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arXiv:1602.08278 · Fluctuation and Noise Letters

Sequential Measurement of Displacement and Conduction Currents in Electronic Devices

Guillermo Albareda, Fabio L. Traversa, A. Benali

Published Jul 7, 2016• 2 citations
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Abstract

The extension of the Ramo–Schockley–Pellegrini theorem for quantum systems allows to define a positive-operator valued measure (POVM) for the total conduction plus displacement electrical current. The resulting current operator is characterized by two parameters, viz. the width of the associated Gaussian functions and the lapse of time between consecutive measurements. For large Gaussian dispersions and small time intervals, the operator obeys to a continuous weak-measurement scheme. Contrarily, in the limit of very narrow Gaussian widths and a single-shot measurement, the operator corresponds to a standard von Neumann (projective) measurement. We have implemented the resulting measurement protocol into a quantum electron transport simulator. Numerical results for a resonant tunneling diode show the great sensibility of current–voltage characteristics to different parameter configurations of the total current operator.

DOI
10.1142/s0219477516400046

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The extension of the Ramo–Schockley–Pellegrini theorem for quantum systems allows to define a positive-operator valued measure (POVM) for the total conduction plus displacement electrical current. The resulting current operator is characterized by two parameters, viz. the width of the associated Gaussian functions and the lapse of time between consecutive measurements. For large Gaussian dispersions and small time intervals, the operator obeys to a continuous weak-measurement scheme. Contrarily, in the limit of very narrow Gaussian widths and a single-shot measurement, the operator corresponds to a standard von Neumann (projective) measurement. We have implemented the resulting measurement protocol into a quantum electron transport simulator. Numerical results for a resonant tunneling diode show the great sensibility of current–voltage characteristics to different parameter configurations of the total current operator.
Weak values allow the measurement of observables associated with noncommuting operators. Up to now, position-momentum weak values have been mainly developed for (relativistic) photons. In this Letter, a proposal for the measurement of such weak values in typical electronic devices is presented. Inspired by the Ramo-Shockley-Pellegrini theorem that provides a relation between current and electron velocity, it is shown that the displacement current measured in multiterminal configurations can provide either a weak measurement of the momentum or strong measurement of position. This proposal opens new opportunities for fundamental and applied physics with state-of-the-art electronic technology. As an example, a setup for the measurement of the Bohmian velocity of (nonrelativistic) electrons is presented and tested with numerical experiments.
Motivated by a recent approach to solve quantum dynamics with full Coulomb correlations [X. Oriols, Phys. Rev. Lett.98 (2007) 066803], we present here an extension of the Ramo–Shockley–Pellegrini theorem for quantum systems to compute the total (conduction plus displacement) current in terms of quantum (Bohmian) trajectories. By way of test, we derive an extension of the Ramo-Shockley-Pellegrini theorem using standard quantum mechanics and we compare it to our former result. As expected, both formulations give identical results, however we emphasize the numerical viability of computing self-consistently the total current by means of quantum trajectories in front of the difficulties to do it in terms of standard quantum mechanics.
With the aim of manufacturing faster and smaller devices, the electronic industry is today entering into the nanoscale and the high frequency regimes. In this particular scenario, the dynamics of the electron charge becomes affected by quantum mechanical laws, both, for its spatial or temporal description. We have recently shown that Bohmian trajectories allow a direct treatment of the time-dependent many-particle interaction among electrons with an accuracy comparable to Density Functional Theory techniques. In addition, Bohmian mechanics, by combining wave functions and trajectories, provides a very simple description on how to describe multi-time measurements in quantum scenarios. Using the previous formalism, in this work we present a general purpose time-dependent 3D quantum electron transport simulator named BITLLES (Bohmian Interacting Transport in large low-dimensional Electronic Structures) especially indicated for AC, transients and noise predictions. As a numerical example of its capabilities, we compute the full electrical characteristics (DC, High frequency and fluctuations) of a Resonant Tunneling Diode.
A recent proposal for modeling time-dependent quantum electron transport with Coulomb and exchange correlations using quantum (Bohm) trajectories (Oriols 2007 Phys. Rev. Lett. 98 066803) is extended towards the computation of the total (particle plus displacement) current in mesoscopic devices. In particular, two different methods for the practical computation of the total current are compared. The first method computes the particle and the displacement currents from the rate of Bohm particles crossing a particular surface and the time-dependent variations of the electric field there. The second method uses the Ramo–Shockley theorem to compute the total current on that surface from the knowledge of the Bohm particle dynamics in a 3D volume and the time-dependent variations of the electric field on the boundaries of that volume. From a computational point of view, it is shown that both methods achieve local current conservation, but the second is preferred because it is free from 'spurious' peaks. A numerical example, a Bohm trajectory crossing a double-barrier tunneling structure, is presented, supporting the conclusions.
Measuring properties of quantum systems is governed by a stochastic (collapse or state-reduction) law that unavoidably yields an uncertainty (variance) associated with the corresponding mean values. This non-classical source of uncertainty is known to be manifested as noise in the electrical current of nanoscale electron devices, and hence it can flaw the good performance of more complex quantum gates. We propose a protocol to alleviate this quantum uncertainty that consists of (i) redesigning the device to accommodate a large number of electrons inside the active region, either by enlarging the lateral or longitudinal areas of the device and (ii) re-normalizing the total current to the number of electrons. How the above two steps can be accommodated using the present semiconductor technology has been discussed and numerically studied for a resonant tunneling diode and a Mach-Zehnder interferometer, for classical and quantum computations, respectively. It is shown that the resulting protocol formally resembles the so-called collective measurements, although, its practical implementation is substantially different.
In the quantum theory of measurement, the positive operator-valued measure (POVM) is an important concept, and its implementation can be useful. A POVM consists of a set of non-negative quantum-mechanical Hermitian operators that add up to the identity. The probability that a quantum system is in a particular state is given by the expectation value of the POVM operator corresponding to that state. Following a brief review of the mathematics and mention of the history of POVMs in quantum theory, a particular implementation of a POVM for use in the measurement of nonorthogonal photon polarization states is reviewed. The implementation consists simply of a Wollaston prism, a mirror, two beam splitters, a polarization rotator and three phototubes arranged in an interferometric configuration, and it is shown analytically that the device faithfully represents the POVM. Based on Neumark's extension theorem, the two-dimensional Hilbert space of the POVM implementation can be embedded in the three-dimensional Hilbert space of an ordinary projective-valued measure. Also, analytical expressions are given for the maximum Renyi information loss from the device to a disturbing probe, and for the error and inconclusive rates induced by the probe. Various aspects of the problem of probe optimization are elaborated.