When reading literature on transmon, or in general charge, superconducting qubits the explanation usually starts from why two metallic islands with a bridge can be seen as LC-circuit, how that is a harmonic oscillator in mathematical terms, then the harmonic oscillator is quantized and finally the non-linearity is added and explained that this is implemented by a Josephson Junction. I understand these mathematical descriptions. But what is missing for me:
How does the quantization happen in the physical implementation? Why does the superconductivity quantize the harmonic oscillator? Is there an explanation for which one does not need to understand BCS theory in depth?
