An important characteristic of a quantum LC oscillator is th…

An important characteristic of a quantum LC oscillator is that its energy eigenstates are equally spaced.  In contrast, a Transmon (i.e., quantum anharmonic oscillator with capacitive energy EC{“version”:”1.1″,”math”:”\(E_C\)”} and inductive energy EJ{“version”:”1.1″,”math”:”\(E_J\)”}) due to Josephson junction introduces shifts in the energy levels of the oscillator.  To first order in perturbation theory, what is the energy spacing between the ground (i.e., |0⟩{“version”:”1.1″,”math”:”\(\vert 0 \rangle\)”}) and the first (i.e., |1⟩{“version”:”1.1″,”math”:”\(\vert 1 \rangle\)”}) excited state?