a An experimental curve (blue) of the transmission amplitude with a dip centered on the qubit transition frequency. It is fitted by a Lorentzian (red curve). b The qubit energy spectrum. The green vertical line shows the section where data for a plot (a) was measured. The green dashed rectangle represents a region of spectral line splittings shown in more detail on a subplot (c). c Spectral line splittings demonstrating interaction between the qubit and four quasinormal modes (QNMs) of the phononic crystal at four frequencies. d The simulated transmission phase color plot obtained from simulations of the system. It reproduces the experimental anticrossings shown on (c).