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arXiv:1211.2311 · Journal of Physics Condensed Matter

Dephasing of electrons in the Aharonov–Bohm interferometer with a single-molecular vibrational junction

Wenxi Lai, Yunhui Xing, Zhongshui Ma

Published Apr 25, 2013• 6 citations
arXivHTMLPDF

Abstract

Phase relaxation of electrons transferring through an electromechanical transistor is studied using the Aharonov-Bohm interferometer. Using the quantum master equation approach, the phase properties of an electron are numerically analyzed based on the interference fringes. The coherence of the electron is partially destroyed by its scattering on excited levels of the local nanomechanical oscillator. The transmission amplitudes with respect to two adjacent mechanical vibrational levels have a phase difference of π. The character of the π phase shift depends on the oscillator frequency only and is robust over a wide range of values of the applied voltage, tunneling length and damping rate of the mechanical oscillator.

DOI
10.1088/0953-8984/25/20/205304

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Phase relaxation of electrons transferring through an electromechanical transistor is studied using the Aharonov-Bohm interferometer. Using the quantum master equation approach, the phase properties of an electron are numerically analyzed based on the interference fringes. The coherence of the electron is partially destroyed by its scattering on excited levels of the local nanomechanical oscillator. The transmission amplitudes with respect to two adjacent mechanical vibrational levels have a phase difference of π. The character of the π phase shift depends on the oscillator frequency only and is robust over a wide range of values of the applied voltage, tunneling length and damping rate of the mechanical oscillator.
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.
Matter-wave interferometry is a highly sensitive tool to measure small perturbations in a quantum system.This property allows the creation of precision sensors for dephasing mechanisms such as mechanical vibrations.They are a challenge for phase measurements under perturbing conditions that cannot be perfectly decoupled from the interferometer, e.g.for mobile interferometric devices or vibrations with a broad frequency range.Here, we demonstrate a method based on second-order correlation theory in combination with Fourier analysis, to use an electron interferometer as a sensor that precisely characterizes the mechanical vibration spectrum of the interferometer.Using the high spatial and temporal single-particle resolution of a delay line detector, the data allows to reveal the original contrast and spatial periodicity of the interference pattern from 'washed-out' matter-wave interferograms that have been vibrationally disturbed in the frequency region between 100 and 1000 Hz.Other than with electromagnetic dephasing, due to excitations of higher harmonics and additional frequencies induced from the environment, the parts in the setup oscillate with frequencies that can be different to the applied ones.The developed numerical search algorithm is capable to determine those unknown oscillations and corresponding amplitudes.The technique can identify vibrational dephasing and decrease damping and shielding requirements in electron, ion, neutron, atom and molecule interferometers that generate a spatial fringe pattern on the detector plane.
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The nonequilibrium real-time dynamics of electron decoherence is explored in the quantum transport through the nanoscale double-dot Aharonov-Bohm interferometers. We solve the exact master equation to find the exact quantum state of the device, from which the changes of the electron coherence through the magnetic flux in the nonequilibrium transport processes is obtained explicitly. We find that the relative phase between the two charge states of the degenerate double dot localizes to $\frac{\ensuremath{\pi}}{2}$ or $\ensuremath{-}\frac{\ensuremath{\pi}}{2}$ for all different magnetic fluxes, due to decoherence. This nontrivial decoherence process can be manifested in the measurable occupation numbers.
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We investigate the dependence of decoherence on the mode number M in a multiple-mode Aharonov-Bohm (AB) interferometer. The design of the AB interferometer allows us to precisely determine M by the additivity rule of ballistic conductors; meanwhile, the decoherence rate is simultaneously deduced by the variance of the AB oscillation amplitude. The AB amplitude decreases and fluctuates with depopulating M. Moreover, the normalized amplitude exhibits a maximum at a specific M (∼9). Data analysis reveals that the charge-fluctuation-induced dephasing, which depends on the geometry and the charge relaxation resistance of the system, could play an essential role in the decoherence process. Our results suggest that the phase coherence, in principle, can be optimized using a deliberated design and pave one of the ways toward the engineering of quantum coherence.