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International Journal of Modern Physics B

Characteristics of Aharonov–Bohm Electron Interference in Two-Mode Squeezed Vacuum

Bin Shao, Jian Zou

Published May 10, 1998• 1 citation
Publisher

Abstract

Electron interference related to Aharonov–Bohm effect in the presence of the two-mode quantized radiation field is investigated. Characteristics of Shapiro steps, the visibility of the interference fringe and the temporal behavior of electron interference in correlated and uncorrelated two-mode radiation field are discussed. It is shown that for the correlated two-mode squeezed vacuum the integer Shapiro steps are obtained and the time evolution of the intensity of electron interference can exhibit very interesting periodic spontaneous collapse and revival (CR), while for the uncorrelated two-mode coherent state the fractional Shapiro steps are obtained and the CR phenomenon does not occur. In addition, the relation between CR and the quantum fluctuation in electron interference is also discussed.

DOI
10.1142/s0217979298000648

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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 Shapiro steps, the visibility of the interference fringe and the temporal behavior of electron interference in correlated and uncorrelated two-mode radiation field are discussed. It is shown that for the correlated two-mode squeezed vacuum the integer Shapiro steps are obtained and the time evolution of the intensity of electron interference can exhibit very interesting periodic spontaneous collapse and revival (CR), while for the uncorrelated two-mode coherent state the fractional Shapiro steps are obtained and the CR phenomenon does not occur. In addition, the relation between CR and the quantum fluctuation in electron interference is also discussed.
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.
The coupling of the quantized electromagnetic field to coherent electrons is investigated. The effects both of photon emission and of the electromagnetic vacuum fluctuations upon electron interference are analyzed. The modifications of the vacuum fluctuations due to a conducting plate lead to a decrease in the amplitude of the interference oscillations. The possibility of observing this effect is discussed. It is also shown that there is an analogue of the Aharonov-Bohm effect in which electron interference is sensitive to vacuum fluctuations in regions from which the electrons are excluded.
In this paper we study the dynamics of a three-level atom interacting with a two-mode squeezed vacuum, a highly correlated state in which each mode contains the same number of quanta yet exhibits a thermal photon distribution. Under exact resonance, the Rabi oscillations exhibit an irregular behavior reminiscent of those in the thermal-state Jaynes-Cummings model. If the individual field modes are sufficiently detuned from the intermediate atomic level, the Rabi oscillations become quasiperiodic. The three-level system in this case reduces to an effective two-level system in which two-photon processes dominate. The times of revivals of the Rabi oscillations in this limit depend only on the atom-field coupling constants and the detuning. For comparison, we present a parallel study of the case in which the initial field is prepared in an uncorrelated two-mode state, such as a two-mode thermal state or a two-mode coherent state. Under the full resonance condition, the former leads to an irregular evolution of the Rabi oscillations, while the latter leads to the usual collapse and revival phenomena. If the individual modes are sufficiently detuned from the intermediate atomic level, we observe the same quasiperiodicity of the Rabi oscillations as in the case of the two-mode squeezed vacuum but with a doubling of revival times (for equal atom-field coupling constants). Whereas the two-mode squeezed vacuum and the two-mode thermal-state transition dynamics lead to correlation between the field modes, the two-mode coherent state leads to anticorrelation (when sufficiently detuned from the intermediate atomic level).