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We develop a scheme to prepare a macroscopic maximally entangled state (MMES)between two atomic ensembles using adaptive quantum nondemolition (QND)measurements. The quantum state of the system is evolved using a sequence ofQND measurements followed by adaptive unitaries, such that the desiredmeasurement outcome is obtained with asymptotically unit probability. Thisprocedure is repeated in z and x spin basis alternately such that the stateconverges deterministically towards the maximally entangled state. Up to alocal spin-basis rotation, the maximally entangled state has zero total spinangular momentum, i.e. it is a singlet state. Our protocol does not performpostselection and works beyond the Holstein-Primakoff regime for the atomicspin degrees of freedom, producing genuine macroscopic entanglement.

Macroscopic maximally entangled state preparation between two atomic ensembles