Microscopic dynamics and an effective Landau-Zener transition in the quasi-adiabatic preparation of spatially ordered states of Rydberg excitations

TL;DR

This paper investigates the microscopic dynamics of adiabatic Rydberg state preparation in finite 1D lattices, revealing an effective Landau-Zener transition mechanism that explains the fidelity of creating ordered Rydberg excitations.

Contribution

It demonstrates that the complex many-body dynamics can be approximated by an effective two-level system, enabling accurate fidelity estimates using Landau-Zener theory.

Findings

The system follows the strongest excitation paths during state preparation.

An effective two-level model captures the essential dynamics.

Fidelity estimates align with Landau-Zener predictions.

Abstract

We examine the adiabatic preparation of spatially-ordered Rydberg excitations of atoms in finite one-dimensional lattices by frequency-chirped laser pulses, as realized in a number of recent experiments simulating quantum Ising model. Our aims are to unravel the microscopic mechanism of the phase transition from the unexcited state of atoms to the antiferromagnetic-like state of Rydberg excitations by traversing an extended gapless phase, and to estimate the preparation fidelity of the target state in a moderately sized system amenable to detailed numerical analysis. We find that, in the basis of the bare atomic states, the system climbs the ladder of Rydberg excitations predominantly along the strongest-amplitude paths towards the final ordered state. We show that, despite its complexity, the interacting many-body system can be described as an effective two-level system involving a pair of lowest-energy instantaneous collective eigenstates of the time-dependent Hamiltonian. The final preparation fidelity of the target state can then be well approximated by the Landau-Zener formula, while the nonadiabatic population leakage during the passage can be estimated using a perturbative approach applied to the instantaneous collective eigenstates.