Laser Cooling and Hyperfine Measurements of Radium-225 Ions

Technical Summary: Laser Cooling and Hyperfine Measurements of Radium-225 Ions

Problem and Motivation
Atoms with magnetic field-insensitive transitions are highly desirable for quantum information science (QIS) and precision measurements. Specifically, alkali-like ions with a single unpaired electron and half-integer nuclear spin ($I=1/2$) possess a ground state qubit formed by two $m_F=0$ spin projection states. These states are first-order insensitive to magnetic field noise, making them ideal for laser-driven gates and optical clocks. While such features exist in ions like $^{171}\text{Yb}^+$ and $^{133}\text{Ba}^+$, the $^{225}\text{Ra}^+$ ion ($I=1/2$) offers distinct advantages, including a low charge-to-mass ratio and optical transitions at convenient infrared wavelengths (828 nm and 1079 nm). These properties could enable compact, transportable optical clocks using integrated photonics. However, working with $^{225}\text{Ra}$ presents a significant challenge due to its short half-life of 15 days. Prior to this work, there was a discrepancy in the literature regarding the ground state hyperfine splitting, and the hyperfine structure of the excited $^2\text{D}_{3/2}$ state had not been measured.

Methodology
The authors established a long-term experimental platform for laser cooling and trapping of single $^{225}\text{Ra}^+$ ions within a sealed vacuum system.

• Source Generation: To overcome the short half-life, the team utilized a molecular beam epitaxy (MBE) oven containing 8 $\mu$Ci of $^{229}\text{Th}$ (7800 yr half-life) deposited in a titanium crucible. The continuous decay of $^{229}\text{Th}$ replenishes the $^{225}\text{Ra}$ source, generating approximately $3 \times 10^{11}$ atoms over one $^{225}\text{Ra}$ half-life. The oven is heated to 350–500 °C to effuse radium atoms.
• Trapping and Cooling: Neutral radium atoms are photoionized via a two-stage process (483 nm to $^1\text{P}_1$, then 450 nm to ionize) and loaded into a linear Paul trap. The ions are laser-cooled using transitions from the $^2\text{S}_{1/2}$ and $^2\text{D}_{3/2}$ states to the $^2\text{P}_{1/2}$ state at 468 nm. A repump laser at 1079 nm returns ions from the metastable $^2\text{D}_{3/2}$ state to the ground state.
• Spectroscopy and Control: Four lasers address all hyperfine levels, with frequencies stabilized to an optical cavity. Microwave spectroscopy (using a horn 10 cm from the trap) drives transitions between the ground state hyperfine levels. State preparation and measurement (SPAM) utilize the $^2\text{S}_{1/2} \leftrightarrow ^2\text{P}_{1/2}$ and $^2\text{D}_{3/2} \leftrightarrow ^2\text{P}_{1/2}$ transitions.
• Measurement Techniques: The team employed interleaved Ramsey and Rabi spectroscopy sequences to measure the ground state hyperfine splitting. Quadratic Zeeman shifts were characterized by varying the magnetic field strength using permanent magnets. Hyperfine constants for excited states were determined by scanning the first-order sidebands of fiber electro-optic modulators (EOMs) across relevant transitions.

Key Contributions and Results
The paper reports the first comprehensive laser cooling and hyperfine spectroscopy of trapped $^{225}\text{Ra}^+$ ions, yielding the following specific results:

1. Ground State Hyperfine Constant: The authors measured the ground state hyperfine constant $A(^2\text{S}_{1/2}) = -27.684\,511\,052(5)$ GHz. This result resolves a previous 3.6$\sigma$ discrepancy in the literature, aligning with the earlier measurement by Ahmad et al. [24] rather than the later re-measurement by Neu et al. [25].
2. Quadratic Zeeman Coefficient: The quadratic Zeeman shift coefficient for the clock transition ($^2\text{S}_{1/2}(F=0, m_F=0) \leftrightarrow ^2\text{S}_{1/2}(F=1, m_F=0)$) was determined to be $C_2 = 142.3(1.0)$ Hz G$^{-2}$, consistent with theoretical calculations.
3. Excited State Hyperfine Constants:
   • For the $^2\text{P}_{1/2}$ state: $A(^2\text{P}_{1/2}) = -5.447(4)$ GHz. This improves the precision of previous measurements by a factor of 1.9.
   • For the $^2\text{D}_{3/2}$ state: $A(^2\text{D}_{3/2}) = -619.7(1.1)$ MHz. This represents the first measurement of this constant.
4. State Preparation and Measurement (SPAM): The team demonstrated high-fidelity control of the hyperfine qubit using only the three lowest electronic levels (no auxiliary shelving). They achieved a SPAM fidelity of $F = 0.9951(9)$, with false identification fractions of $\epsilon_0 = 0.0035(8)$ and $\epsilon_1 = 0.007(2)$.

Significance and Claims
The authors claim that this work establishes $^{225}\text{Ra}^+$ as a viable candidate for both optical clocks and quantum information science applications.

• Clock Potential: The demonstrated ability to operate a $^{225}\text{Ra}^+$ trap for over two years in a sealed system, combined with the large hyperfine splittings, supports the development of an optical clock operable with only two infrared wavelengths.
• QIS Applications: The high SPAM fidelity and the straightforward initialization/control of the $I=1/2$ hyperfine qubit make the system suitable for QIS.
• Nuclear Physics: The precise hyperfine measurements allow for a more refined determination of the Bohr-Weisskopf effect (nuclear magnetization distribution), reducing uncertainties in theoretical models of nuclear structure.
• Future Pathways: The work lays the groundwork for synthesizing laser-cooled radium molecules for enhanced sensitivity to time-reversal symmetry tests (Schiff moment) and provides a potential route to trapping actinium ions ($^{225}\text{Ac}^{2+}$) via the beta-decay of trapped $^{225}\text{Ra}^+$.