Einstein-Podolsky-Rosen entanglement and asymmetric steering between distant macroscopic mechanical and magnonic systems

Huatang Tan,Jie Li

doi:10.1103/physrevresearch.3.013192

Abstract

We propose a deterministic scheme for establishing hybrid Einstein-Podolsky-Rosen (EPR) entanglement channel between a macroscopic mechanical oscillator and a magnon mode in a distant yttrium-iron-garnet (YIG) sphere across about ten gigahertz of frequency difference. The system consists of a driven electromechanical cavity which is unidirectionally coupled to a distant electromagnonical cavity inside which a YIG sphere is placed. We find that far beyond the sideband-resolved regime in the electromechanical subsystem, stationary phonon-magnon EPR entanglement can be achieved. This is realized by utilizing the output field of the electromechanical cavity being an intermediary which distributes the electromechanical entanglement to the magnons, thus establishing a remote phonon-magnon entanglement. The EPR entanglement is strong enough such that phonon-magnon quantum steering can be attainable in an asymmetric manner. This long-distance macroscopic hybrid EPR entanglement and steering enable potential applications not only in fundamental tests of quantum mechanics at the macro scale, but also in quantum networking and one-sided device-independent quantum cryptography based on magnonics and electromechanics.

Highlights

Long-distance entanglement has attracted extensive attention owing to its potential applications to the fundamental test of quantum mechanics [1], quantum networking [2,3], and quantum-enhanced metrology [4]
In cavity optomechanics and electromechanics, which involve the hybrid coupling of massive mechanical resonators to a electromagnetic field [14,15], recent experiments have succeeded in preparing a variety of quantum states of macroscopic mechanical oscillators [16,17,18,19,20,21,22,23], including quantum squeezing and entanglement of mechanical oscillators [16,17,18,19], nonclassical correlations between photons and phonons [20,21], single-phonon Fock states [22], optomechanical Bell nonlocality [23], etc
We see that the EPR entanglement and steering between the mechanical oscillator and the YIG sphere can be achieved in the steady-state regime

Summary

INTRODUCTION

Long-distance entanglement has attracted extensive attention owing to its potential applications to the fundamental test of quantum mechanics [1], quantum networking [2,3], and quantum-enhanced metrology [4]. In cavity optomechanics and electromechanics, which involve the hybrid coupling of massive mechanical resonators to a electromagnetic field [14,15], recent experiments have succeeded in preparing a variety of quantum states of macroscopic mechanical oscillators [16,17,18,19,20,21,22,23], including quantum squeezing and entanglement of mechanical oscillators [16,17,18,19], nonclassical correlations between photons and phonons [20,21], single-phonon Fock states [22], optomechanical Bell nonlocality [23], etc. We consider a microwave-mediated phonon-magnon interface and focus on how to deterministically establish hybrid EPR entanglement channel between a macroscopic mechanical oscillator and a distant YIG sphere across about 10 GHz of frequency difference.

PHONON-MAGNON ENTANGLEMENT AND STEERING

RESULTS

DISCUSSION AND CONCLUSION