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We present schemes for geometric phase compensation in adiabatic passage which can be used for the implementation of quantum logic gates with atomic ensembles consisting of an arbitrary number of strongly interacting atoms. Protocols using double sequences of stimulated Raman adiabatic passage (STIRAP) or adiabatic rapid passage (ARP) pulses are analyzed. Switching the sign of the detuning between two STIRAP sequences, or inverting the phase between two ARP pulses, provides state transfer with well defined amplitude and phase independent of atom number in the Rydberg blockade regime. Using these pulse sequences we present protocols for universal single-qubit and two-qubit operations in atomic ensembles containing an unknown number of atoms.
We review methods for coherently controlling Rydberg quantum states of atomic ensembles using Adiabatic Rapid Passage and Stimulated Raman Adiabatic Passage. These methods are commonly used for population inversion in simple two-level and three-level
We describe a technique for manipulating quantum information stored in collective states of mesoscopic ensembles. Quantum processing is accomplished by optical excitation into states with strong dipole-dipole interactions. The resulting ``dipole bloc
Long range Rydberg blockade interactions have the potential for efficient implementation of quantum gates between multiple atoms. Here we present and analyze a protocol for implementation of a $k$-atom controlled NOT (C$_k$NOT) neutral atom gate. Thi
We show that with adiabatic passage, one can reliably drive two-photon optical transitions between the ground states and interacting Rydberg states in a pair of atoms. For finite Rydberg interaction strengths a new adiabatic pathway towards the doubl
We propose an efficient method to filter out single atoms from trapped ensembles with unknown number of atoms. The method employs stimulated adiabatic passage to reversibly transfer a single atom to the Rydberg state which blocks subsequent Rydberg e