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arXiv:1007.4516 · Physical Review Letters

Entanglement Routers Using Macroscopic Singlets

Abolfazl Bayat, Sougato Bose, Pasquale Sodano

Published Oct 27, 2010• 70 citations
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Abstract

We propose a mechanism where high entanglement between very distant boundary spins is generated by suddenly connecting two long Kondo spin chains. We show that this procedure provides an efficient way to route entanglement between multiple distant sites. We observe that the key features of the entanglement dynamics of the composite spin chain are well described by a simple model of two singlets, each formed by two spins. The proposed routing mechanism is a footprint of the emergence of a Kondo cloud in a Kondo system and can be engineered and observed in varied physical settings.

DOI
10.1103/physrevlett.105.187204

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We propose a mechanism where high entanglement between very distant boundary spins is generated by suddenly connecting two long Kondo spin chains. We show that this procedure provides an efficient way to route entanglement between multiple distant sites. We observe that the key features of the entanglement dynamics of the composite spin chain are well described by a simple model of two singlets, each formed by two spins. The proposed routing mechanism is a footprint of the emergence of a Kondo cloud in a Kondo system and can be engineered and observed in varied physical settings.
We exploit the unique features of the entanglement in the gapless Kondo regime to show that a single local quench at one end of a Kondo spin chain may always induce fast and long lived oscillatory dynamics, which establishes a high quality entanglement between the individual spins at the opposite ends of the chain. This entanglement is a footprint of the presence of the Kondo cloud and may be engineered so as to attain — even for very large chains- a constant high value independent of the length; in addition, it is thermally robust. To better evidence the remarkable peculiarities of the Kondo regime, we carry a parallel analysis of the entanglement properties of the Kondo spin chain model in the gapped dimerised regime where these remarkable features are absent.
We investigate the entanglement properties of the Kondo spin chain when it is prepared in its ground state as well as its dynamics following a single bond quench. We show that a true measure of entanglement such as negativity enables to characterize the unique features of the gapless Kondo regime. We determine the spatial extent of the Kondo screening cloud and propose an ansatz for the ground state in the Kondo regime accessible to this spin chain; we also demonstrate that the impurity spin is indeed maximally entangled with the Kondo cloud. We exploit these features of the entanglement in the gapless Kondo regime to show that a single local quench at one end of a Kondo spin chain may always induce a fast and long lived oscillatory dynamics, which establishes a high quality entanglement between the individual spins at the opposite ends of the chain. This entanglement is a footprint of the presence of the Kondo cloud and may be engineered so as to attain - even for very large chains- a constant high value independent of the length; in addition, it is thermally robust. To better evidence the remarkable peculiarities of the Kondo regime, we carry a parallel analysis of the entanglement properties of the Kondo spin chain model in the gapped dimerised regime where these remarkable features are absent.
We show that, in the gapless Kondo regime, a single local quench at one end of a Kondo spin chain induces a fast and long-lived oscillatory dynamics. This quickly establishes a high-quality entanglement between the spins at the opposite ends of the chain. This entanglement is mediated by the Kondo cloud, attains a constant high value independent of the length for large chains, and shows thermal robustness. In contrast, when the Kondo cloud is absent, e.g., in the gapped dimer regime, only finite-size end to end effects can create some entanglement on a much longer time scale for rather short chains. By decoupling one end of the chain during the dynamics, one can distinguish between this end-end effect which vanishes, and the global Kondo cloud mediated entanglement, which persists. This quench approach paves the way to detect the elusive Kondo cloud through the entanglement between two individual spins. Our results show that nonperturbative cooperative phenomena from condensed matter may be exploited for quantum information.
Quantum entanglement permeates the complex ground states of correlated electron materials defying single-particle descriptions. Coupled magnetic atoms have potential as model systems for entanglement in condensed matter giving the opportunity to create artificial many-body states which can be controlled by tuning the underlying interactions. They provide an avenue to unravel the complexities of correlated-electron materials. Here we use low temperature scanning tunnelling microscopy (STM) and atomic manipulation to tune entanglement in chains of magnetic atoms. We find that a Kondo singlet state can emerge from this entanglement. The many electron Kondo state is based on the screening of the entangled spin ground state of the chain by substrate electrons and can be engineered to envelop at least ten magnetic atoms. The concomitant Kondo resonance measured in the differential conductance enables the electric read-out of entanglement. By tuning composition and coupling strength within atomic chains it is possible to create model spin chains with defined entanglement. This lays the foundation for a new class of experiments to construct exotic correlated-electron materials atom by atom.
We study the problem of entangling two spins at the distant ends of a spin chain by exploiting the nonequilibrium dynamics of the system after a sudden global quench. As initial states we consider a canted or spiral order product state of the spins and singlets of neighboring pairs of spins. We find that within the class of canted order initial states, no entanglement is generated at any time except for the special case of the N\'eel state. While an earlier work has shown that the N\'eel state is indeed an excellent starting resource for the dynamical generation of long-distance entanglement, the curious fact that this is the sole point within a large class of initial product states of the spins was not noted. On the other hand, we find that an initial state which is a series of nearest-neighbor Bell states, and well motivated by some physical realizations, is also a good starting resource for end to end entanglement in a way similar to that of the N\'eel state. The scheme is shown to be robust to random single spin flip in the initial N\'eel state as well as to randomness of the couplings.
We study the ground-state entanglement in systems of spins forming the boundary of a quantum spin network in arbitrary geometries and dimensionality. We show that as long as they are weakly coupled to the bulk of the network, the surface spins are strongly entangled, even when distant and not directly interacting, thereby generalizing the phenomenon of long-distance entanglement occurring in quantum spin chains. Depending on the structure of the couplings between surface and bulk spins, we discuss in detail how the patterns of surface entanglement can range from multipair bipartite to fully multipartite. In the context of quantum information and communication, these results find immediate application to the implementation of quantum routers, that is, devices able to distribute quantum correlations on demand among multiple network nodes.