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Communications in Theoretical Physics

Shapiro Step Features and Quantum Dynamics of Aharonov–Bohm Electron Interference in a Two-Mode Squeezed State

Shao Bin, Zou Jian

Published Sep 15, 1999• 0 citations
Publisher

Abstract

Aharonov–Bohm-type electron interference in a two-mode squeezed state is inves tigated.The properties of Shapiro steps, visibility of the interference fringe and the dynamic behavior of electron interference are discussed. We find that the time evolution of electron interference intensity in the two-mode squeezed state can exhibit very interesting quantum collapse and revival phenomenon.

DOI
10.1088/0253-6102/32/2/235

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Aharonov–Bohm-type electron interference in a two-mode squeezed state is inves tigated.The properties of Shapiro steps, visibility of the interference fringe and the dynamic behavior of electron interference are discussed. We find that the time evolution of electron interference intensity in the two-mode squeezed state can exhibit very interesting quantum collapse and revival phenomenon.
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Electron interference related to Aharonov-Bohm effect in the presence of the two-mode quantized radiation field is investigated. Characteristics of the temporal behavior of electron interference are discussed. It is shown that for the two-mode squeezed vacuum field the time evolution of the intensity of electron interference can exhibit very interesting periodic spontaneous collapse and revival (CR). In addition, the relation between CR and the quantum fluctuation in electron interference is also discussed.
Dynamic behaviour of Aharonov-Bohm-type electron interference in the presence of a nonclassical electromagnetic field is investigated. The visibility of the time-averaged interference pattern is discussed for SU(1,1) coherent state (CS) and a comparison with other states is made. It is shown that the dynamic behaviour of the electron interference exhibits collapse and revival (CR) phenomenon for SU(1,1) CS. It is also shown that CR phenomenon of electron interference is closely related to the fluctuation of a nonclassical electromagnetic field.
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.
Very much like the ubiquitous quantum interference of a single particle with itself, quantum interference of two independent, but indistinguishable, particles is also possible. This interference is a direct result of quantum exchange statistics, however, it is observed only in the joint probability to find the particles in two separated detectors. Here we report the first observation of such interference fringes between two independent and non-interacting electrons in an interferometer proposed by Yurke et al. and Samuelsson et al. Our experiment resembles the "Hanbury Brown and Twiss" (HBT) experiment, which was performed with classical waves. In the experiment, two independent and mutually incoherent electron beams were each partitioned into two trajectories. The combined four trajectories enclosed an Aharonov-Bohm (AB) flux (but not the two trajectories of a single electron). While individual currents were found to be independent of the AB flux, as expected, the cross-correlation between current fluctuations in two opposite points across the device exhibited strong AB oscillations. This is a direct signature of orbital entanglement between two electrons even though they never interact with each other.
Theory predicts that electrons emitted from independent electron sources (metallic contacts) can nevertheless interfere. This interference is manifest in an exchange contribution to the shot noise correlation of currents at different contacts of a mesoscopic conductor. A geometry has been proposed in which second order (single particle) interference due to superposition of amplitudes is absent but fourth order (two-particle) interference exhibits Aharonov-Bohm oscillations. Recently such a geometry has been realized in an experiment and the theoretically predicted two-particle Aharonov-Bohm effect has been detected. We discuss Bell measurements and quantum state tomography using shot noise correlations. We discuss in addition structures in which two-particle interference effects are generated dynamically by varying electrostatic potentials with the help of gates or by generating electron-hole pairs by irradiating contacts of a mesoscopic conductor. These examples emphasize that two-particle processes are not related to a particular geometry but are a general feature of multiparticle observables like shot noise correlations.