Due to long coherence time and exceptional controllability, trapped-ion systems have become a fundamental experimental platform for frontier research fields, including large-scale quantum computing, high-precision atomic clocks, and weak force measurements. Among the various ions suitable for experimental research, 171Yb+ has gained significant attention in recent years due to its nonzero nuclear spin and complex electronic structure of the excited states, which give rise to a rich energy level spectrum. A detailed investigation of its level structure deepens the understanding of its transition mechanisms. In particular, its long-lived metastable states serve as ideal reference for clock transitions and enable qubit encoding. The electric quadrupole (E2) transition between the ground and metastable states is more complex than electric dipole transitions, as it is influenced by the polarization and external magnetic field geometry. Consequently, a comprehensive study of E2 transitions in 171Yb+ not only provides crucial experimental guidance for optimizing energy-level selection and transition efficiency in high-precision optical clocks but also expands precision measurement techniques based on quadrupole transitions. These techniques can be applied to probing potential variations in fundamental physical constants in fundamental physics. Moreover, the long-lived metastable states and multi-level structure of 171Yb+ hold significant potential for quantum information processing. In contrast to standard qubit encoding that relies on two-level systems, utilizing the metastable states allows for qudit encoding, thereby enhancing storage capacity and computational efficiency in quantum computing. Additionally, the dependence of E2 transitions on light field polarization can be exploited to engineer highly controllable photon-atom interactions, which enables the simulation of topological phases and non-Hermitian quantum systems.

We investigate the E2 transition of 171Yb+ ions through theoretical analysis and experimental measurements. Theoretically, we construct a Hamiltonian incorporating multipole interactions and apply the Wigner-Eckart theorem to derive E2 transition matrix elements, which enables the calculation of transition strength coefficients from the ground to the metastable state. Experimentally, a single 171Yb+ ion is confined in a linear Paul trap with four gold-plated ceramic blade electrodes. A combination of radiofrequency (RF) and direct current (DC) fields generates a stable three-dimensional trapping potential. Three pairs of Helmholtz coils provide a controlled magnetic field along orthogonal directions, calibrated via Zeeman splitting of the 2S1/2 state. The experiment is controlled using the advanced real-time infrastructure for quantum physics (ARTIQ), which precisely regulates acousto-optic modulators (AOMs) and microwave channels. The experimental sequence consists of four stages: Doppler cooling, state preparation, E2 transition manipulation, and state detection. The ion is cooled to the Doppler limit with a 369.5 nm laser and initialized to the 2S1/2F=0. The E2 transition is then driven by a single-frequency 435.5 nm laser, whose frequency is precisely tuned via AOM control. A 369.5 nm laser is used to perform fluorescence detection on the 2S1/2F=1, and the population distribution is statistically analyzed. By scanning the laser frequency, Zeeman sublevels of 2D3/2 are selectively excited, which enables the measurement of their Zeeman splitting. To examine geometric effects on the E2 transition, we vary the laser polarization angle relative to the magnetic field while keeping the field and laser propagation directions fixed. This allows precise measurement of the coupling strength variation in the 2S1/2→D23/2 transition, providing insights into the role of geometric factors. To further enhance spectral resolution and improve experimental measurement precision, we employ the Pound-Drever-Hall (PDH) stabilization technique to frequency-lock the 435.5 nm laser.

We calculate the energy level structure of the ytterbium ion below 60000 cm-1, including the even-parity levels 4f146s, 4f145d, 4f136s6p, and 4f135d6p, as well as the odd-parity levels 4f136s2, 4f146p, 4f135d6s, and 4f135d2, covering electronic configurations of 6s-4f-5d-6p (Fig. 1). By constructing the multipole interaction Hamiltonian between the ion and the optical field, we derive the matrix elements for the E2 transition and calculate the relative strength coefficients for transitions from the ground state to metastable states in 171Yb+ (Table 1). Experimentally, we utilize 435.5 nm laser light to realize transitions from 2S1/2 to 2D3/2 in a 171Yb+ ion. By adjusting the angle ψ between the laser polarization vector and the projection of the magnetic field on the wavefront plane of laser while keeping the field direction and laser propagation axis fixed, we further investigate the variation of the E2 transition coupling strength between F=1 state and 2D3/2F=2,M=∓1. As ψ increases from 0° to 90°, fluorescence intensity exhibits a decreasing trend, which indicates that the E2 coupling strength for the 2S1/2→D23/2 transition gradually weakens [Fig. 4(d)]. This trend is consistent with theoretical calculations, which predicts that ξ±1(90°,0°)>ξ±1(90°,45°)>ξ±1(90°,90°)=0. By changing the magnetic field direction, specific level transitions can be selectively coupled [Figs. 4(c) and 5(c)]. Furthermore, by employing the PDH stabilization technique, we achieve a linewidth of the observed fluorescence peak on the order of kHz [Fig. 5(d)]. In this condition, the measurement precision of Zeeman splitting is increased by three times compared to the wavelength-meter-based stabilization results shown in Fig. 4. Our study systematically reveals the critical role of geometric factors in determining the E2 transition coupling strength, thereby providing experimental evidence for precise control of transition selectivity.

We systematically investigate the energy level structure of the 171Yb+ ion, including excited states spanning the 6s-4f-5d-6p shells and their common hyperfine levels. Based on angular momentum theory, the E2 transition matrix elements are derived, with their explicit forms given by Wigner 3-j and 6-j symbols. The transition strength coefficients from the ground state to the metastable state of the 171Yb+ ion are also calculated. Experimental results on the E2 transition from the 2S1/2 to the 2D3/2 state of the 171Yb+ ion show that transition occurs only under specific magnetic field directions and the laser polarization configurations at the resonant frequency. We lay the foundation for precise control of electric quadrupole transitions between the magnetic sublevels of the ground and metastable states and provide an experimental basis for further advancements in quantum information processing and quantum simulation research.