Fig. 1. (a) Sketch of the experimental setup for dipole transition matrix elements with single trapped ion. (b) Yb+ energy-level diagram of low-lying states (not to scale), where r denotes the branching fraction of the 6p P1/22 state into the 5d D3/22 state.

Fig. 2. Simplified time sequence and associated energy level diagram (not to scale) displaying the 6p P1/22-5d D3/22 spontaneous decay rate measurements in a single Yb+ ion.

Fig. 3. The data points are fitted to determine key decay parameters. (a) The fitting curve for the decay parameter b at each 369 nm power p through decay probability P and its pulses duration time by using an exponential function Eq. (2). (b) The fitting curve for the spontaneous decay rate APD through variational decay parameter b and its corresponding laser power p by using Eq. (4). (c) The spontaneous decay rate APD is exponentially plotted against the detuning of the 369 nm laser frequency from the resonance frequency of the 6p P1/22-6s S1/22 transition. The shown data in (a) and (b) correspond to the point in (c) where the detuning is −6 MHz. The transition probability at the resonance frequency is determined to be 0.62796(81) μs−1.

Fig. 4. Comparison of experimental and theoretical branching fractions for the 6p P1/22-5d D3/22 transition in Yb+.