Fig. 3.

Photon number dynamics of the quantum Rabi model in the degenerate-qubit case. a, b Average photon number is probed by applying Ramsey and echo-like pulses to Q _W. The effective Ramsey pulse separation τ determines the photon dynamic range. Because of finite pulse widths, reaching the small τ needed for high dynamic ranges b requires an unbalanced ‘echo’-like sequence. c, e Measured photon number dynamics up to 60 Trotter steps using a low-dynamic-range (LDR) photon number meter ($\tau ~18.7$ ns) with a linear range of ∼0–8 photons (indicated by grey regions in e). Large photon populations in the resonator highlight the non-conservation of excitation number in the quantum Rabi model. The resonator displays clear oscillations up to r > 1.8 in good agreement with the expected qubit revival times (dashed curves). The red feature in the middle reflects the upper limit on the number meter’s dynamic range set by Q _W ‘population wrapping’ at high photon numbers. d Measured photon dynamics up to 90 Trotter steps using a high-dynamic-range (HDR) number meter with $\tau ~6.5$ ns and a linear range of ∼0–20 photons, allowing observation of photon oscillations beyond 1.5 μs of simulated time (more than 75 Trotter steps). This data shows the effect of a residual Kerr nonlinearity at high values of r. e Line slices are plotted for evenly spaced resonator-coupling frequency ratios between the red and blue dashed lines shown in c. Grey regions delineate the linear range of the number meter. f Maximum measured average photon number for each value of r for both LDR and HDR number meters.