# Quantum state engineering by periodical two-step modulation in atomic system

## TL;DR

This paper introduces a novel quantum state engineering method using periodical two-step modulation in multilevel atomic systems, enabling precise control of Rydberg states and transitions with robustness and simple waveform implementation.

## Contribution

It develops an effective Hamiltonian approach for multilevel systems under large detunings and demonstrates versatile quantum state control without requiring two-photon resonance.

## Key findings

- Achieves direct ground-to-Rydberg state transition without two-photon resonance.
- Switches between Rydberg blockade and antiblockade regimes.
- Robust control with simple square-wave laser modulation.

## Abstract

By periodical two-step modulation, we demonstrate that the dynamics of multilevel system can still evolve even in multiple large detunings regime, and provide the effective Hamiltonian (of interest) for this system. We then illustrate this periodical modulation in quantum state engineering, including achieving direct transition from the ground state to the Rydberg state or the desired superposition of two Rydberg states without satisfying two-photon resonance condition, switching between Rydberg blockade regime and Rydberg antiblockade regime, stimulating distinct atomic transitions by the same laser field, and implementing selective transitions in the same multilevel system. Particularly, it is robust against perturbation of control parameters. Another advantage is that the waveform of laser field has simple square-wave form which is readily implemented in experiments. Thus, it offers us a novel method of quantum state engineering in quantum information processing.