Entanglement Routers Using Macroscopic Singlets

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.

Figure 1

(a) The composite system made of two separate Kondo spin chains initialized in their ground states in the Kondo regime. Equation (5) is satisfied by tuning $J_k^{\prime }$. (b) To induce dynamics, one switches on the interaction between the two chains by the amount $J_m$.

Figure 2

(a) The entanglement dynamics vs time $t$ ($J_2=0$) for a composite system of $N=32$ when $N_L=N_R$. (b) The maximal entanglement $E_m$ vs $N$. (c) $t^{*}$ vs $N$.

Figure 3

(a) Optimal $J_m$ vs $N$ for $N_L=N_R$ in the Kondo regime. (b) The asymptotic behavior of $\Phi (N)$ vs ${log}^2(\frac{N}{2})$.

Figure 4

Nonsymmetric case where $N=32$ and $N_L$ and $N_R$ are varied: (a) $E_m$ vs $N_L/N$. (b) $t^{*}$ vs $N_L/N$.

Figure 5

A four-node router in which each user controls one boundary spin. A dispatcher connects two chains to induce dynamics in a channel composed of two spin chains.