Precision spectroscopy of a trapped $^{173}$Yb$^+$ ion using a bath of ultracold atoms

This paper demonstrates precision laser spectroscopy of a trapped $^{173}$Yb$^+$ ion cooled by ultracold atoms via spin-exchange collisions, yielding magnetic and electric hyperfine interaction constants for the $6^2P_{3/2}$ state that are 6–9 times more precise than previous measurements.

The Gist

Imagine you have a very delicate, high-precision musical instrument (a trapped ion) that you want to tune perfectly. The problem? This instrument is so sensitive that if you try to play a note to tune it, the vibration might knock it out of tune, or it might get stuck in a weird, silent state where you can't hear it anymore.

In the world of quantum physics, this instrument is a Ytterbium ion (specifically the isotope $^{173}\text{Yb}^+$). Scientists want to study its "notes" (energy levels) to build better atomic clocks or quantum computers. But this specific ion is tricky: it has a complex internal structure that makes it hard to cool down and keep stable using standard laser tricks.

Here is how the researchers solved this problem, using a "bath" of ultracold atoms as a helper.

The Problem: The Hot, Stuck Instrument

Usually, to study an ion, scientists use lasers to "cool" it, slowing it down until it's almost frozen. However, for this specific Ytterbium ion, the laser cooling process is like trying to catch a greased pig; the ion has too many internal "doors" (energy levels) it can fall through. Once it falls into the wrong door, it stops responding to the lasers, and the experiment fails.

The Solution: The Ultracold "Cooling Pool"

Instead of trying to force the ion to cool down with lasers, the scientists put the ion into a bath of ultracold Lithium atoms.

Think of the Lithium atoms as a crowd of tiny, perfectly synchronized dancers moving in slow motion (they are cooled to near absolute zero). The Ytterbium ion is the clumsy guest in the middle of the dance floor.

• The Dance (Spin-Exchange Collisions): Every time the ion bumps into a Lithium atom, they swap energy. Because the Lithium atoms are so cold and organized, they act like a sponge, soaking up the ion's excess heat and "resetting" its internal state.
• The Reset: If the ion accidentally falls into a "wrong" energy state (a dark state), a collision with a Lithium atom kicks it back to the "ground floor" (the correct starting state). It's like a bouncer at a club who keeps shoving the wrong people out the back door so only the VIPs (the ground state) remain inside.

The Experiment: Listening to the Notes

Once the ion is being constantly "reset" by the Lithium bath, the scientists shine a specific blue-violet laser light (329 nm) on it.

• The Goal: They want to see exactly what frequency of light makes the ion jump to a higher energy level.
• The Detection Trick: They can't just "see" the ion jump. Instead, they use a clever trick. If the laser hits the ion at the right frequency, the ion eventually falls into a long-lived "sleep" state.
• The Alarm: When the ion is asleep, it becomes vulnerable. It bumps into a Lithium atom, and they swap charges (the Lithium steals an electron from the Ytterbium). Suddenly, the Ytterbium is no longer an ion; it's a neutral atom.
• The Result: The trap, which only holds charged ions, immediately lets the neutral atom go. The ion disappears! The scientists know they hit the right frequency because the ion vanished from the trap.

The Results: A Sharper Picture

By using this "Lithium bath" method, the scientists were able to measure the ion's energy levels with incredible precision.

• The Analogy: Imagine trying to measure the height of a wobbly tree in a storm. Previous methods were like trying to measure it while the wind blew it around (low precision). This new method is like tying the tree to a giant, steady anchor (the ultracold bath), allowing them to measure it with a ruler that has millimeter markings instead of just inches.
• The Achievement: Their measurements were 6 to 9 times more precise than previous experiments done with a hollow-cathode discharge (an old, less controlled method). They confirmed the magnetic and electric properties of the ion's structure with high confidence.

Why Does This Matter?

This technique is a game-changer for two reasons:

1. Complex Ions: It opens the door to studying other ions that are too "messy" or complex to be cooled by lasers alone.
2. Future Tech: Better measurements mean better atomic clocks (which keep time for GPS and the internet) and more stable qubits for quantum computers.

In summary: The scientists didn't try to force the difficult ion to behave. Instead, they gave it a "cooling bath" of ultracold atoms that constantly cleaned up its mess, allowing them to listen to its true voice with crystal-clear precision.

Technical Summary

1. Problem Statement

Precision laser spectroscopy of trapped ions is a cornerstone of atomic physics, quantum computing, and optical clock development. However, certain isotopes present significant challenges:

• Complex Level Structures: The $^{173}\text{Yb}^+$ ion has a nuclear spin of $I=5/2$, resulting in a large number of hyperfine sublevels. This complexity makes standard laser cooling and state detection difficult because the ion can easily "leak" into dark states (metastable states) that are not addressed by the cooling lasers.
• Limitations of Sympathetic Cooling: While sympathetic cooling with laser-cooled ions (e.g., $^{174}\text{Yb}^+$) can cool the translational (external) motion of a target ion, it does not cool the internal (hyperfine) degrees of freedom.
• Previous Methods: Traditional neutral buffer gas cooling (using room-temperature gases) cools internal states but lacks the precision and low collision energies required for high-resolution spectroscopy. Previous high-precision measurements of $^{173}\text{Yb}^+$ were limited by the resolution of hollow-cathode discharge experiments.

The Goal: To demonstrate a method for precision spectroscopy of a trapped $^{173}\text{Yb}^+$ ion that is not directly laser-cooled, by utilizing a bath of ultracold atoms to continuously cool its internal hyperfine states and detect excitation via state-selective ion loss.

