The transfer of the quantum correlation from two-mode nonclassical state field to the supercurrents in two distant SQUID rings

We have considered two distant mesoscopic superconducting quantuminterference device (SQUID) rings A and B in the presence of two-modenonclassical state fields and investigated the correlation of thesupercurrents in the two rings using the normalized correlationfunction $C_{rm AB}$. We show that when the parameter $alpha$ isvery small for the separable state with the density matrix $hat{rho } = (left| {alpha , - alpha } rightrangle leftlangle{alpha , - alpha } right| + left| { - alpha ,alpha }rightrangle leftlangle { - alpha ,alpha } right|) / 2$ andentangled coherent state (ECS) $left| u rightrangle = N_1 (left|{alpha , - alpha } rightrangle + left| { - alpha ,alpha }rightrangle )$ fields, the dynamic behaviours of the normalizedcorrelation function $C_{rm AB}$ are similar, but it is quitedifferent for the entangled coherent state $left| {u}'rightrangle = N_2 (left| {alpha , - alpha } rightrangle -left| { - alpha ,alpha } rightrangle )$ field. When theparameter $alpha $ is very large, the dynamic behaviours of $C_{rmAB}$ are almost the same for the separable state, entangled coherentstate $left| u rightrangle $ and $left| {u}' rightrangle $fields. For the two-mode squeezed vacuum state field the maximum of$C_{rm AB}$ increases monotonically with the squeezing parameter$r$, and as $r to infty $, $C_{rm AB} to 1$. This means that thesupercurrents in the two rings A and B are quantum mechanicallycorrelated perfectly. It is concluded that not all the quantumcorrelations in the two-mode nonclassical state field can betransferred to the supercurrents; and the transfer depends on thestate of the two-mode nonclassical state field prepared.