High-Resolution Spectroscopy of $^{173}$Yb$^{+}$ Ions

This paper reports the first efficient laser cooling, state preparation, and high-resolution spectroscopy of a single trapped $^{173}\rm{Yb}^+$ ion, enabling the precise measurement of the 436 nm electric quadrupole transition and the hyperfine structure of the ${}^2\!D_{3/2}$ state to determine the nuclear magnetic octupole moment with unprecedented accuracy.

The Gist

Imagine the atom as a tiny, intricate clockwork machine. For decades, scientists have been trying to tune this machine with extreme precision to build the world's most accurate clocks and to peek behind the curtain of the universe's fundamental laws. Most of the time, they've been working with a specific version of the Ytterbium atom (an element like gold or silver) that is relatively simple to handle.

However, there is a more complex, "deformed" version of this atom, called Ytterbium-173. Think of it like a slightly squashed, spinning top instead of a perfect sphere. Because it's squashed and spins faster, it has a much more complicated internal structure (called "hyperfine structure"). Until now, this complexity made it too difficult to study, so scientists mostly ignored it.

This paper is like a master locksmith finally figuring out how to pick the lock on this complex atom. Here is what they did, explained simply:

1. Taming the Wild Atom (Laser Cooling)

To study an atom, you have to stop it from jiggling around. If it's moving fast, it's like trying to read a license plate on a speeding car. The team used lasers to "cool" a single Ytterbium-173 ion until it was almost frozen in place.

• The Challenge: Usually, when you shine a laser to cool an atom, it accidentally knocks the atom into a "dark room" (a state where it stops glowing), making it invisible to your detectors.
• The Solution: They designed a special "traffic light" system using lasers. They found a specific path that keeps the atom visible while it cools, ensuring they never lose track of their tiny subject.

2. The Hidden Door (The 436 nm Transition)

Once the atom was calm, they tried to open a specific "door" in its energy structure. This door is a transition (a jump between energy levels) that no one had ever successfully opened before for this specific atom.

• The Analogy: Imagine a piano where most keys are well-known, but one specific key has been rusted shut for years. They managed to hit that key perfectly with a laser, causing the atom to sing a specific note.
• The Result: They measured the difference in pitch between this new atom and the older, simpler version (Ytterbium-171) with incredible precision—down to a tiny fraction of a Hertz (a unit of sound frequency).

3. Listening to the Spin (Microwave Spectroscopy)

The Ytterbium-173 nucleus is like a tiny magnet that is wobbling and spinning. This wobble creates a "hum" or a specific pattern of energy levels.

• The Experiment: They used microwaves (like the kind in your kitchen, but much more precise) to listen to these wobbles. By mapping out exactly how the nucleus spins, they could calculate a very specific property of the nucleus called the magnetic octupole moment.
• The Metaphor: Think of the nucleus as a lopsided spinning top. The "octupole moment" is a measurement of just how lopsided it is. Previous measurements were like guessing the shape of the top from a blurry photo. This team took a high-definition 3D scan, reducing the uncertainty of their guess by more than 100 times.

4. Why This Matters (The "Why")

Why go through all this trouble?

• Better Clocks: Because this atom has such a complex structure, it might be even better at keeping time than the simpler versions, potentially leading to clocks that are even more accurate.
• Testing Physics: The way this atom behaves helps scientists test if the laws of physics are the same everywhere. It's like checking if the rules of gravity change if you look at them through a slightly different lens.
• Solving a Puzzle: There was a long-standing debate about the shape of this specific nucleus. Some scientists thought it was one shape; others thought another. This experiment provides the clearest evidence yet, settling the argument by showing the nucleus is indeed slightly "squashed" in a specific way.

In Summary

The researchers successfully taught a complex, difficult-to-handle atom to sit still, opened a door in its energy structure that had been locked for years, and used that to measure the shape of its nucleus with record-breaking precision. They didn't just look at the atom; they listened to its internal "hum" and used that sound to rewrite our understanding of its nuclear shape.

Technical Summary

Technical Summary: High-Resolution Spectroscopy of 173Yb+ Ions

Problem and Motivation
While singly ionized ytterbium ($Yb^+$) isotopes have been extensively utilized in fundamental research, including optical clocks and quantum computing, the $^{173}Yb^+$ isotope remains poorly characterized despite its potential. With a nuclear spin of $I=5/2$ and a deformed nucleus, $^{173}Yb^+$ offers a richer hyperfine structure (HFS) than the commonly used $^{171}Yb^+$ ($I=1/2$). This richness is advantageous for studying nuclear-spin-dependent parity-nonconservation (PNC), developing qudit-based quantum architectures, and probing nuclear deformation. However, experimental progress has been hindered by the complexity of its HFS and the lack of efficient laser cooling and state detection schemes compatible with the metastable $^2D_{3/2}$ state. Previous studies were limited to buffer-gas-cooled ions or specific state preparations that did not allow for coherent spectroscopy of the $^2S_{1/2} \to ^2D_{3/2}$ electric quadrupole (E2) transition.

