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We study the dynamics of a quantum superconducting circuit which is theanalogue of an atom in a high-Q cavity. The circuit consists of a Josephsoncharge qubit coupled to a superconducting resonator. The charge qubit can betreated as a two level quantum system whose energy separation is split by theJosephson energy $E_j$. The superconducting resonator in our proposal is theanalogue of a photon box and is described by a quantum harmonic oscillator withcharacteristic frequency $\omega_r$. The coupling between the charge qubit andthe resonator is realized by a coupling capacitance $C_c$. We have studied theeigenstates as well as the dynamics of the quantum circuit. Interestingphenomena occur when the Josephson energy equals the oscillator frequency,$E_j=\hbar\omega_r$. Then the quantum circuit is described by entangled states.We have deduced the time evolution of these states in the limit of weakcoupling between the charge qubit and the resonator. We found Rabi oscillationsof the excited charge qubit eigenstate. This effect is explained by thespontaneous emission and re-absorption of a single photon in thesuperconducting resonator.

Entangled States in a Josephson Charge Qubit Coupled to a Superconducting Resonator