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IEE Proceedings - Science Measurement and Technology

Mesoscopic Josephson arrays interactingwith non-classical electromagnetic fields and theirapplications

A. Konstadopoulou, J.M. Hollingworth, M. J. Everitt, Apostol Vourdas, Terrence D. Clark, Jason F. Ralph

Published Sep 5, 2001• 3 citations
Publisher

Abstract

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.

DOI
10.1049/ip-smt:20010394

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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.
Mesoscopic Josephson devices, interacting with non-classical microwaves, are studied. The phase difference in Josephson's equations is a quantum mechanical operator, whose expectation value with respect to the density matrix describing the microwaves, determines the current. Dual phenomena with vortex condensates in Josephson array insulators are also considered. Dual Josephson junctions for vortices, made from two insulators separated by a weak link through which the vortices tunnel, are described by dual Josephson equations.
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.
A Josephson array ring in the insulating phase with circulating vortices is considered. The persistent vortex current is calculated as a function of the charge at the center of the ring and the temperature, for the case of negligible dissipation. A weak link is introduced in the ring and the tunneling of vortices through it is described with the ``dual Josephson equations.'' The Hamiltonian that describes the interaction of these devices with electromagnetic fields is quantized. The use of such nonlinear devices as amplifiers and frequency converters of nonclassical microwaves is discussed.
The interaction of mesoscopic interference devices with nonclassical electromagnetic fields is studied. The external quantum fields induce a phase factor in the electric charges. This phase factor, which is a generalization of the standard Aharonov–Bohm phase factor, is in the case of nonclassical electromagnetic fields a quantum mechanical operator. Its expectation value depends on the density matrix describing the nonclassical photons and determines the interference. Several examples are discussed, which show that the quantum noise of the nonclassical photons partly destroys the electron interference fringes. An interesting application arises in the context of distant electron interference devices, irradiated with entangled photons. In this case the interfering electrons in the two devices become entangled. The same ideas are applied in the context of SQUID rings irradiated with nonclassical electromagnetic fields. It is shown that the statistics of the Cooper pairs tunnelling through the Josephson junction depends on the statistics of the photons.