrating that the HFE1 mechanism dominates over the pure E3 mechanism for the $F_e=2$ and $F_e=4$ states.
• AC Stark Shift Suppression: The study experimentally demonstrated that the shortened lifetime of the quenched state allows for the same Rabi frequency to be achieved with significantly lower optical power, drastically reducing the AC Stark shift.

4. Key Results

• Transition Frequencies:

  • The absolute frequency of the unquenched $|2S_{1/2}, F_g=3\rangle \to |2F_{7/2}, F_e=6\rangle$ transition was measured as 642.11917656354(43) THz.
  • Hyperfine splittings for the $^2F_{7/2}$ state were measured and tabulated (e.g., $F_e=4$ is shifted by ~5.3 GHz relative to $F_e=6$).

• Lifetime and Decay Rates:

  • The unquenched $F_e=6$ state retains the long lifetime of ~1.6 years (pure E3).
  • The $F_e=4$ state exhibits a drastically shortened lifetime of approximately 49(21) days due to the HFE1 channel. This is roughly 12 times shorter than the unperturbed state.
  • The effective E1 transition rate for $F_g=3 \to F_e=4$ is ~25 times larger than the theoretical pure E3 rate.

• Rabi Frequency Enhancement:

  • For the same optical intensity, the Rabi frequency for the quenched $F_e=4$ transition is ~4.2 times larger than that of the unquenched $F_e=6$ transition.
  • Conversely, to achieve the same Rabi frequency, the quenched transition requires ~18 times less laser power.

• AC Stark Shift Suppression:

  • Using a 3-ion Coulomb crystal, the team demonstrated a ~20-fold (specifically 22(5)) suppression of the differential AC Stark shift when using the quenched transition compared to the reference transition.
  • This allows for simultaneous excitation of multiple ions with a Gaussian beam, a feat difficult to achieve with the high-power requirements of the unquenched transition.

• Quadratic Zeeman Sensitivity:

  • The $F_g=3 \to F_e=6$ transition exhibits the smallest second-order Zeeman sensitivity ($-33.7$ mHz/$\mu\text{T}^2$).
  • However, the $F_e=4$ state has a very large sensitivity ($8060$ mHz/$\mu\text{K}^2$), which poses a challenge for coherence time but can be managed via magnetic field control or hyperfine averaging.

5. Significance and Outlook

This work represents a major step forward for multi-ion optical clocks and quantum computing based on Ytterbium ions.

• Scalability: The reduction of the AC Stark shift by an order of magnitude removes a primary bottleneck for scaling Yb+ clocks to large ion crystals (e.g., 100+ ions). This enables advanced protocols like zero-dead-time clocks and cascaded clocks.
• Quantum Computing: The $F_e=4$ state, with its tens-of-days lifetime and strong coupling, is identified as a promising candidate for a "shelving" state in quantum logic operations, offering high detection fidelity.
• Nuclear Physics: The precise measurement of hyperfine splittings in $^{173}\text{Yb}^+$ provides critical data for resolving discrepancies in nuclear magnetic octupole moments and testing nuclear structure models.
• Fundamental Physics: The ability to operate multi-ion clocks with reduced systematic shifts enhances the sensitivity of these systems to searches for dark matter, variations in fundamental constants, and tests of Lorentz invariance.

In conclusion, the paper demonstrates that nuclear spin quenching in $^{173}\text{Yb}^+$ is a viable and powerful mechanism to overcome the power-scaling limitations of E3 optical clocks, paving the way for next-generation multi-ion timekeeping and quantum information processing.