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 quantum interference device (SQUID) rings A and B in the presence of two-mode nonclassical state fields and investigated the correlation of the supercurrents in the two rings using the normalized correlation function C_\rm AB. We show that when the parameter \alpha is very small for the separable state with the density matrix \hat \rho = (\left| \alpha , - \alpha \right\rangle \left\langle \alpha , - \alpha \right| + \left| - \alpha ,\alpha \right\rangle \left\langle - \alpha ,\alpha \right|) / 2 and entangled coherent state (ECS) \left| u \right\rangle = N_1 (\left| \alpha , - \alpha \right\rangle + \left| - \alpha ,\alpha \right\rangle ) fields, the dynamic behaviours of the normalized correlation function C_\rm AB are similar, but it is quite different for the entangled coherent state \left| u' \right\rangle = N_2 (\left| \alpha , - \alpha \right\rangle - \left| - \alpha ,\alpha \right\rangle ) field. When the parameter \alpha is very large, the dynamic behaviours of C_\rm AB are almost the same for the separable state, entangled coherent state \left| u \right\rangle and \left| u' \right\rangle 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 the supercurrents in the two rings A and B are quantum mechanically correlated perfectly. It is concluded that not all the quantum correlations in the two-mode nonclassical state field can be transferred to the supercurrents; and the transfer depends on the state of the two-mode nonclassical state field prepared.