Methodology
The authors developed a comprehensive experimental scheme to trap, cool, and manipulate a single $^{173}Yb^+$ ion in a Paul endcap trap under ultrahigh vacuum.

• Laser Cooling and Repumping: A cooling scheme compatible with $^2D_{3/2}$ state detection was implemented. By selecting specific hyperfine transitions ($^2S_{1/2}(F=3) \to ^2P_{1/2}(F=2)$ at 370 nm and $^2D_{3/2}(F=4) \to ^3[3/2]_{1/2}(F=3)$ at 935 nm) and utilizing electro-optic modulators (EOMs) to generate necessary sidebands, the authors prevented population loss to the $^2D_{3/2}(F=1)$ "dark" state during cooling. This allowed the ion's state to be detected via the absence of fluorescence.
• State Preparation: A projective state preparation (PSP) technique was employed using the 436 nm E2 transition. By repeatedly applying 436 nm pulses and detecting fluorescence, the ion was projected into the $^2D_{3/2}(F=1)$ state, followed by a transfer to the specific Zeeman sublevel $^2S_{1/2}(F=3, m_F=0)$.
• Spectroscopy:
  • Optical: The previously unobserved $^2S_{1/2}(F=3) \to ^2D_{3/2}(F=1)$ E2 transition at 436 nm was coherently excited. The probe laser was offset-locked to a $^{171}Yb^+$ optical clock, inheriting its stability.
  • Microwave (MW): MW spectroscopy referenced to a hydrogen maser was used to resolve the HFS of the $^2S_{1/2}$ and $^2D_{3/2}$ states. The $^2S_{1/2}$ HFS served as an in situ magnetic field sensor to characterize second-order Zeeman shifts.
• Theoretical Analysis: Calculations were performed using a linearized coupled-cluster single-double (LCCSD) method and the AMBiT package to determine energy levels, HFS constants, and second-order energy corrections necessary for extracting nuclear moments.

Key Results

• Isotope Shift: The isotope shift between $^{171}Yb^+$ and $^{173}Yb^+$ on the $^2S_{1/2} \to ^2D_{3/2}$ transition was determined with an uncertainty of 1.4 Hz, yielding an unperturbed value of $6,186,981,108.3(14)$ Hz.
• Hyperfine Structure: The HFS of the $^2S_{1/2}$ and $^2D_{3/2}$ states was resolved with relative uncertainties below $10^{-8}$. The measured HFS constants for the $^2D_{3/2}$ state were $A = -118.25807(12)$ MHz, $B = 963.60980(57)$ MHz, and $C = 113(13)$ Hz.
• Nuclear Magnetic Octupole Moment: Using the measured HFS constant $C$ and theoretical calculations, the nuclear magnetic octupole moment ($\Omega$) of $^{173}Yb$ was inferred to be $\Omega = -0.062(8)$ (b $\times \mu_N$). This result reduces the uncertainty by more than two orders of magnitude compared to previous studies and resolves a long-standing debate regarding the sign and magnitude of this moment.
• Hyperfine Anomalies: The differential hyperfine anomaly (DHA) between $^{171}Yb$ and $^{173}Yb$ was determined for both the $^2S_{1/2}$ and $^2D_{3/2}$ states, yielding values of $-0.65(8)\%$ and $-0.41(8)\%$, respectively.
• Ion Temperature: The ion was cooled to a mean motional state of $\bar{n} = 18.5(33)$, corresponding to a temperature of $0.69(11)$ mK, close to the Doppler limit.

Significance and Claims
The paper establishes the foundation for high-precision spectroscopy of $^{173}Yb^+$ ions. The authors claim that their developed cooling and detection scheme enables the coherent excitation of the $^2S_{1/2} \to ^2D_{3/2}$ transition, which is a promising candidate for studying nuclear-spin-dependent PNC interactions. Furthermore, the precise determination of the nuclear magnetic octupole moment addresses recent theoretical debates and provides a benchmark for nuclear structure models. The work also demonstrates that the $^2S_{1/2}(F=3) \to ^2D_{3/2}(F=1)$ transition is a viable alternative to the standard $^{171}Yb^+$ clock transition, potentially enabling the construction of optical clocks based on $^{173}Yb^+$. Finally, the ability to perform differential studies between $^{171}Yb^+$ and $^{173}Yb^+$ with high precision reduces the theoretical effort required to predict energy differences for searches of new physics.