Fig. 3: Closed loops that lead to mode conversion.

a Counterclockwise loop starting at \(\left|{\psi }_{+}\right\rangle\) and ending at \(\left|{\psi }_{-}\right\rangle\). b Clockwise loop starting at \(\left|{\psi }_{-}\right\rangle\) and ending at \(\left|{\psi }_{+}\right\rangle\). Evolution of the system’s state along the closed loop trajectory is characterized by the fidelity \(\langle {\psi }_{+}|\rho (t)\left|{\psi }_{+}\right\rangle\) in (a) and the fidelity \(\langle {\psi }_{-}|\rho (t)\left|{\psi }_{-}\right\rangle\) in (b). The circles and error bars respectively denote the average and standard deviations of 10000 measurements. The solid curves are obtained by simulating master equations. Durations of the five strokes are T₁ = T₅ = 6 μs, T₃ = 12 μs, and T₂ = T₄ = 150 μs. Other parameters are Ω/2π = 120 kHz, Δ_min/2π = −400 kHz, Δ_max/2π = 400 kHz, γ_min ≈ 0 kHz, and γ_max ≈ 1.45 MHz