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Physical Review A

Destruction of the interference by external nonclassical microwaves: The effect of quantum and classical noise on the phase factor

Apostol Vourdas

Published Oct 12, 2001• 11 citations
Publisher

Abstract

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 $1,$ 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.

DOI
10.1103/physreva.64.053814

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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.
Electron interference in mesoscopic devices irradiated by external nonclassical microwaves is considered. In the case of one-mode microwaves, it is shown that both the average intensity and the spectral density of the interfering electrons are sensitive to the quantum noise of the microwaves. The results for various quantum states of the microwaves are compared and contrasted with the classical case. Separable and entangled two-mode microwaves are also considered and their effect on electron average intensity and autocorrelation, 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.
Electron interference in the presence of nonclassical microwaves with frequency ${\mathrm{\ensuremath{\omega}}}_{1}$ and classical RF radiation with frequency ${\mathrm{\ensuremath{\omega}}}_{2}$, is studied. The relative phase factor between the two electron beams is a quantum-mechanical operator, whose expectation value with regard to the density matrix describing the nonclassical microwaves, determines the interference. It is shown that the visibility of the time-averaged intensity is a constant for all irrational values of ${\mathrm{\ensuremath{\omega}}}_{1}$/${\mathrm{\ensuremath{\omega}}}_{2}$, and shows peaks (fractional Shapiro steps) at all rational values. These peaks can provide direct experimental evidence of the highly nonlinear processes of frequency conversion from N photons with frequency ${\mathrm{\ensuremath{\omega}}}_{1}$, to M photons with frequency ${\mathrm{\ensuremath{\omega}}}_{2}$. Results for various types of nonclassical microwaves (e.g., coherent states, squeezed states, number eigenstates, etc.) are derived and a comparison with the corresponding classical case is made. The difference is due to partial interference destruction from the quantum fluctuations in the nonclassical microwaves, and demonstrates the sensitivity of the interference to these quantum fluctuations. \textcopyright{} 1996 The American Physical Society.
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.
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.
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.