Two-qubit gates using adiabatic passage of the Stark-tuned Förster resonances in Rydberg atoms

We propose schemes of controlled-Z and controlled-NOT gates with ultracold neutral atoms based on deterministic phase accumulation during double adiabatic passage of the Stark-tuned Förster resonance of Rydberg states. The effect of deterministic phase accumulation during double adiabatic passage in a two-level quantum system has been analyzed in detail. Adiabatic rapid passage using nonlinearly chirped pulses with rectangle intensity profile has been discussed. Nonlinear time dependence of the energy detuning from the Förster resonance is used to achieve a high fidelity of population transfer between Rydberg states. Fidelity of two-qubit gates has been studied with an example of the $90S+96S\to 90P+95P$ Stark-tuned Förster resonance in Cs Rydberg atoms.