Rydberg atoms with principal quantum number n⪢1 have exaggerated atomic properties including dipole-dipole interactions that scale as n4 and radiative lifetimes that scale as n3. It was proposed a decade ago to take advantage of these properties to implement quantum gates between neutral atom qubits. The availability of a strong long-range interaction that can be coherently turned on and off is an enabling resource for a wide range of quantum information tasks stretching far beyond the original gate proposal. Rydberg enabled capabilities include long-range two-qubit gates, collective encoding of multiqubit registers, implementation of robust light-atom quantum interfaces, and the potential for simulating quantum many-body physics. The advances of the last decade are reviewed, covering both theoretical and experimental aspects of Rydberg-mediated quantum information processing.

Spin-exchange optical pumping of mixtures of alkali-metal vapors and noble gases can be used to efficiently polarize the nuclei of the noble-gas atoms. Liters of noble gases at standard temperature and pressure and with nuclear spin polarizations of several tens of percent are now used in many applications. The authors describe the basic phenomena that govern the spin-exchange process and review the physics of angular momentum transfer and loss in optical pumping and spin-exchange collisions.

When two single Rydberg atoms—those having electrons in highly excited states—interact, one can be used to control the quantum state of the other. Two independent experiments now demonstrate a ‘Rydberg blockade’, an effect that might make long-range quantum gates between neutral atoms possible. Blockade interactions whereby a single particle prevents the flow or excitation of other particles provide a mechanism for control of quantum states, including entanglement of two or more particles. Blockade has been observed for electrons1,2,3, photons4 and cold atoms5. Furthermore, dipolar interactions between highly excited atoms have been proposed as a mechanism for ‘Rydberg blockade’6,7, which might provide a novel approach to a number of quantum protocols8,9,10,11. Dipolar interactions between Rydberg atoms were observed several decades ago12 and have been studied recently in a many-body regime using cold atoms13,14,15,16,17,18. However, to harness Rydberg blockade for controlled quantum dynamics, it is necessary to achieve strong interactions between single pairs of atoms. Here, we demonstrate that a single Rydberg-excited rubidium atom blocks excitation of a second atom located more than 10 μm away. The observed probability of double excitation is less than 20%, consistent with a theoretical model of the Rydberg interaction augmented by Monte Carlo simulations that account for experimental imperfections.

We present the first demonstration of a CNOT gate between two individually addressed neutral atoms. Our implementation of the CNOT uses Rydberg blockade interactions between neutral atoms held in optical traps separated by >8\,\,$\mu${}m. Using two different gate protocols we measure CNOT fidelities of F=0.73 and 0.72 based on truth table probabilities. The gate was used to generate Bell states with fidelity F=0.48\ifmmode\pm\else\textpm\fi{}0.06. After correcting for atom loss we obtain an a~posteriori entanglement fidelity of F=0.58.

We analyze the effects of Zeeman degeneracies on the long-range interactions between like Rydberg atoms, with particular emphasis on applications to quantum-information processing using the van der Waals blockade. We present a general analysis of how degeneracies affect the primary error sources in blockade experiments, emphasizing that blockade errors are sensitive primarily to the weakest possible atom-atom interactions between the degenerate states, not the mean interaction strength. We present explicit calculations of the van der Waals potentials in the limit where the fine-structure interaction is large compared to the atom-atom interactions. The results are presented for all potential angular momentum channels involving $\mathit{s}$, $\mathit{p}$, and $\mathit{d}$ states. For most channels there are one or more combinations of Zeeman levels that have extremely small dipole-dipole interactions and are therefore poor candidates for effective blockade experiments. Channels with promising properties are identified and discussed. We also present numerical calculations of Rb and Cs dipole matrix elements and relevant energy levels using quantum defect theory, allowing for convenient quantitative estimates of the van der Waals interactions to be made for principal quantum numbers up to 100. Finally, we combine the blockade and van der Waals results to quantitatively analyze the angular distribution of the blockade shift and its consequence for angular momentum channels and geometries of particular interest for blockade experiments with Rb.

We present a detailed analysis and design of a neutral atom quantum logic device based on atoms in optical traps interacting via dipole-dipole coupling of Rydberg states. The dominant physical mechanisms leading to decoherence and loss of fidelity are enumerated. Our results support the feasibility of performing single- and two-qubit gates at MHz rates with decoherence probability and fidelity errors at the level of ${10}^{-3}$ for each operation. Current limitations and possible approaches to further improvement of the device are discussed.