Fig. 4

Photon dynamics in phase space in the DSC regime (degenerate-qubit case) from maximum-likelihood Wigner tomography. a Selected frames from a ‘movie’ (measured over ∼40 h) showing the phase-space evolution of the resonator reduced state for r ∼ 0.9 (frames labelled by Trotter step n and simulated time), with the final panel showing the full trajectories determined from 2D double-Gaussian fits to the raw data (the full movie is provided in the Supplementary Movie 1). Plotted tomograms are maximum-likelihood reconstructions of direct Wigner tomography measured data with a systematic phase correction (see Methods section). When the effective drive on the intracavity field created by the Rabi interaction has a strength comparable to the resonator’s natural frequency (i.e., \({g^{\rm{R}}}\sim \omega _{\rm{r}}^{\rm{R}}\)), this drive is able to create a significant displacement of the cavity field before the phase-space rotation caused by \(\omega _{\rm{r}}^{\rm{R}}\) brings the field back towards the origin. This effect is observed clearly here in the creation of two well-resolved, rotating peaks and subsequent re-coalescence which are characteristic signatures of DSC dynamics. Deviation from the ideal circular trajectories (orange curves) arises from photon decay. The measured trajectory shows excellent agreement with a numerical Trotter simulation at g ^R/2π = 1.79 MHz which includes resonator T _1,r = 3.5 μs (green curves). From the fits, we calculate an estimated Wigner function width σ = 0.526 ± 0.003, instead of the predicted 0.5, indicating a displacement calibration error of ∼5% (Supplementary Note 6). Background noise arises from phase instability of microwave sources and frequency stability of the Wigner qubit over the long measurement. b–e Conditional phase-space evolution illustrated by the resonator Wigner function for different initial states of Q _R: b \(\left| 0 \right\rangle\), c \(\left| 1 \right\rangle\), d \(\left| + \right\rangle\) and e \(\left| - \right\rangle\). The phase-space trajectory of R _R depends on the qubit state in the σ _x basis, consistent with creation of Bell-cat hybrid entanglement between Q _R and R _R of the form: \({\left| + \right\rangle _{\rm{Q}}}{\left| { + \alpha } \right\rangle _{\rm{R}}} - {\left| - \right\rangle _{\rm{Q}}}{\left| { - \alpha } \right\rangle _{\rm{R}}}\).