Unexpectedly Allowed Transition in Two Inductively Coupled Transmons

We present experimental results in which the unexpected zero-two transition of a circuit composed of two inductively coupled transmons is observed. This transition shows an unusual magnetic flux dependence with a clear disappearance at zero magnetic flux. In a transmon qubit, the symmetry of the wave functions prevents this transition to occur due to selection rule. In our circuit, the Josephson effect introduces strong couplings between the two normal modes of the artificial atom. This leads to a coherent superposition of states from the two modes, enabling such transitions to occur.