Entangled States in a Single-Qubit Structure with SQUID Coupled with a Super-conducting Resonator

In this paper, the number-phase quantization scheme of the mesoscopic circuit, which consists of a single-qubit structure with superconducting quantum interference device coupledwith a super-conducting resonator, is given. By introducing a unitary matrix and by means of spectral decomposition, the Hamiltonian operator of the system is exactly formulated incompact forms in spin-1/2 notation. The eigenvalues and the eigenstates of the system are investigated. It is found that using this system the entangled states can not only be prepared, butalso be manipulated by tuning the magnetic flux through thesuper-conducting loop.