Hyperfine spectroscopy of optical-cycling transitions in singly ionized thulium

This paper establishes a complete spectroscopic roadmap for optical cycling in singly ionized thulium-169 and characterizes a metastable state as a robust qubit candidate, thereby laying the foundational groundwork for advanced quantum applications.

The Gist

Imagine you are trying to build a tiny, super-fast computer using individual atoms. To do this, you need to catch an atom, freeze it in place, and teach it to "talk" to lasers so you can control it. This paper is about a team of scientists who decided to try this with a very special atom: Thulium (specifically, a positively charged version called Thulium ion, or Tm+).

Think of Thulium as a complex, multi-story building with many rooms (energy levels). The scientists wanted to turn this building into a "quantum computer" where they could store information (qubits) and process it. Here is the story of their journey, explained simply.

1. The Goal: A New Kind of Quantum Computer

Most quantum computers today use simple atoms (like the ones in a standard lightbulb filament). These are easy to control, but they are like one-room apartments: they don't have enough space to store complex information or separate "processing" from "memory."

Thulium is different. It's like a skyscraper. It has many floors (energy levels) and a huge number of rooms. This makes it perfect for advanced quantum tasks, but it's also much harder to navigate. The scientists' goal was to map out this skyscraper and figure out how to get the atom to stay in the right rooms without getting lost.

2. The Challenge: The "Leaky" Elevator

To control an atom, scientists use lasers to make it bounce up and down between energy levels, like an elevator. This bouncing creates a "traffic light" effect: if the atom is in the right room, it glows (fluoresces); if it's in the wrong room, it goes dark.

The problem with Thulium is that the "elevator" is leaky.

• When they tried to push the atom up with a 313 nm (UV) laser, it would sometimes fall down the wrong stairs into a "basement" (a long-lived, dark state) where it gets stuck and stops glowing.
• They also tried a 450 nm (Blue) laser, but that elevator was slow and also had leaks.

The Analogy: Imagine trying to wash a car with a hose (the laser). If the car has a giant hole in the bottom (the leak), the water just drains away, and you never get the car clean. The scientists had to find a way to plug those holes.

3. The Solution: The "Plumbing" Fix (Repumping)

The team discovered exactly where the leaks were. They found that when the atom fell into the "basement" (a specific energy level they nicknamed the "Gollum" state because it's deep and hidden), it needed a specific "rescue laser" to pull it back up.

They identified several "rescue pipes" (lasers at 846 nm, 1153 nm, and 1306 nm) that act like a vacuum cleaner, sucking the stuck atoms out of the basement and putting them back on the main elevator.

• The Result: By adding these rescue lasers, they created a closed loop. The atom can now bounce up and down thousands of times without getting stuck. This is called optical cycling, and it's the first step to cooling the atom down to near absolute zero.

4. The Discovery: The "Gollum" State as a Memory Bank

While the leaks were a problem for cooling, the scientists realized the "basement" (the Gollum state) was actually a goldmine.

• Why? Because once an atom falls there, it stays there for a very long time (over 5 minutes). In the quantum world, 5 minutes is an eternity!
• The Analogy: Think of the main laser cycle as a busy highway where cars (atoms) are zooming around. The Gollum state is a quiet, secure parking garage. You can park a car there, lock it up, and know it will be exactly where you left it hours later.
• The Application: This makes the Gollum state a perfect quantum memory. You can store a piece of information (a qubit) there, and it won't fade away.

5. The "Secret Code" (Microwaves)

To read and write information in this parking garage, the scientists used microwaves (like the kind in your kitchen, but much more precise).

• They found that the parking garage has two main sections (hyperfine levels).
• They discovered a weird, beautiful symmetry: because of the atom's internal structure, many of the "doors" between these sections are degenerate (they open at the exact same frequency).
• The Analogy: Imagine a hotel where 24 different rooms all share the same key. This is actually a good thing! It means you don't need 24 different keys (lasers) to control the atom; you can use fewer, simpler tools to move the information around.

6. The Hurdles: Why It's Not Ready Yet

Despite mapping the whole building and finding the keys, the scientists admit they haven't successfully "cooled" the atom yet.

• The Problem: Even with the rescue lasers, the atom still gets stuck in other dark rooms for a few milliseconds. It's like the car is still leaking a little bit of water.
• The Fix: They suspect they just need to find a few more "rescue pipes" (lasers at 749 nm) to plug the remaining leaks. They also tried using a different atom (Barium) to help cool the Thulium, but the Barium was too "pushy" and knocked the Thulium out of the trap.

Summary: What Does This Mean for the Future?

This paper is the blueprint for a new quantum computer.

1. The Map: They drew the complete map of the Thulium atom's energy levels.
2. The Plumbing: They found the leaks and the rescue lasers needed to keep the atom cycling.
3. The Memory: They identified a super-stable "parking garage" (the Gollum state) perfect for storing quantum data.
4. The Control: They proved you can use microwaves to control the data in that garage with extreme precision.

The Bottom Line: Thulium is a complex, high-rise building that is hard to manage, but the scientists have finally found the keys and the plumbing. Once they fix the last few leaks, this "skyscraper" could become a powerful new home for the quantum computers of the future, capable of solving problems that are impossible for today's machines.

Technical Summary

1. Problem Statement

While neutral-atom quantum platforms (alkalis, alkaline-earth-like atoms, rare-earths) are mature, trapped-ion quantum computing has largely been restricted to alkaline-earth and alkaline-earth-like ions with simple $ns$ $^2S_{1/2}$ ground states. These simple structures lack the rich internal state manifolds required for advanced architectures, such as partitioning roles between processing and memory qubits (e.g., the "omg" qubit protocol).

