Modified SQUID Operator Equation for a Single-Qubit Structure Coupled to a Quantum Resonator

Role of self-inductance in superconducting quantum interference device (SQUID) charge qubit is considered. It is found that when an SQUID charge qubit is coupled to a quantum LC resonator, the SQUID voltage operator equation is modified in accompanying with the modification of operator Faraday equation describing the inductance. It is shown that when the extra energy is applied to the junction, the mean phase will be squeezed according to a damping factor.