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Chinese Physics

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

Peng Zhao-Hui, 邹健, 邵彬

Published Sep 1, 2007• 0 citations
Publisher

Abstract

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.

DOI
10.1088/1009-1963/16/9/012

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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.
In this paper we consider two distant mesoscopic superconducting quantum interference device (SQUID) rings A and B in the presence of two-mode squeezed vacuum state field, and aim to see the effect of the field on the correlation of supercurrents in the two rings. We know the degree of entanglement of the two-mode squeezed vacuum state increases with the squeezing parameter r. In this paper we find that the correlation of the supercurrents increases with the parameter r too, meaning that the correlation of the supercurrents increases with the degree of entanglement of the field.
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.
Two mesoscopic SQUID rings which are far from each other, are considered.A source of twomode 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.
We consider the entanglement of two remote qubits induced by local interaction with the two-mode nonclassical state fields. We investigate the transfer of entanglement from different two-mode nonclassical state fields to a pair of separable and mixed qubits. We find that no matter what state the qubit subsystem is initially prepared in, at the specific time $gt\ensuremath{\simeq}11.07$ the entanglement of the Bell state fields can be almost completely transferred to the qubit subsystem, i.e., the Bell state fields can drive an initially separable and very mixed state of qubits into an almost pure highly entangled state suitable for quantum information processing. For the entangled coherent state fields $\ensuremath{\mid}u⟩={N}_{1}(\ensuremath{\mid}\ensuremath{\alpha},\ensuremath{-}\ensuremath{\alpha}⟩+\ensuremath{\mid}\ensuremath{-}\ensuremath{\alpha},\ensuremath{\alpha}⟩)$ and $\ensuremath{\mid}{u}^{\ensuremath{'}}⟩={N}_{2}(\ensuremath{\mid}\ensuremath{\alpha},\ensuremath{-}\ensuremath{\alpha}⟩\ensuremath{-}\ensuremath{\mid}\ensuremath{-}\ensuremath{\alpha},\ensuremath{\alpha}⟩)$ we find that when $\ensuremath{\mid}\ensuremath{\alpha}\ensuremath{\mid}$ is small, the dynamic behaviors of the entanglement between two qubits are quite different. For $\ensuremath{\mid}u⟩$ there is almost no entanglement between two qubits while for $\ensuremath{\mid}{u}^{\ensuremath{'}}⟩$ the dynamic behavior of the entanglement between two qubits is very similar to that of the Bell state field. For large $\ensuremath{\mid}\ensuremath{\alpha}\ensuremath{\mid}$ we find that the dynamic behaviors of entanglement between two qubits are almost the same for these two fields, and when $gt\ensuremath{\sim}\ensuremath{\mid}\ensuremath{\alpha}\ensuremath{\mid}\ensuremath{\pi}$ the entanglement between two qubits reaches its maximum and is almost independent of initial mixedness of the qubit subsystem. For the two-mode squeezed vacuum state field we find that when $r\ensuremath{\sim}0.86$ and $gt\ensuremath{\simeq}11.07$ the entanglement transfer reaches its maximum which also almost does not depend on the initial mixedness of the qubit subsystem.
In this paper we investigate the behavior of a fully quantum mechanical system consisting of a mesoscopic SQUID ring coupled to one or two electromagnetic field modes. We show that we can use a static magnetic flux threading the SQUID ring to control the transfer of energy, the entanglement and the statistical properties of the fields coupled to the ring. We also demonstrate that at, and around, certain values of static flux the effective coupling between the components of the system is large. The position of these regions in static flux is dependent on the energy level structure of the ring and the relative field mode frequencies, In these regions we find that the entanglement of states in the coupled system, and the energy transfer between its components, is strong.