Rydberg ensemble based CNOT$^{\mathrm{N}}$ gates using STIRAP*

Schemes for implementation of CNOT gates in atomic ensembles are important for realization of quantum computing. We present here a theoretical scheme of a CNOT$^{\mathrm{N}}$ gate with an ensemble of three-level atoms in the lambda configuration and a single two-level control atom. We work in the regime of Rydberg blockade for the ensemble atoms due to excitation of the Rydberg control atom. It is shown that using STIRAP, atoms from one ground state of the ensemble can be adiabatically transferred to the other ground state, depending on the state of the control atom. A thorough analysis of adiabatic conditions for this scheme and the influence of the radiative decay is provided. We show that the CNOT$^{\mathrm{N}}$ process is immune to the decay rate of the excited level in ensemble atoms.