Quantum metrology harnesses entanglement to improve measurement precision beyond classical limits. While standard protocols rely on two-level qubits to estimate a single parameter, extending them to entangled multi-level qudits enables the optimal simultaneous estimation of multiple parameters within a single probe. However, generating such multi-level entanglement and harnessing it for joint multi-parameter estimation in atomic clocks has remained an outstanding challenge. Here, we experimentally demonstrate genuine qutrit entanglement and joint multi-parameter estimation in an optical clock platform. Leveraging control over the ground state and two fine-structure clock states of
88Sr atoms trapped in triple-magic optical tweezers, we generate a maximally entangled two-qutrit state with a loss-postselected fidelity of F = 0.85(1), certifying genuine multi-level entanglement. Taking advantage of this high-dimensional entanglement, we theoretically construct and experimentally realize an optimal two-qutrit metrological probe state and noise-robust readout circuit to simultaneously estimate injected phases on two optical clock transitions. We observe a joint estimation variance below the ideal individual two-level sensing threshold, and show theoretically that this advantage persists at state-of-the-art atom numbers under circuit-level noise. These results demonstrate the key building blocks towards quantum information science with high-dimensional states encoded in the internal energy levels of neutral atoms.
We report the characterization of the forced damped harmonic oscillations of 133 Cs atoms in a magneto-optical trap, which was realized by modulating the intensity of the lasers counterpropagating along the anti-Helmholtz coil axis. Trap parameters such as trap frequency, damping coefficient, and magnitude of the driving force were determined from the resonant vibrational amplitude of the 133 Cs atomic cloud depending on the modulation frequency of the modulated laser intensity. The experimental results were compared with the theoretical ones based on the simple two-level and multi-level atom models, considering all possible transition lines used to trap the 133 Cs atom, and were found to be consistent with their theoretical counterparts. Furthermore, we theoretically examined the effect of the repumping laser on trap parameters.