Entanglement and the Jaynes-Cummings model with Rydberg-dressed atoms*

Controlling quantum entanglement between parts of a many-body system is the key to unlocking the power of quantum information processing for applications such as quantum computation, high-precision sensing, and simulation of many-body physics. Spin degrees of freedom of ultracold neutral atoms in their ground electronic state provide a natural platform given their long coherence times and our ability to control them with magneto-optical fields, but creating strong coherent coupling between spins has been challenging. We demonstrate for the first time a strong and tunable Rydberg-dressed interaction between spins of individually trapped cesium atoms with energy shifts of order 1 MHz in units of Planck's constant\footnote{Y.-Y. Jau, A. M. Hankin, T. Keating, I. H. Deutsch, and G. W. Biedermann, Nature Physics, {\bf 12}, 71-74 (2016).}. We spectroscopically demonstrate that this system is isomorphic to a Jaynes-Cummings Hamiltonian, and observe the $\sqrt{N}$ nonlinearity of the Jaynes-Cummings ladder with a single symmetric Rydberg excitation. This interaction enables a ground-state {\em spin-flip blockade}, whereby simultaneous hyperfine spin flips of two atoms are blockaded due to their mutual interaction. We employ this spin-flip blockade to rapidly produce single-step Bell-state entanglement between atoms.