Many-body dynamics of Rydberg excitation using the $\Omega$-expansion

TL;DR

This paper develops a theoretical framework using the $\Omega$-expansion to analyze the many-body excitation dynamics of Rydberg atoms in ultracold gases, providing explicit formulas and recurrence relations for different interaction regimes.

Contribution

It introduces a systematic $\Omega$-expansion method in the Heisenberg picture for calculating excitation probabilities and correlations in Rydberg systems, including explicit formulas up to fourth order.

Findings

Derived recurrence relations for excitation dynamics

Explicit expansion formulas up to $\Omega^4$ for large homogeneous samples

Averaged results over random atomic distributions

Abstract

We investigate the excitation dynamics of Rydberg atoms in ultracold atomic samples by expanding the excitation probability and the correlation function between excited atoms in powers of the isolated atom Rabi frequency $\Omega$. In the Heisenberg picture, we give recurrence relations to calculate any order of the expansions, which ere expected to be well-behaved for arbitrarily strong interactions. For homogeneous large samples, we give the explicit form of the expansions, up to $\Omega^4$, averaged over all possible random spatial distributions of atoms, for the most important cases of excitation pulses and interactions.