Generating double NOON states of photons in circuit QED

To generate a NOON state with a large photon number N, the number of operational steps could be large and the fidelity will decrease rapidly with N. Here we propose a method to generate a type of quantum entangled states, (|NN00)+|00NN))/2, called "double NOON" states, with a setup of two superconducting flux qutrits and five circuit cavities. This scheme operates essentially by employing a two-photon process; i.e., two photons are simultaneously and separately emitted into two cavities when each coupler qutrit is initially in a higher-energy excited state. As a consequence, the "double" NOON state creation needs only N+2 operational steps. One application of double NOON states is to get a phase error of 1/(2N) in phase measurement. In comparison, to achieve the same error, a normal NOON state of the form (|2N,0)+|0,2N))/2 is needed, which requires at least 2N operational steps to prepare by using the existing schemes. Our numerical simulation demonstrates that high-fidelity generation of the double NOON states with N≤10 even for imperfect devices is feasible with the present circuit QED technique.