2. Methodology

Experimental Setup

• Hybrid Trap: The experiment utilizes a hybrid ion-neutral trap. A linear Paul trap holds the ions, while a Magneto-Optical Trap (MOT) and Optical Dipole Trap (ODT) hold a cloud of ultracold fermionic $^6\text{Li}$ atoms.
• Ion Preparation:
  • A "bright" $^{174}\text{Yb}^+$ ion is loaded and Doppler-cooled to $\sim 0.5$ mK to serve as a probe.
  • A single "dark" $^{173}\text{Yb}^+$ ion is loaded via isotope-selective photoionization.
  • The two ions form a Coulomb crystal. The $^{174}\text{Yb}^+$ acts as a sympathetic coolant for the translational motion of the $^{173}\text{Yb}^+$.
• Atomic Bath: A cloud of $\sim 2 \times 10^4$ $^6\text{Li}$ atoms is prepared at $\sim 5$ $\mu$K and overlapped with the ion crystal using piezo-controlled mirrors.
• Spectroscopy Scheme:
  • Transition: The experiment probes the $6^2S_{1/2} \to 6^2P_{3/2}$ transition at 329 nm.
  • Laser System: A frequency-quadrupled diode laser is stabilized to an ultra-stable optical cavity. The frequency is scanned using an Acousto-Optic Modulator (AOM).
  • Pulse Sequence: A train of 100 laser pulses (15 $\mu$s width, 10 ms interval) is applied. The short pulse duration minimizes collisional broadening during the laser interaction.
  • Internal Cooling Mechanism: Between pulses, the $^{173}\text{Yb}^+$ ion interacts with the $^6\text{Li}$ bath. Spin-exchange collisions continuously repump the ion from excited hyperfine states back to the $F=3$ ground state, effectively closing the optical cycle and preventing leakage into dark states.

Detection Method: State-Selective Charge Transfer

• Unlike standard fluorescence detection (which is difficult for $^{173}\text{Yb}^+$ due to its complex structure), this experiment uses charge transfer as the detection signal.
• Mechanism:
  1. If the 329 nm laser excites the ion, it may spontaneously decay into metastable states ($^2D_{3/2}$ or $^2D_{5/2}$).
  2. The $^2D_{5/2}$ state further decays to the extremely long-lived $^2F_{7/2}$ state.
  3. Ions in these metastable states have a significantly higher probability of undergoing a charge-transfer collision with a $^6\text{Li}$ atom ($\text{Yb}^+ + \text{Li} \to \text{Yb} + \text{Li}^+$).
  4. The resulting $\text{Li}^+$ ion is too light to be stably trapped in the Paul trap and is lost.
  5. Signal: The loss of the $^{173}\text{Yb}^+$ ion is detected by observing the shift in the position of the remaining "bright" $^{174}\text{Yb}^+$ probe ion.

3. Key Contributions

1. Novel Cooling Technique: Demonstrated that an ultracold atomic bath can continuously cool the internal hyperfine degrees of freedom of a trapped ion via spin-exchange collisions, enabling spectroscopy on ions that are difficult to laser cool directly.
2. High-Precision Spectroscopy: Successfully measured the hyperfine structure of the $6^2P_{3/2}$ state in $^{173}\text{Yb}^+$ with unprecedented precision for this isotope.
3. Charge-Transfer Detection: Validated a robust detection scheme based on state-selective charge transfer and ion loss, bypassing the need for complex fluorescence detection schemes for complex ions.
4. Benchmarking: Validated the method by comparing results with $^{171}\text{Yb}^+$ (where standard laser cooling works) and confirming that the resonance centers coincide, despite the presence of the atomic bath.

4. Results

• Hyperfine Constants: The authors measured the magnetic dipole ($A$) and electric quadrupole ($B$) hyperfine interaction constants for the $6^2P_{3/2}$ state:
  • $A = -241(1)$ MHz
  • $B = 1460(8)$ MHz
  • These results are in agreement with previous hollow-cathode discharge measurements but are 6 to 9 times more precise.
• Transition Frequency: The absolute frequency of the $6^2S_{1/2} \to 6^2P_{3/2}$ central line was estimated to be 911.136272(20) THz.
• Spectral Features:
  • Three distinct peaks were observed corresponding to transitions from $F=3$ to $F'=\{2, 3, 4\}$.
  • The resonance linewidth in the presence of atoms was broader ($79 \pm 16$ MHz) compared to ion-only measurements ($50 \pm 5$ MHz). This broadening is attributed to kinetic energy release from inelastic collisions and collisions during laser interrogation.
• Comparison with Theory: The experimental values deviate from theoretical predictions (relativistic coupled-cluster and many-body perturbation theory). The authors attribute this to the difficulty in modeling the strong mixing of the $6^2P_{3/2}$ state with the $4f^{13}5d6s$ configuration.

5. Significance and Impact

• Optical Clocks and Qudits: $^{173}\text{Yb}^+$ is a promising candidate for next-generation optical clocks and qudit-based quantum computing due to its nuclear spin and hyperfine structure. This work provides the necessary high-precision data to refine these applications.
• New Physics: The ability to perform precision spectroscopy on $^{173}\text{Yb}^+$ allows for better tests of fundamental physics, including searches for variations in fundamental constants and new physics beyond the Standard Model.
• Generalizability: The technique is not limited to Ytterbium. It can be extended to other atomic ions with complex level structures, molecular ions, and anions, provided chemical reactions with the ultracold buffer gas are suppressed.
• Quantum Dynamics: The setup enables the study of quantum dynamics in ion-atom mixtures at collision energies in the $\mu$K regime, facilitating research into spin dynamics and collisional physics.

In conclusion, this paper establishes a powerful new paradigm for precision spectroscopy where ultracold atoms act not just as a coolant for motion, but as an active agent for internal state preparation, unlocking high-precision measurements for ions previously considered too complex for such techniques.