Abstract
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.
Highlights
In diverse systems, long-range interactions between magnetic adatoms on surfaces were investigated both theoretically and in experiments[1,2,3,4,5,6,7,8,9,10,11]
Relevant to the case of quantum spin chain, it means: if spins within mediator are strongly entangled with each other, entanglement between spin on distant A(B) probe and the mediator will be weak for small exchange interaction between them, that should lead to a strong entanglement between SA and SB spins
The physics is the same in the case of antiferromagnetically coupled dimerized chain unveiled in strontium-copper oxide[25]: singlet states formed by dimers exhibit a strong entanglement and if the interaction between dimers is weak, SA and SB spins will be entangled, if they have a weak interactions with dimerized chain
Summary
Generation of entanglement in the ground state between remote spins in a Sr14Cu24O41 bulk. Thereby, the mediator is represented by an entangled dimerized spin chain and its weak interaction with A and B probes, ascribed by small MI (SA − S1, S10 − SB), leads to the strong quantum correlations (or LDE) of their spins (SA − SB). As shown, the strength of generated LDE between probes is practically saturated It is provided both by the ground state calculations of entanglement distribution and by the chosen ratio|J1/J2| ~ 0.1 of coupling strengths between spins in considered quantum spin chain. It is well seen, that a large amount of entanglement between A and B probes (MIA,B → 2) and, the onset of LDE between them are observed for the mediators with an even number of spins, while for their odd number counterparts the entanglement is vanished (MIA,B → 0) and LDE is not created, except Nmed = 1.
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