Journal of the Physical Society of Japan

Quantum Interference and Inelastic Scattering in a Model Which–Way Device

A. MacKinnon, Andrew D. Armour

Published Jan 3, 2003• 1 citation

Abstract

A which–way device is one which is designed to detect which of 2 paths is taken by a quantum particle, whether Schrödinger's cat is dead or alive. One possible such device is represented by an Aharonov–Bohm ring with a quantum dot on one branch. A charged cantilever or spring is brought close to the dot as a detector of the presence of an electron. The conventional view of such a device is that any change in the state of the cantilever implies a change in the electron state which will in turn destroy the interference effects. In this paper we show that it is in fact possible to change the state of the oscillator while preserving the quantum interference phenomenon.

DOI: 10.1143/jpsjs.72sa.118

Related papers

Possibility of an electromechanical which-path interferometer

Andrew D. Armour, M. P. Blencowe

We investigate the possibility of an electromechanical which-path interferometer, in which electrons traveling through an Aharonov-Bohm ring incorporating a quantum dot in one of the arms are dephased by an interaction with the fundamental flexural mode of a radio-frequency cantilever. The cantilever is positioned so that its tip lies just above the dot and a bias is applied so that an electric field exists between the dot and the tip. This electric field is modified when an additional electron hops onto the dot, coupling the flexural mode of the cantilever and the microscopic electronic degrees of freedom. We analyze the transmission properties of this system and the dependence of interference fringe visibility on the cantilever-dot coupling and on the mechanical properties of the cantilever. The fringes are progressively destroyed as the interaction with the cantilever is turned up, in part due to dephasing arising from the entanglement of the electron and cantilever states and also due to the thermal smearing that results from fluctuations in the state of the cantilever. When the dwell time of the electron on the dot is comparable to or longer than the cantilever period, we find coherent features in the transmission amplitude. These features are washed out when the cantilever is decohered by its coupling to the environment.

arXiv:cond-mat/0101157Physical review. B, Condensed matterJun 20, 200137 citations

A mesoscopic quantum eraser

Gregor Hackenbroich, Bernd Rosenow, Hans A. Weidenmüller

Motivated by a recent experiment by Buks et al. ( Nature 391 (1998) 871) we consider electron transport through an Aharonov-Bohm interferometer with a quantum dot in one of its arms. The quantum dot is coupled to a quantum system with a finite number of states acting as a which-path detector. The Aharonov-Bohm interference is calculated using a two-particle scattering approach for the joint transitions in detector and quantum dot. Tracing over the detector yields dephasing and a reduction of the interference amplitude. We show that the interference can be restored by a suitable measurement on the detector and propose a mesoscopic quantum eraser based on this principle.

arXiv:cond-mat/9811180Europhysics Letters (EPL)Dec 15, 19988 citations

Electron Interference in a Quantum Ring with a Tunable Magnetic Field Shield

Minky Seo, Hwanchul Jung, Yunhcul Chung

A quantum ring device that can turn on and off the external magnetic field on the ring is developed.The device is to study the effect of the interaction between electrons and external magnetic fields on Aharonov-Bohm interference.The switching is realized by employing a superconducting shield gate and turning on and off the superconductivity on the gate with applied current or magnetic field.The electron interference due to Aharonov-Bohm effect is observed regardless of the presence of the external magnetic field on the electron path of the ring.The result is consistent with the fact that effects of potentials on charged particles exists even in the region where all the field vanish hence no direct interaction between electron and magnetic field is allowed.

Applied Science and Convergence TechnologyMar 31, 20212 citations

Complementarity in a Closed-Loop Aharonov-Bohm Interferometer

Gyong Luck Khym, Kicheon Kang, Dong-In Chang +2 more

We study complementarity in a two-terminal closed-loop Aharonov-Bohm interferometer with a quantum dot embedded in an arm of the ring and a nearby charge detector capacitively coupled to the quantum dot. We show that perfect charge detection does riot give full information of the electronic path, so it does not completely suppress the interference. We propose that this property can be verified even in the limit of weak charge detection by investigating the dephasing of the first and the second harmonics of the Aharonov-Bohm oscillation. The first harmonic of the AB oscillation is reduced monotonically as a function of the charge detection strength. In contrast, the second harmonic interference remains unaffected due to the fact that charge detection is not able to detect the electronic path responsible for the second harmonic. Our theory confirms that the particle-like behavior of an electron emerges from the path information itself rather than from the disturbance.

Journal of the Korean Physical SocietyDec 15, 20080 citations

Loss of interference in an Aharonov-Bohm ring

Sandeep Joshi, Debendranath Sahoo, Jayannavar, A. M.

We study a simple model of dephasing of Aharonov-Bohm oscillations in the transmission of an electron across a mesoscopic ring. A magnetic impurity in one of the arms of the ring couples to the electron spin via an exchange interaction. This interaction leads to spin flip scattering and induces dephasing via entanglement. This is akin to the models evoked earlier to explain destruction of interference due to which-path information in double-slit experiments. Total transmission is found to be symmetric under flux reversal but not the spin polarization.

arXiv:cond-mat/0101436Jan 29, 20011 citation

The Aharonov-Bohm Effect: An Exploration of Quantum Interference and Electromagnetic Potentials

Bahman Zohuri

The AB (Aharonov-Bohm) effect is a pivotal quantum mechanical phenomenon that illustrates the fundamental role of the electromagnetic vector potential A in determining the phase of a charged particle's wave function, even in regions where the magnetic field B is zero.This effect demonstrates that quantum particles are influenced not only by the fields directly present but also by the potentials associated with those fields.In the AB effect, an electron beam is split into two paths, with one path encircling a solenoid and the other bypassing it.Despite the absence of a magnetic field in the regions traversed by the beams, the vector potential A associated with the magnetic flux  through the solenoid induces a phase shift in the electron's wave function.This phase shift, quantified by qc     , manifests as a change in the interference pattern observed in the detection screen.The phenomenon underscores the principle of gauge invariance in QED (quantum electrodynamics), where physical observables remain invariant under local gauge transformations of the vector and scalar potentials.This reinforces the notion that the vector potential A has a profound impact on quantum systems, beyond its classical role.This article outlines the AB effect, including its theoretical framework, experimental observations, and implications.The focus on the role of the vector potential in quantum mechanics provides a comprehensive understanding of this important phenomenon.

Journal of Energy and Power EngineeringJun 28, 20241 citation