# Efficient generation of many-body entangled states by multilevel oscillations

## TL;DR

This paper presents a method to efficiently generate high-fidelity many-body entangled states in a spinor Bose-Einstein condensate using multilevel oscillations combined with adiabatic drives, achieving robustness and high fidelity.

## Contribution

The authors introduce a novel protocol combining multilevel oscillations and adiabatic drives to produce entangled states with high fidelity and robustness in BECs, reducing control precision requirements.

## Key findings

- Achieved over 96% fidelity in generating entangled states.
- Successfully produced many-body singlet and twin-Fock states.
- Demonstrated robustness against atom number fluctuations and magnetic field stray.

## Abstract

We generate high-fidelity massively entangled states in an antiferromagnetic spin-1 Bose-Einstein condensate (BEC) by utilizing multilevel oscillations. Combining the multilevel oscillations with additional adiabatic drives, we greatly shorten the necessary evolution time and relax the requirement on the control accuracy of quadratic Zeeman splitting, from micro-Gauss to milli-Gauss, for a $^{23}$Na spinor BEC. The achieved high fidelities over $96\%$ show that two kinds of massively entangled states, the many-body singlet state and the twin-Fock state, are almost perfectly generated. The generalized spin squeezing parameter drops to a value far below the standard quantum limit even with the presence of atom number fluctuations and stray magnetic fields, illustrating the robustness of our protocol under real experimental conditions. The generated many-body entangled states can be employed to achieve the Heisenberg-limit quantum precision measurement and to attack nonclassical problems in quantum information science.