# Fidelity *F* of the full transfer driven by Gaussian pulses plus weak coupling decay versus the three-photon resonance mismatch Delta _{mathit {{
m eff}}}=Delta _R-(Delta _B-Delta _C-alpha _C Omega _C/2)

**Figure 6.** Fidelity *F* of the full transfer driven by Gaussian pulses plus weak coupling decay versus the three-photon resonance mismatch \Delta _{\mathit {{\rm eff}}}=\Delta _R-(\Delta _B-\Delta _C-\alpha _C \Omega _C/2). Common laser parameters are \Omega _B^0/2\pi =400 MHz and \Omega _R^0/2\pi =40 MHz. The strong coupling cases for the weak transition are for Ω_{C}/2π = 10 MHz, Δ_{C}/2π = 100 MHz, Δ*t* = 20μs and Δ_{B}/2π = 100 MHz (dashed blue line) and Δ_{B}/2π = 190 MHz (dot-dashed black line). The weak coupling cases are for Ω_{C}/2π = 1 MHz, Δ_{C}/2π = 10 MHz Δ*t* = 45 μs, Δ_{B}/2π = 100 MHz (red dotted line) and Δ_{B}/2π = 10 MHz (green solid line).

**Abstract**

A stimulated Raman adiabatic passage (STIRAP)-like scheme is proposed to exploit a three-photon resonance taking place in alkaline-earth-metal ions. This scheme is designed for state transfer between the two fine structure components of the metastable D-state which are two excited states that can serve as optical or THz qubit. The advantage of a coherent three-photon process compared to a two-photon STIRAP lies in the possibility of exact cancellation of the first-order Doppler shift which opens the way for an application to a sample composed of many ions. The transfer efficiency and its dependence with experimental parameters are analysed by numerical simulations. This efficiency is shown to reach a fidelity as high as (1–8 **×** 10^{−5}) with realistic parameters. The scheme is also extended to the synthesis of a linear combination of three stable or metastable states.