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Fluctuation and Noise Letters

Noise in Quantum Devices: A Unified Computational Approach for Different Scattering Mechanisms

Damiano Marian, Enrique Colomés

Published Aug 15, 2016• 2 citations
Publisher

Abstract

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.

DOI
10.1142/s0219477516400083

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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.
Without access to the full quantum state, modeling dissipation in an open system requires approximations. The physical soundness of such approximations relies on using realistic microscopic models of dissipation that satisfy completely positive dynamical maps. Here we present an approach based on the use of the Bohmian conditional wave function that, by construction, ensures a completely positive dynamical map for either Markovian or non-Markovian scenarios while allowing the implementation of realistic dissipation sources. Our approach is applied to compute the current-voltage characteristic of a resonant tunneling device with a parabolic-band structure, including electron-lattice interactions. A stochastic Schr\"odinger equation is solved for the conditional wave function of each simulated electron. We also extend our approach to (graphenelike) materials with a linear band structure using Bohmian conditional spinors for a stochastic Dirac equation.
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).
An effective single-particle Schrodinger equation to include dissipation into quantum devices is presented. This effective equation is fully understood in the context of Bohmian mechanics, a theory of particles and waves, where it is possible to define unambiguously the wave function of a subsystem, the so-called conditional wave function. In particular the change in energy and momentum of an electron when interacting with a phonon is presented, both theoretically and numerically. This work is a first step to include dissipation into the fully-quantum simulator BITLLES.
The experimental current measured in quantum‐based devices fluctuates around average values due to the quantum mechanical wave‐particle duality. An alternative quantum noise approach, based on the de Broglie‐Bohm interpretation of the quantum theory, is presented. Since this formalism directly deals with the wave and particle nature of electrons, it provides an excellent framework to study quantum noise. In fact, most of the numerical techniques used in classical Monte Carlo simulations can be directly adapted to our quantum formalism. Simulated noise results for interacting electrons tunnelling through double barriers are presented in agreement with experimental results. The present approach opens a new path for studying electron transport and quantum noise in mesoscopic systems.
Moore’s law has been the milestone for electronics improvement, and the cause for the exponential growth in our computational abilities and for reaching nanoscale electron devices. At such dimensions, classical simulation tools must be substituted by quantum ones. Such substitution implies to tackle new fundamental problems. First, the many-body problem makes (almost) impossible the exact simulation of many particles scenarios. Second, the measurement problem is especially relevant in high-frequency scenarios where multi-time measurements are mandatory. Alternatively to the orthodox theory, Bohmian mechanics emerges as a quantum theory which is specially well-equipped for the simulation of high-frequency characteristic of quantum electron devices. The Bohmian theory provides the conditional wave function that guides particles with well-defined positions. In this thesis, I explored quantum transport using Bohmian mechanics, putting special emphasis to graphene, a 2D material with linear bandstructure, which is expected to play an important role in the next future electronics. Differently from other materials, graphene obeys the bispinor Dirac equation, electrons behave as massless particles, exhibiting exotic behaviors, such as the Klein Tunneling effect. During the thesis, the quantum BITLLES simulator has been improved to correctly model electron nanodevices with either linear (by the inclusion of the complex bispinor Dirac equation) or parabolic bandstructures in either ballistic or dissipative (by the inclusion of the complete positive Bohmian scattering approach) systems. Thus, the BITLLES has become the candidate for substituting the versatile semiclassical Monte Carlo approach in the quantum regime, while keeping the versatility to predict DC, AC and noise performances. As practical applications, during the thesis, unexpected scattering probabilities in a Hong-Ou-Mandel experiment were predicted. In addition, different current-voltage characteristics were analyzed. Finally, a new limit (due to the discrete nature of charge) for ultra-small logic applications working at THz frequencies was predicted.