Rare-earth ions with open 4f-shells, like Thulium ($^{169}\text{Tm}^+$), offer large total electronic angular momentum ($J$) manifolds and unique nuclear spin properties ($I=1/2$) that could enable robust qubit architectures. However, prior to this work, there were no experimental demonstrations of laser cooling for open-4f-shell rare-earth ions, and the complete spectroscopic roadmap (hyperfine structure, transition strengths, and leakage channels) required for optical cycling was unknown.

2. Methodology

The authors employed a multi-faceted experimental approach to map the energy levels and hyperfine structure (HFS) of $^{169}\text{Tm}^+$:

• Experimental Setups:
  • Hollow-Cathode Lamp (HCL): Used for preliminary absorption spectroscopy to locate strong transitions and measure HFS quickly and cost-effectively.
  • Ablation Cell: A vacuum chamber where a Tm target was ablated by 1064 nm laser pulses to generate a plume of Tm$^+$ ions for initial fluorescence detection.
  • Linear Quadrupole Ion Trap: The primary apparatus for high-resolution fluorescence spectroscopy. Tm$^+$ ions were loaded via 532 nm laser ablation. The trap operated with or without Helium (He) buffer gas to study quenching effects.
• Spectroscopic Techniques:
  • Fluorescence Spectroscopy: Used to identify optical cycling transitions at 313 nm and 448/453 nm.
  • Repumping Search: Systematically scanned near-infrared wavelengths (749 nm to 1307 nm) to identify transitions that return population from metastable "leakage" states back to the cooling cycle.
  • Microwave Spectroscopy: Performed on a metastable state to resolve Zeeman sublevels and measure hyperfine splitting with kHz precision.
  • Lifetime Measurements: Utilized a pump-probe sequence (313 nm pump, 450 nm probe, 846 nm repump) to measure the decay time of the metastable state.

3. Key Contributions

The paper establishes the first complete spectroscopic foundation for laser cooling and quantum control of $^{169}\text{Tm}^+$:

• Optical Cycling Roadmap: Identified and characterized two primary cooling schemes:
  1. 313 nm Cycle: Connects the ground state ($^3F_4$) to a $J=5$ excited state. It offers a high scattering rate but suffers from significant leakage to metastable states.
  2. 450 nm Cycle: Connects the ground state to $J=4$ states (448/453 nm). It has a narrower linewidth (better for Doppler cooling limits) but weaker transition strengths.
• Leakage Channel Identification: Mapped the decay pathways from excited states. Crucially, they identified that population eventually accumulates in a long-lived metastable state at 12,457.29 cm$^{-1}$ (the "Gollum" state, $^3H_6$) and other intermediate states.
• Repumping Strategy: Determined the necessary near-infrared repumping lasers (specifically 846 nm, 1153 nm, and 1287 nm) to close the optical cycles by returning population from the metastable states to the cooling transitions.
• Hyperfine Constants: Measured the magnetic-dipole hyperfine $A$ constants for all relevant levels involved in the cooling cycles, providing the frequency references needed for laser stabilization.

4. Key Results

• Hyperfine Structure (HFS):

  • Determined $A$ constants for excited states (e.g., $A \approx -0.72$ GHz for the 319,268 cm$^{-1}$ state).
  • Confirmed that due to $I=1/2$, each fine-structure level splits into only two hyperfine components ($F = J \pm 1/2$), simplifying the frequency requirements for closed population transfer.
  • HFS splittings range from 1 to 5 GHz, ideal for microwave-based qubit operations.

• Metastable State Characterization ("Gollum" State):

  • Lifetime: Measured a minimum lifetime of 5.2(3) minutes for the 12,457.29 cm$^{-1}$ state. This is sufficiently long for qubit storage and gate operations.
  • Microwave Spectroscopy: Resolved the Zeeman structure of the $F=11/2$ and $F=13/2$ sublevels. The splitting is 2.554 GHz.
  • Degeneracy Anomaly: Observed a unique degeneracy in the microwave transitions due to the specific ratio of Landé $g$-factors for $I=1/2$ and integer $J$. This results in fewer distinct peaks than naively expected, which can be exploited to minimize the number of frequency tones required for state initialization.

• Cooling Challenges:

  • Despite mapping the cycles, direct laser cooling was not yet achieved in the experiment.
  • Cause: Population "shelving" into intermediate odd-parity states (e.g., at 8,957 cm$^{-1}$) on millisecond timescales severely limits the photon scattering rate.
  • Buffer Gas Effect: The addition of Helium buffer gas significantly increased the fluorescence signal, suggesting it quenches undiscovered long-lived leakage channels.

5. Significance

This work provides the critical "blueprint" for using $^{169}\text{Tm}^+$ as a quantum platform:

1. New Quantum Platform: It validates $^{169}\text{Tm}^+$ as a candidate for advanced quantum architectures that require distinct qubit types (processing vs. memory) within a single ion species.
2. High-$J$ Advantage: The large angular momentum ($J=6$ for the metastable state) enables robust absorption-emission error correction codes (Æ codes).
3. Simplified Control: The $I=1/2$ nuclear spin reduces the complexity of the hyperfine structure, making state preparation and measurement (SPAM) more feasible compared to other rare-earth ions.
4. Future Pathways: The paper outlines the specific laser inventory (UV, visible, and IR wavelengths) and repumping strategies required to achieve direct Doppler cooling. It also suggests sympathetic cooling with ions of similar mass (e.g., $^{171}\text{Yb}^+$) as a solution to current co-trapping difficulties with Barium.

In summary, the authors have successfully mapped the complex energy landscape of singly ionized thulium, identified a robust metastable qubit candidate with a multi-minute lifetime, and defined the necessary experimental conditions to realize laser cooling and quantum control in this system.