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Journal of Optics B Quantum and Semiclassical Optics

Entanglement of distant superconducting quantum interference device rings

Zuriati Ahmad Zukarnain, A. Konstadopoulou, Apostol Vourdas, Rosanna Migliore, ANTONINO MESSINA

Published Nov 22, 2005• 1 citation
Publisher

Abstract

We consider two distant mesoscopic SQUID rings, approximated with two-level systems, interacting with two-mode microwaves. The Hamiltonian of the system is used to calculate its time evolution. The cases with microwaves which at t = 0 are in separable states (classically correlated) or entangled states (quantum mechanically correlated) are studied. It is shown that the Josephson currents in the two SQUID rings are also correlated.

DOI
10.1088/1464-4266/7/12/039

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We consider two distant mesoscopic SQUID rings, approximated with two-level systems, interacting with two-mode microwaves. The Hamiltonian of the system is used to calculate its time evolution. The cases with microwaves which at t = 0 are in separable states (classically correlated) or entangled states (quantum mechanically correlated) are studied. It is shown that the Josephson currents in the two SQUID rings are also correlated.
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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 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.
We present a simple scheme for the preparation of entangled states of the e.m. modes of two spatially separated microwave cavities exploiting their interaction with two superconducting SQUID rings embedded within them. The scheme requires that the two SQUID qubits are initially prepared in an entangled state and the possibility of controlling both the coupling strengths and the interaction times. We also briefly discuss the importance of such a theoretical scheme in view of possible applications in the context of quantum computing and its experimental feasibility.
In this paper we consider the interaction of a quantum-mechanical superconducting quantum interference device (SQUID) with a classical monochromatic electromagnetic (EM) field. We solve the time-dependent Schrödinger equation for the SQUID ring in this EM field. We demonstrate that non-perturbative transitions between the low-lying states of the ring, due to coherent multiphoton absorption processes, dominate, even when the single-photon energy is small compared with the energy separation between these states. We present experimental data on small-capacitance SQUID rings, interacting with microwave fields, which point to the existence of such non-perturbative transitions.