Rabi Oscillations and Entanglement between two Rydberg Atoms in an Optical Cavity studied by the Jaynes-Cummings Model and Quantum Circuits on Qiskit

Rydberg atoms are highly excited atoms in which one electron has a large principal quantum number. Due to their unusual atomic properties, Rydberg atoms are promising building blocks of two-qubit gates and light-atom quantum interfaces in quantum information processing. For two atoms at close distance (< 10 mm) the Rydberg blockade prevents the two atoms to be simultaneously in the excited state whereas this blockade is absent for atoms far apart. Recently, this effect was used to engineer a quantum processor based on two-dimensional arrays of neutral atoms which are trapped and transported by optical tweezers. Motivated by these experiments, we study the light-atom interaction and entanglement of two Rydberg atoms interacting by the Rydberg blockade in an optical cavity using the Jaynes-Cummings model. We find a rich variety of Rabi oscillations and entanglement as a function of initial conditions and interaction time, which may be used to generate two-qubit gates. Furthermore, we develop and simulate a quantum circuit of this system using Qiskit, an open-source software development kit designed to emulate the operation of a real quantum computer, and discuss the fidelity of the quantum circuit.