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International Workshop on Computational Electronics

On the back-action of THz measurement on the total current of quantum devices

Damiano Marian, Nino Zanghı̀, Xavier Oriols

Published Jun 1, 2014• 3 citations
Publisher

Abstract

Measuring a quantum system implies some kind of perturbation of the system itself. A novel approach to include the perturbation of the quantum electron device, i.e. the back-action, due to the TeraHertz (THz) measurement of the total current is presented. The approach is based on a microscopic description of the interaction between the quantum system and the measuring apparatus, in terms of conditional (Bohmian) wave functions. The disturbance of the quantum system due to measurements at THz frequencies and the (perturbed) value of the total current is numerically computed for a simple two-terminal device. Contrarily to traditional strong (i.e. projective) measurements, it is shown that the measurement of the total current at THz frequencies can be modeled by a weak measurement. An additional unavoidable source of fluctuations of the current is predicted at THz frequencies due to the back-action (i.e. the quantum measurement).

DOI
10.1109/iwce.2014.6865844

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Measuring a quantum system implies some kind of perturbation of the system itself. A novel approach to include the perturbation of the quantum electron device, i.e. the back-action, due to the TeraHertz (THz) measurement of the total current is presented. The approach is based on a microscopic description of the interaction between the quantum system and the measuring apparatus, in terms of conditional (Bohmian) wave functions. The disturbance of the quantum system due to measurements at THz frequencies and the (perturbed) value of the total current is numerically computed for a simple two-terminal device. Contrarily to traditional strong (i.e. projective) measurements, it is shown that the measurement of the total current at THz frequencies can be modeled by a weak measurement. An additional unavoidable source of fluctuations of the current is predicted at THz frequencies due to the back-action (i.e. the quantum measurement).
Abstract. From a quantum point of view, it is mandatory to include the measurement process when predicting the time evolution of a quantum system. In this paper, a model to treat the measurement of the terahertz (THz) electrical current in quantum devices is presented. The explicit interaction of a quantum system with an external measuring apparatus is analyzed through the unambiguous notion of the Bohmian conditional wave function , the wave function of a subsystem. It it shown that such a THz quantum measurement process can be modeled as a weak measurement: the systems suffer a small perturbation due to the apparatus, but the current is measured with a great uncertainty. This uncertainty implies that a new source of noise appears at THz frequencies. Numerical (quantum Monte Carlo) experiments are performed confirming the weak character of this measurement. This work also indicates that at low frequencies this noise is negligible and it can be ignored. From a classical point of view, the origin of this noise due to the measurement at THz frequencies can be attributed to the plasmonic effect of those electrons at the contacts (by interpreting the contacts themselves as part of the measuring apparatus).
The interest on weak measurements is rapidly growing during the last years as a unique tool to better understand and predict new quantum phenomena. Up to now many theoretical and experimental weak-measurement techniques deal with (relativistic) photons or cold atoms, but there is much less investigation on (non-relativistic) electrons in up-to-date electronics technologies. We propose a way to perform weak measurements in nanoelectronic devices through the measurement of the total current (particle plus displacement component) in such devices. We study the interaction between an electron in the active region of a electron device with a metal surface working as a sensing electrode by means of the (Bohmian) conditional wave function. We perform numerical (Monte Carlo) simulations to reconstruct the Bohmian trajectories in the iconic double slit experiment. This work opens new paths for understanding the quantum properties of an electronic system as well as for exploring new quantum engineering applications in solid state physics.
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.
We show that in the framework of one-dimensional Bohmian Quantum Mechanics [D Bohm, Phys. Rev. 85 166 and 180 (1952)], for a particle subject to a potential undergoing a weak adiabatic change, the time averages of the particle's positions typically differ markedly from the ensemble averages. We apply this result to the case where the weak perturbing potential is the back-action of a measuring device (i.e. a protective measurement). It is shown that under these conditions, most trajectories never cross the position measured (as already shown for a particular example in a previous paper).
Measuring a quantum system can randomly perturb its state. The strength and nature of this back-action depend on the quantity that is measured. In a partial measurement performed by an ideal apparatus, quantum physics predicts that the system remains in a pure state whose evolution can be tracked perfectly from the measurement record. We demonstrated this property using a superconducting qubit dispersively coupled to a cavity traversed by a microwave signal. The back-action on the qubit state of a single measurement of both signal quadratures was observed and shown to produce a stochastic operation whose action is determined by the measurement result. This accurate monitoring of a qubit state is an essential prerequisite for measurement-based feedback control of quantum systems.
Information about the internal properties of a system can only be obtained through interactions of the system with an external meter. However, such interactions generally result in entanglement between the system and the meter, making it difficult to trace the measurement result back to a specific value of the physical property in the system. It is therefore possible that the outcomes of quantum measurements depend in a nontrivial manner on the dynamics of the measurement interaction, possibly providing a physical explanation for the role of measurement contexts in quantum mechanics. Here we show that the effects of the measurement interaction on the meter can be described entirely in terms of the quantum coherent system dynamics associated with the back-action on the system. For sufficiently small back-action uncertainties, the physical property of the system is described by a weak value obtained from the Hamilton-Jacobi equation of the back-action dynamics. At higher measurement resolutions, the observed values are determined by quantum interferences between different amounts of back-action. Eigenvalues emerge when the quantum interferences between different back-actions correspond to a Fourier transform in the back-action parameter. We conclude that the values of physical properties obtained in quantum measurements originate from the quantum coherent properties of the back-action dynamics generated by that physical property during an interaction. Measurement outcomes represent elements of the dynamics and cannot be explained by measurement independent elements of reality.