Entangled states in a Josephson charge qubit coupled to a superconducting resonator

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We study the dynamics of a quantum superconducting circuit which is the analogue of an atom in a high-Q cavity. The circuit consists of a Josephson charge qubit coupled to a superconducting resonator. The charge qubit can be treated as a two level quantum system whose energy separation is split by the Josephson energy Eⱼ. The superconducting resonator in our proposal is the analogue of a photon box and is described by a quantum harmonic oscillator with characteristic frequency ωᵣ. The coupling between the charge qubit and the resonator is realized by a coupling capacitance Cc. We have studied the eigenstates as well as the dynamics of the quantum circuit. Interesting phenomena occur when the Josephson energy equals the oscillator frequency, Eⱼ=ℏωᵣ. Then the quantum circuit is described by entangled states. We have deduced the time evolution of these states in the limit of weak coupling between the charge qubit and the resonator. We found Rabi oscillations of the excited charge qubit eigenstate. This effect is explained by the spontaneous emission and re-absorption of a single photon in the superconducting resonator.