Fig. 3: Qubit population dynamics with an excited resonator mode.

The qubit starts in the ground state and transitions the bosonic modes, one of which is excited. Each column of the panels corresponds to a different initial state, where the resonators are excited in ascending order (b_i for the ith resonator). In the experiment a–d, a single resonator is prepared in a state with a low average population. e–h QuTiP simulation of the dynamics (compare a to e, etc.). We find coherent oscillations of the qubit population. As expected from a series of beamsplitters, the amplitude depends strongly on the excited resonator, i.e., where the photon is injected in the beamsplitter setup. i Transient dynamics for t_rise = 50 ns for a larger average photon number in resonator b₁. Shaded areas indicate the standard deviation of the qubit population. Neighboring traces are shifted by 0.25 to improve visibility. By increasing the duration t_p (shown for 250, 300, 400, 550, and 750 ns) of the pump pulse higher Fock states contribute to the dynamics of the system. The \(\sqrt{n}\)-scaling of the effective coupling strength between qubit and resonator with the photon number n of the respective Fock state increases the Landau-Zener tunneling probability, see Eq. (2). Initially, this results in a greater oscillation amplitude and a larger final value of the qubit population after the transit, but gradually shifts towards an adiabatic transition. For t_p = 750 ns, the coherent oscillations of the qubit population are fully suppressed and the qubit is (approximately) in the excited state upon reaching ω_f.