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Creation of the Remote Spin Entanglement with a Nanomechanical Cantilever

V. I. Tsifrinovich

Published May 30, 2024• 1 citation
Publisher

Abstract

We consider creation of entanglement between the remote electron spins using a magnetic nanoparticle attached to a cantilever tip (CT). We assume that the frequency of the CT vibrations matches the Larmor frequency of the spin (the CT-spin resonance). In the conditions of the CT-spin resonance the CT-spin system is described by the exactly solvable Jaynes-Kummings model. In this work using the evolution operator of the Jaynes-Kummings model we show that a movable CT can create an entangled state between the remote spins. The most striking result is that the entanglement between the remote spins can be achieved without measurement of the vibrational state of the CT.

DOI
10.20944/preprints202405.1985.v1

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We consider creation of entanglement between the remote electron spins using a magnetic nanoparticle attached to a cantilever tip (CT). We assume that the frequency of the CT vibrations matches the Larmor frequency of the spin (the CT-spin resonance). In the conditions of the CT-spin resonance the CT-spin system is described by the exactly solvable Jaynes-Kummings model. In this work using the evolution operator of the Jaynes-Kummings model we show that a movable CT can create an entangled state between the remote spins. The most striking result is that the entanglement between the remote spins can be achieved without measurement of the vibrational state of the CT.
We consider the creation of entanglement between remote electron spins using a magnetic nanoparticle attached to a cantilever tip (CT). We assume that the frequency of the CT vibrations matches the Larmor frequency of the spin (CT–spin resonance). Under the conditions of CT–spin resonance, the CT–spin system is described using the Jaynes–Cummings model. In this work, using the evolution operator of the Jaynes–Cummings model, we show that a movable CT can create an entangled state between remote spins. The most striking result is that the entanglement between the remote spins can be achieved without measuring the vibrational state of the CT.
We consider a system of two spins under a scanning tunneling microscope bias and derive its master equation. We find that the tunneling elements to the electronic contacts (tip and substrate) generate an exchange interaction between the spins as well as a Dzyaloshinskii-Moriya interaction in the presence of spin-orbit coupling. The tunnel current spectrum then shows additional lines compared to conventional spin-resonance experiments. When the spins have degenerate Larmor frequencies and equal tunneling amplitudes (without spin orbit), there is a dark state with a vanishing decay rate. The coupling to the electronic environment generates significant spin-spin entanglement via the dark state, even if the initial state is nonentangled.
Several recent experiments have shown that long-range exchange interactions can determine collective magnetic ground states of nanostructures in bulk and on surfaces. The ability to generate and control entanglement in a system with long-range interaction will be of great importance for future quantum technology. An important step forward to reach this goal is the creation of entangled states for spins of distant magnetic atoms. Herein, the generation of long-distance entanglement between remote spins at large separations in bulk and on surface is studied theoretically, based on a quantum spin Hamiltonian and time-dependent Schrödinger equation for experimentally realized conditions. We demonstrate that long-distance entanglement can be generated between remote spins by using an appropriate quantum spin chain (a quantum mediator), composed by sets of antiferromagnetically coupled spin dimers. Ground state properties and quantum spin dynamics of entangled atoms are studied. We demonstrate that one can increase or suppress entanglement by adding a single spin in the mediator. The obtained result is explained by monogamy property of entanglement distribution inside a quantum spin system. We present a novel approach for non-local sensing of remote magnetic adatoms via spin entanglement.
We consider a spin-1/2 anisotropic XYXYXY model with time-dependent spin-spin coupling as means of creating long-distance entanglement. We predict the emergence of significant entanglement between the first spin and the last spin whenever the ac part of the coupling has a frequency matching the Zeeman splitting. In particular, we find that the concurrence assumes its maximum with a vanishing dc part. Mapping the time-dependent Hamiltonian within a rotating-wave approximation to an effective static model provides qualitative and quantitative understanding of this entanglement resonance. Numerical results for the duration of the entanglement creation and its length dependence substantiate the effective static picture.