Rydberg-atom-based creation of an N -particle Greenberger-Horne-Zeilinger state using stimulated Raman adiabatic passage

Abstract

Schemes for creation of $N$-particle entangled Greenberger-Horne-Zeilinger (GHZ) states are important for understanding multiparticle nonclassical correlations. Here, a theoretical scheme for creation of a multiparticle GHZ state implemented on a target ensemble of N, $\mathrm{\ensuremath{\Lambda}}$ three-level Rydberg atoms and a single Rydberg atom as a control using stimulated Raman adiabatic passage (STIRAP) is presented. We work in the Rydberg blockade regime for the ensemble atoms induced due to excitation of the control atom to a high-lying Rydberg level. It is shown that using STIRAP, atoms from one ground state of the ensemble can be adiabatically transferred with high fidelity to the other ground state, depending on the state of the control atom. Measurement of the control atom in a specific basis after this conditional transfer facilitates one-step creation of an $N$-particle GHZ state. A thorough analysis of adiabatic conditions for this scheme and the influence of radiative decay from the excited Rydberg levels is presented. We show that this scheme is immune to the decay rate of the excited level in ensemble atoms and provides a robust way of creating GHZ states.