Microwave Spectroscopy of a Josephson Junction Rhombi Chain*

It has been proposed that Josephson Junction (JJ) Rhombi chains can be used as a superconducting qubit symmetry protected from local noises [1]. We have studied the microwave response of a two-rhombi chain coupled to a lumped-element microwave resonator. The resonance frequency of this circuit was measured as a function of the phase $\varphi$ across the JJ Rhombi chain. The effective inductance of the JJ Rhombi as a function of $\varphi$ oscillates with a period $\Delta\varphi$=$\pi$ when the magnetic flux $\Phi$ in the Rhombi approaches half a flux quantum. In this regime, microwave spectroscopy of the first excited state of the JJ Rhombi was performed as a function of $\varphi$ and the gate-controlled charge on the central island of the two-Rhombi chain. The results of the microwave spectroscopy are in agreement with numerical simulations. We also discuss the results of time domain measurements of the Rhombi chain which establishes a baseline for the future coherence time measurements for longer (and, thus, more protected) chains. \\[4pt] [1] S. Gladchenko et al., ``Superconducting Nanocircuits for Topologically Protected Qubits,'' Nature Physics 5, 48 (2009).