Optical repumping of triplet $P$-states enhances magneto-optical trapping of ytterbium atoms

Abstract: Radiative decay from the excited $^1P_1$ state to metastable $^3P_2$ and $^3P_0$ states is expected to limit attainable trapped atomic population in a magneto-optic trap of ytterbium (Yb) atoms. In experiments we have carried out with optical repumping of $^3P_{0,2}$ states to $^3P_1$, we observe enhancement of trapped atoms yield in the excited $^1P_1$ state. The individual decay rate to each metastable state is measured and the results show an excellent agreement with the theoretical values.

• The paper demonstrates that optical repumping from triplet P-states significantly reduces radiative losses in Yb MOT, improving trap lifetime by nearly 100%.
• It employs a five-level rate equation model with precise laser stabilization to measure decay rates and optimize repumping efficiency.
• The methodology paves the way for enhanced quantum state preparation in cold atom experiments, benefiting optical clocks and ultracold collision studies.

Optical Repumping of Triplet P-States Enhances Magneto-Optical Trapping of Ytterbium Atoms

Introduction

The presented study investigates the population dynamics and trapping efficiency of $^{174}$Yb atoms in a magneto-optic trap (MOT), specifically addressing the limiting role of radiative decays from the $^1P_1$ excited state to the metastable $^3P_0$ and $^3P_2$ triplet states. The inevitable leakage into these dark states has been a key bottleneck for maximizing MOT populations in Yb-based experiments. The authors experimentally implement and analyze targeted optical repumping from both $^3P_0$ and $^3P_2$ to $^3S_1$, enabling a significant enhancement in MOT atom numbers and lifetimes. The work also provides precision measurements of individual decay rates to the metastable states, benchmarking them against theoretical calculations.

Experimental Framework

The experimental setup centers on a six-beam MOT engineered for $^{174}$Yb, employing a diode laser at 398.9 nm, 15 MHz red-detuned from the $^1S_0$–$^1P_1$ resonance. The MOT operates with optimized parameters: a saturation parameter $s$ varied to set the fraction $f$ of the atomic population in the excited $^1P_1$ manifold (ranging from 0.05 to 0.2), and a Zeeman slower employing a 500 MHz detuning and approximately $10^{10}$–$10^{11}$ atoms/s flux from an effusive source at 400°C.

Shelving to $^3P_{0,2}$ was actively countered via additional ECDLs at 649.1 nm (for $^3P_0$–$^3S_1$) and 770.2 nm (for $^3P_2$–$^3S_1$), ensuring closed repumping cycles and enhanced recycling. The laser systems were stabilized using direct fluorescence monitoring for frequency locking. Calibration involved two-photon transitions facilitated by auxiliary lasers at 556 nm and 680 nm.

Population Dynamics and Rate Equation Analysis

To model the MOT and repumping system, the population evolution is described as a five-level scheme, focusing on the ground state, excited state, and three metastable triplet P-states. The rate equations capture the loading, radiative, and collisional dynamics, including Yb-background and Yb-Yb collisions. The authors introduce four operational regimes:

• NR (No Repumping): Decay occurs to both $^3P_0$ and $^3P_2$.
• A: Only $^3P_2$ is repumped.
• B: Only $^3P_0$ is repumped.
• A+B: Both $^3P_0$ and $^3P_2$ are simultaneously repumped.

Master equation calculations incorporating the various decay, loading, and collisional parameters underpin the quantitative analysis. The trapping loss rate $\Gamma$ is formulated as a function of the population fraction $f$ in the excited state and background/ballistic Yb flux collision terms, and the nonlinear Yb-Yb collisional coefficient $\beta(f)$.

Results: Repumping-Enhanced MOT Performance and Decay Rate Measurement

Systematic studies of the temporal decay of trapped atoms, performed via fluorescence monitoring following the cessation of Yb flux, enable a high-precision measurement of individual decay pathways. Fitting to the analytic solution of the rate equations allows extraction of $\Gamma$ under varied repumping conditions and leads to key findings:

• Full repumping of both $^3P_0$ and $^3P_2$ (case A+B) nearly eliminates radiative loss channels other than those arising from collisions, reducing the decay rate to less than $6.3 \times 10^{-3}\ \mathrm{s}^{-1}$ and increasing the trap lifetime by approximately 100%.
• Steady-state trapped atom number $N(0)$ exhibits only a 30% increase, attributed to the nontrivial dependence of the collisional loss rate on the atomic flux from the Zeeman slower (i.e., $\Gamma$ is a function of the loading rate $\eta$).

Linear regression of the loss rates as a function of $f$ for the four repumping scenarios yields decay rates $a_{\mathrm{NR}} = 6.48\ \mathrm{s}^{-1}$, $a_{\mathrm{A}} = 6.27\ \mathrm{s}^{-1}$, $a_{\mathrm{B}} = 4.14\ \mathrm{s}^{-1}$, all in agreement with theoretical values for $^3P_0$ and $^3P_2$ decay ($a_0 = 6.18\ \mathrm{s}^{-1}$, $a_2 = 0.37\ \mathrm{s}^{-1}$). This continues to validate the repumping scheme and the associated master equation modeling.

The uncertainty in the extracted rates, dominated by the estimation of $f$ (laser power inhomogeneity, detuning inaccuracies, magnetic field inhomogeneity), is benchmarked at 33%. This represents an improvement over earlier experimental values and narrows the gap between measurement and theory.

Implications and Prospects

The demonstration of loss suppression and population enhancement via efficient optical repumping provides a direct pathway for improved quantum state preparation in Yb-based cold atom experiments. By enabling increased steady-state populations and lifetimes, the method has immediate utility for high-precision metrological platforms, including optical lattice clocks and fundamental symmetry investigation devices, where population loss to dark metastable states is deleterious.

Moreover, the ability to accurately measure individual decay rates in these complex multilevel systems refines the modeling of cold atom kinetics and offers essential parameters for simulating ultracold collision and many-body physics in systems employing alkaline-earth-like atoms.

From a practical perspective, the approach facilitates more efficient loading for downstream applications, such as Bose-Einstein condensation, degenerate Fermi gases, and controlled molecule formation, without the added complexity of more intense vacuum requirements or altered magnetic trapping protocols.

Further research may extend these repumping protocols to isotopically-pure or fermionic ytterbium, test the limits of repumping for larger atomic ensembles, or integrate the method into multiplexed quantum information platforms where state purity and lifetime are critical.

Conclusion

The study provides a comprehensive experimental and theoretical investigation into the impact of optical repumping of triplet P-states on MOT efficiency for $^{174}$Yb. Enhanced atom number and trap lifetime are demonstrated, together with improved precision in decay rate measurement, and the results confirm theoretical predictions. This work establishes a scalable, broadly applicable methodology for the active elimination of population shelving in alkaline-earth and similar atomic species, advancing both fundamental research and technological applications in ultracold atomic physics.