Generating spin squeezing states and Greenberger-Horne-Zeilinger entanglement using a hybrid phonon-spin ensemble in diamond

TL;DR

This paper proposes a scheme to generate spin squeezing and GHZ entanglement in a diamond-based hybrid phonon-spin system, demonstrating significant squeezing and entanglement fidelity with robustness against thermal noise.

Contribution

It introduces a geometric-phase-based method for creating spin squeezing and GHZ states in a hybrid phonon-spin ensemble in diamond, with detailed numerical analysis.

Findings

Achieved 5.9 dB spin squeezing for 20 spins.

Created GHZ state with 0.62 fidelity at cryogenic temperatures.

Scheme is robust against thermal mechanical noise.

Abstract

Quantum squeezing and entanglement of spins can be used to improve the sensitivity in quantum metrology. Here we propose a scheme to create collective coupling of an ensemble of spins to mechanical vibrational mode actuated by an external magnetic field. We find an evolution time where the mechanical motion decouples from the spins, and the accumulated geometric phase yields a squeezing of $5.9~\text{dB}$ for $20$ spins. We also show the creation of a Greenberger-Horne-Zeilinger spin state for $20$ spins with a fidelity of $\sim 0.62$ at cryogenic temperature. The numerical simulations show that the geometric-phase based scheme is mostly immune to thermal mechanical noise.