Generation of genuine $\chi$-type four-particle entangled state of superconducting artificial atoms with broken symmetry

We propose a scheme for generating a genuine $\chi$-type four-particle entangled state of superconducting artificial atoms with broken symmetry by using one-dimensional transmission line resonator as a data bus. The $\mathrm{\Delta }$-type three-level artificial atom we use in the scheme is different from natural atom and has cyclic transitions. After suitable interaction time and simple operations, the desired entangled state can be obtained. Since artificial atomic excited states and photonic states are adiabatically eliminated, our scheme is robust against the spontaneous emissions of artificial atoms and the decays of transmission line resonator.