In contrast to natural atoms, the potential energies for superconducting flux qubit (SFQ) circuits can be artificially controlled. When the inversion symmetry of the potential energy is broken, we find that the multi-photon processes can coexist in the multi-level SFQ circuits. Moreover, there are not only transverse but also longitudinal couplings between the external magnetic fields and the SFQs when the inversion symmetry of potential energy is broken. The longitudinal coupling would induce some new phenomena in the SFQs. Here we will show how the longitudinal coupling can result in the coexistence of multi-photon processes in a two-level system formed by a SFQ circuit. We also show that the SFQs can become transparent to the transverse coupling fields when the longitudinal coupling fields satisfy the certain conditions. We further show that the quantum Zeno effect can also be induced by the longitudinal coupling in the SFQs. Finally we clarify why the longitudinal coupling can induce coexistence and disappearance of single- and two-photon processes for a driven SFQ, which is coupled to a single-mode quantized field.
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