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arXiv:quant-ph/0502113 · Journal of Optics B Quantum and Semiclassical Optics

Electron interference in mesoscopic devices in the presence of nonclassical electromagnetic fields

Dimitris I. Tsomokos, Chee Ching Chong, Apostol Vourdas

Published May 16, 2005• 3 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1464-4266/7/6/r01

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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.
Electron interference in mesoscopic devices irradiated by external monochromatic nonclassical microwaves is considered. The relative phase factor between two electron paths is a quantum mechanical operator whose expectation value with respect to the density matrix of the nonclassical microwaves is studied. It is shown that, due to both classical and quantum noise in the microwaves, the absolute value of the phase factor is less than 1,1,1, causing partial destruction of the interference. Separable and entangled two-mode nonclassical microwaves are also considered and their effect on the expectation value of the phase factor is studied.
Two electron interference experiments which are far from each other are considered. They are irradiated with correlated nonclassical electromagnetic fields, produced by the same source. The phase factors are in this case operators, and their expectation values with respect to the density matrix of the electromagnetic field quantify the observed electron fringes. The correlated photons create correlations between the observed electron intensities. Both cases of classically correlated (separable) and quantum mechanically correlated (entangled) electromagnetic fields are considered. It is shown that the induced correlation between the distant electron interferences is sensitive to the nature of the correlation between the irradiating photons.
Interfering electrons in a mesoscopic ring are irradiated with both classical and nonclassical microwaves. The average intensity of the charges is calculated as a function of time and it is found that it depends on the nature of the irradiating electromagnetic field. For various quantum states of the microwaves, the electron autocorrelation function is calculated and it shows that the quantum noise of the external field affects the interference of the charges. Two-mode entangled microwaves are also considered and the results for electron average intensity and autocorrelation are compared with those of the corresponding separable state. In both cases, the results depend on whether the ratio of the two frequencies is rational or irrational.
Interfering electrons in a mesoscopic ring are irradiated with both classical and nonclassical microwaves. The average intensity of the charges is calculated as a function of time and it is found that it depends on the nature of the irradiating electromagnetic field. For various quantum states of the microwaves, the electron autocorrelation function is calculated and it shows that the quantum noise of the external field affects the interference of the charges. Two-mode entangled microwaves are also considered and the results are compared with those of the corresponding separable state. In both cases, the results depend on whether the ratio of the two frequencies is rational or irrational.
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.
The topological phase factor induced on interfering electrons by external quantum electromagnetic fields has been studied. Two and three electron interference experiments inside distant cavities are considered and the influence of correlated photons on the phase factors is investigated. It is shown that the classical or quantum correlations of the irradiating photons are transferred to the topological phases. The effect is quantified in terms of Weyl functions for the density operators of the photons and illustrated with particular examples. The scheme employs the generalized phase factor as a mechanism for information transfer from the photons to the electric charges. In this sense, the scheme may be useful in the context of flying qubits (corresponding to photons) and stationary qubits (electrons), as well as the conversion from one type to the other.