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arXiv:cond-mat/0411439 · Journal of Physics Condensed Matter

Entangled quantum currents in distant mesoscopic Josephson junctions

Dimitris I. Tsomokos, C C Chong, Apostol Vourdas

Published Dec 7, 2004• 6 citations
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Abstract

Two mesoscopic SQUID rings which are far from each other, are considered. A source of two-mode nonclassical microwaves irradiates the two rings with correlated photons. The Josephson currents are in this case quantum mechanical operators, and their expectation values with respect to the density matrix of the microwaves, yield the experimentally observed currents. Classically correlated (separable) and quantum mechanically correlated (entangled) microwaves are considered, and their effect on the Josephson currents is quantified. Results for two different examples that involve microwaves in number states and coherent states are derived. It is shown that the quantum statistics of the tunnelling electron pairs through the Josephson junctions in the two rings, are correlated.

DOI
10.1088/0953-8984/16/50/008

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A ring made from a Josephson array in the insulating phase is considered. The ring contains a ‘dual Josephson junction’ (Josephson junction for vortices). External non-classical electromagnetic fields are coupled to the device and interact with the vortices that circulate the ring. The time evolution of this two-mode fully quantum mechanical system is studied. The effect of the quantum statistics of the photons on the quantum statistics of the vortices is discussed. The entanglement between the two systems is quantified.
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 CAB. We show that when the parameteris very small for the separable state with the density matrix ˆ � = (|�, −�i h �, −�| + |−�,�i h− �,�|)/2 and entangled coherent state (ECS) |ui = N1(|�, −�i + |−�,�i ) fields, the dynamic behaviours of the normalized correlation function CAB are similar, but it is quite different for the entangled coherent state |ui = N2(|�, −�i − |− �,�i ) field. When the parameteris very large, the dynamic behaviours of CAB are almost the same for the separable state, entangled coherent state |ui and |ui fields. For the two-mode squeezed vacuum state field the maximum of CAB increases monotonically with the squeezing parameter r, and as r → ∞, CAB → 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.