“…(f is arbitrary phase and N=1, 2, 3...), which are widely applied in quantum lithography [3,4], quantum metrology [5,6], quantum imaging [7], and quantum information processing [8,9]. Many schemes have been proposed for generating photonic NOON states [10][11][12][13][14][15][16][17][18], however, most of them are based on the step-by-step strategy that means the time of generating NOON states will increase with increasing photon-number. On the other hand, atoms as important and excellent media, draw a great deal of attention [19][20][21][22] due to their various applications in quantum information and quantum metrology [23][24][25][26].…”