Figure 1: Experimental scheme and dynamic and adiabatic transition by anti-Jaynes–Cummings interaction.

(a) ¹⁷¹Yb⁺ system in a harmonic potential. The qubit level in S_1/2 manifold, and are coupled by the Raman laser beams, where the beat-note frequency is near resonant to the qubit levels, ω_HF. When the beat-note frequency is tuned to ∼ω_HF+ω_X, the scheme produces the anti-Jaynes–Cummings interaction or blue-sideband transition. We denote Ω as the Rabi frequency on the qubit transition and Δ is the frequency difference between the beat-note frequency of Raman beams and ω_HF+ω_X. The Raman beams are realized by picosecond pulse train similar to the scheme in ref. 45. (b) The controls of experimental parameters of Ω and Δ for the uniform blue-sideband transition. Naturally, the Rabi frequency of the blue-sideband transition is dependent on the motional quantum number n. To remove the n-dependency, we control Ω and Δ as the red and blue curves such as Ω(t)=Ω₀[sign(T/2−t)sin(πt/T)+iβ] and Δ(t)=Δ₀sign(T/2−t)cos(πt/T). The phase iβ in Ω is the counter-diabatic term to suppress the transition during the evolution. Here Ω₀=(2π)38.5 kHz, β=0.075 and Δ₀=1.6Ω₀. (c) The basic operation of the uniform blue-sideband transition without the dependence by the pulse shaping of b. (d) The experimental demonstration of the uniform blue-sideband transitions. The total time to execute the transitions is 91 μs for any (n=0, 1, ... 5).