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

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 antiferromagneticlike 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 show that, despite its complexity, the interacting many-body system can be de-scribed 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.

Automated summary

This study examines the adiabatic preparation of spatially ordered Rydberg excitations of atoms in finite one-dimensional lattices. It aims to unravel the microscopic mechanism of the phase transition and estimate the preparation fidelity of the target state. The study shows that the many-body system can be described as an effective two-level system and the final preparation fidelity can be approximated using the Landau-Zener formula.