The Rayleigh–Lorentz invariant for superconducting resonators and optimal adiabatic qubit-information detection

Dynamical properties of a resonator can be analyzed using the Rayleigh–Lorentz invariant which is not an exact constant but varies more or less over time depending on variations of parameters. We investigate the time behavior of this invariant for a superconducting nano-resonator in order for better understanding of qubit-information detection with the resonator. Superconducting resonators which uses parametric resonance in a Josephson junction circuit can be utilized in implementing diverse next generation nano-optic and nano-electronic devices such as quantum computing systems. Through the analyses of the temporal evolution of the invariant, we derive a condition for optimal adiabatic qubit-information detection with the resonator. This condition is helpful for controlling the dynamics of the resonators over long periods of time. It is necessary to consider it when designing a nano-resonator used for quantum nondemolition readouts of qubit states, crucial in quantum computation.