One-step engineering many-atom NOON state

We propose a one-step scheme for driving many atoms into a NOON state. In this scheme, two cavities are coupled to each other through the photon-hopping interaction and each cavity contains N four-level atoms. The 2N atoms are driven into a NOON state via a phase-shift which depends on the collective atomic excitations. Interestingly, the time of generating the NOON state is independent of the atom number, i.e., it is unchanged with the increasing of the atom number. Also, our scheme is insensitive to cavity decay and can effectively suppress atomic spontaneous emission.