# Entangling power of holonomic gates in atom-cavity systems

## TL;DR

This paper proposes a novel method for creating entanglement between two atoms in a cavity using nonadiabatic holonomies and the quantum Zeno effect, advancing the development of universal quantum gates.

## Contribution

It introduces a tripod interaction Hamiltonian enabling geometric entanglement, demonstrating a new approach for nonadiabatic holonomic two-qubit gate implementation.

## Key findings

- Achieves arbitrary geometric entangling power.
- Utilizes quantum Zeno effect for control.
- Progress toward universal holonomic quantum gates.

## Abstract

Our goal is to provide a new approach to the construction of geometry-induced entanglement between a pair of $\Lambda$ type atoms in a system consists of $N$ identical atoms by means of nonadiabatic quantum holonomies. By employing the quantum Zeno effect, we introduce a tripod type interaction Hamiltonian between two selected atoms trapped in an optical cavity, which allows arbitrary geometric entangling power. This would be a substantial step toward resolving the feasibility of realizing universal nonadiabatic holonomic entangling two-qubit gates.