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Magnetochemistry

The Creation of Remote Spin Entanglement with a Nanomechanical Cantilever

V. I. Tsifrinovich

Published Sep 29, 2024• 0 citations
Publisher

Abstract

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.

DOI
10.3390/magnetochemistry10100071

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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 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.
A detailed treatment of the entanglement dynamics of two distant but non-identical systems is presented. We study the entanglement evolution of two remote atoms interacting independently with a cavity field, as in the double Jaynes–Cummings model. The four-qubit pairwise concurrences are studied, allowing for asymmetric atom–cavity couplings and off-resonant interactions. Counter to intuition, imperfect matching can prove advantageous to entanglement creation and evolution. For two types of initial entanglement, corresponding to spin-correlated and anti-correlated Bell states Φ and Ψ, a full, periodic and directed transfer of entanglement into a specific qubit pair is possible, for resonant interactions, depending on the choice of relative couplings. Furthermore, entanglement transfer and sudden death (ESD) can be prevented using off-resonant interactions, although for some initial states, detunings will trigger an otherwise frozen entanglement, to allow a full entanglement transfer.
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.
Abstract We show that the entanglement between two atomic spins, coupled via XY interaction, can be achieved with the aid of a single photon in a controllable manner. Assuming a constant spin-photon coupling, two distinct cases are considered — excitation with a constant and with a linear time-dependent photon frequency. We demonstrate that these problems reduce to the study of the well known Jaynes-Cummings and Jaynes-Cummings – Landau-Zener models, respectively, where the two-level system is formed by the zero-momentum mode states of the dimer. Owing to the exact solubility of both models, by tuning the relevant parameters, one can design and coherently control the dynamics of the excitation process. For instance, one can adiabatically switch from an atomic spin system initialized in a state with both spins down to the maximally entangled triplet state.