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arXiv:1009.4738 · Physical Review Letters

Charge Sensing Amplification via Weak Values Measurement

Oded Zilberberg, Alessandro Romito, Yuval Gefen

Published Feb 24, 2011• 79 citations
arXivHTMLPDF

Abstract

A protocol employing weak values (WVs) to obtain ultrasensitive amplification of weak signals in the context of a solid-state setup is proposed. We consider an Aharonov-Bohm interferometer where both the orbital and the spin degrees of freedom are weakly affected by the presence of an external charge to be detected. The interplay between the spin and the orbital WVs leads to a significant amplification even in the presence of finite temperature, voltage, and external noise.

DOI
10.1103/physrevlett.106.080405

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A protocol employing weak values (WVs) to obtain ultrasensitive amplification of weak signals in the context of a solid-state setup is proposed. We consider an Aharonov-Bohm interferometer where both the orbital and the spin degrees of freedom are weakly affected by the presence of an external charge to be detected. The interplay between the spin and the orbital WVs leads to a significant amplification even in the presence of finite temperature, voltage, and external noise.
We present a weak measurement protocol that permits a sensitive estimation of angular rotations based on the concept of weak-value amplification. The shift in the state of a pointer, in both angular position and the conjugate orbital angular momentum bases, is used to estimate angular rotations. This is done by an amplification of both the real and imaginary parts of the weak-value of a polarization operator that has been coupled to the pointer, which is a spatial mode, via a spin-orbit coupling. Our experiment demonstrates the first realization of weak-value amplification in the azimuthal degree of freedom. We have achieved effective amplification factors as large as 100, providing a sensitivity that is on par with more complicated methods that employ quantum states of light or extremely large values of orbital angular momentum.
Weak value (WV) protocols may lead to extreme expectation values that are larger than the corresponding orthodox expectation values. Recent works have proposed to implement this concept in nano-scale electronic systems. Here we address the issue of how one calibrates the setup in question, maximizes the measurement's sensitivity, and extracts distinctly large WVs. Our concrete setup consists of two Mach-Zehnder interferometers (MZIs): the "system" and the "detector". Such setups have already been implemented in experiment.
The weak measurement proposed by Aharonov and his colleagues extracts information of a physical quantity of the system by the post selection as the shifts of the argument of the probe wavefunction. The shift is called the weak value and is larger for the post-selected state more orthogonal to the initial state. Recently, the signal amplification by the weak measurement has been extensively studied. In the present work, we explicitly obtain the optimal probe wavefunction and the amplification factor for a given weak value, which is calculated from the experimental setup. It is shown that the amplification factor has no upper bound in contrast to the Gaussian probe wavefunction and that the amplified signal is sharp.
In the Demonstration it is possible to choose whether to plot the charge's weak value, D2<Q2>S1(in units of the electron charge), as a function of the voltage bias (measured in μV), the phase difference, or the temperature (measured in mK). (The phase difference includes the Aharonov–Bohm flux and the phases of the transmission coefficients of both the quantum point contacts.) In all cases it is possible to control the other parameters, including the transparencies of both the quantum point contacts and the duration of the measurement (measured in nsec). In the upper panel of the Demonstration we also plot the upper bound for standard quantum average of the charge in arm 2 (the lower bound is obviously 0): the weak value is clearly beyond the marked bounds
Optical interferometry plays an essential role in precision metrology such as in gravitational wave detection, gyroscopes, and environmental sensing. Weak value amplification enables reaching the shot-noise-limit of sensitivity, which is difficult for most optical sensors, by amplifying the interferometric signal without amplifying certain technical noises. We implement a generalized form of weak value amplification on an integrated photonic platform with a multi-mode interferometer. Our results pave the way for a more sensitive, robust, and compact platform for measuring phase, which can be adapted to fields such as coherent communications and the quantum domain. In this work, we show a 7 dB signal enhancement in our weak value device over a standard Mach-Zehnder interferometer with equal detected optical power, as well as frequency measurements with 2 kHz sensitivity by adding a ring resonator.