A theoretical scheme is presented for the adiabatic generation of N-quNit singlet states with $Ngeqslant3$, which may be more feasible than previous ones in a cavity. In this proposal, the system may be robust both parameter fluctuations and dissipation along a dark state. In addition, quantum information is only stored in atomic ground states and there is no energy exchanged between atoms and photons in a cavity so as to reduce the influence of atomic spontaneous emission and cavity decays.
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