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arXiv:1602.06575 · Journal of Statistical Mechanics Theory and Experiment

On the noise induced by the measurement of the THz electrical current in quantum devices

Damiano Marian, Xavier Oriols, N Zanghì

Published May 1, 2016• 2 citations
arXivHTMLPDF

Abstract

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).

DOI
10.1088/1742-5468/2016/05/054011

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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).
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).
When talking about noise in quantum devices two issues must be faced: how to model the evolution of an electronic system with scattering and how this noise is practically computed in a quantum device simulator. In the present paper, we address both problems from a practical and computational point of view. In particular, as the electronic quantum subsystem is an open (normally far from equilibrium) system, we use the notion of conditional wave function, the wave function of a subsystem in Bohmian mechanics, an alternative version of quantum mechanics which along with the wave function posited definite positions for the particles. This allows us to define an effective equation in several physical situations, ranging from the simple tunneling barrier to the interaction with a bath of phonons. Finally, we present how this development can be used to compute quantum noise in a quantum device simulator.
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.
Mesoscopic physics considers systems of appropriate size and at time scales of the order of decoherence time, which allows us to analyse the transformation of information from a quantum state to a classical signal, occurring in a process of quantum measurement. We concentrate on the limiting cases of weak and strong coupling between a mesoscopic source of noise and a subsystem functioning as a detector. In the ``weak coupling'' part we elaborate on the idea of cross-correlation measurements for quantum noise detection and develop a set of original methods to tackle the perturbation theory up to fourth order. In the ``strong coupling'' part we provide an exact solution for one-dimensional system out of equilibrium, strongly interacting with a localized state and predict some remarkable experimentally verifiable features, such as Fermi-edge singularity in the noise induced transition rates and unusually pronounced manifestation of non-Gaussian noise effects.
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 present the measurements and the theoretical model of the frequency-dependent noise temperature of a superconductor lattice-cooled hot-electron bolometer mixer in the terahertz frequency range. The increase of the noise temperature with frequency is a cumulative effect of the nonuniform distribution of the high-frequency current in the bolometer and the charge imbalance, which occurs at the edges of the normal domain and at the contacts with normal metal. We show that under optimal operation the fluctuation sensitivity of the mixer is determined by thermodynamic fluctuations of the noise power, whereas at small biases there appears additional noise, which is probably due to the flux flow. We propose the prescription of how to minimize the influence of the current distribution on the mixer performance.