Fig. 4: Spectroscopy measurements.

a–d Two-tone reflection spectroscopy (background subtracted) of the lowest transitions of the circuit along the four edges of the primitive cell in the two-dimensional external flux landscape (inset diagrams), and (e–h) accompanying readout spectroscopy. Theoretical transition frequencies from the ground state (semi-transparent white lines) are obtained from numerical diagonalization of the five-mode circuit model with seven fitted Hamiltonian parameters (see Table 1). Additionally, transition frequencies from the first excited state (semi-transparent blue lines) are shown when the first excited state has a transition frequency that falls below 2.5 GHz and is therefore thermally occupied. Note that this model includes the nearly harmonic readout and parasitic modes [labeled in (a)]. Scans around the \(\left\vert 0\right\rangle \to \left\vert n\right\rangle\) transitions for n = 1 − 4 [labeled in (d)] are enlarged in Fig. S8.