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.
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.
The experimental current measured in mesoscopic systems fluctuates around average values as a consequence of the wave‐particle nature of electrons. An alternative quantum noise approach, based on Bohm trajectories, is presented. This formalism directly deals with the wave and particle nature of electrons and provides an intuitive framework to study quantum noise. The approach allows the direct consideration of coulomb correlation among electrons. In fact, most of the numerical techniques used in classical Monte Carlo simulations of electron devices can be directly adapted to our approach. 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.
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.
Quantum transport is commonly studied with the use of quasi-particle infinite- extended states. This leads to a powerful formalism, the scattering-states theory, able to capture in compact formulas quantities of interest, such as average current, noise, etc.. However, when investigating the spatial size-dependence of quasi-particle wave packets in quantum noise with exchange and tunneling, unexpected new terms appear in the quantum noise expression. For this purpose, the two particle transmission and reflection probabilities for two initial one-particle wave packets (with opposite central momentums) spatially localized at each side of a potential barrier are studied. After the interaction, each wave packet splits into a transmitted and a reflected component. It can be shown that the probability of detecting two (identically injected) electrons at the same side of the barrier is different from zero in very common (single or double barrier) scenarios. This originates an increase of quantum noise which cannot be obtained through the scattering states formalism.
After the seminal work of R. Landauer in 1957 relating the electrical resistance of a conductor to its scattering properties, much progress has been made in our ability to predict the performance of electron devices in the DC (stationary) regime. Computational tools to describe their dynamical behavior (including the AC, transient and noise performance), however, are far from being as trustworthy as would be desired by the electronic industry. While there is no fundamental limitation to correctly modeling the high-frequency quantum transport and its fluctuations, certainly more careful attention must be paid to delicate issues such as overall charge neutrality, total current conservation, or the back action of the measuring apparatus. In this review, we will show how the core ideas behind the Bohmian formulation of quantum mechanics can be exploited to design an efficient Monte Carlo algorithm that provides a quantitative description of electron transport in open quantum systems. By making the most of trajectory-based and wave function methods, the BITLLES simulator, a free software developed by the authors, extends the capabilities that the semi-classical Monte Carlo simulation technique has offered for decades (DC, AC, noise, transients) to the quantum regime.
It is proved that many-particle Bohm trajectories can be computed from single-particle time-dependent Schrödinger equations. From this result, a practical algorithm for the computation of transport properties of many-electron systems with exchange and Coulomb correlations is derived. As a test, two-particle Bohm trajectories in a tunneling scenario are compared to exact results with an excellent agreement. The algorithm opens the path for implementing a many-particle quantum transport (Monte Carlo) simulator, beyond the Fermi liquid paradigm.
'l*he noise is the was a saying of Rolf Landauer, l one of the founding fathers of mesoscopic physics. What he meant was that fluctuations in time of a measurement can be a source of Information that is not present in the time-averaged value. As figure l reminds us, some types of noise are more interesting than others. A physicist with access to sensitive ways of distinguishing the granularity in a signal may delight in the noise. Noise plays a uniquely informative role in the particle-wave duality. In 1909, Albert Einstein realized that electromagnetic fluctuations vary depending on whether the energy is carried by waves or by particles. The magnitude of energy fluctuations scales linearly with the mean energy for classical waves, but it scales with the square root of the mean energy for classical particles. Since a photon is neither a classical wave nor a classical particle, the linear and square-root contributions coexist. Typically, the square-root (particle) contribution dominates at optical frequencies and the linear (wave) contribution takes over at radio frequencies. If Isaac Newton could have measured noise as the time-dependent fluctuations from the mean intensity, he would have been able to settle his dispute with Christiaan Huygens on the corpuscular nature of light—without actually needing to observe an individual photon. Such is the power of noise. The diagnostic power of photon noise was further developed in the 1960s, when it was discovered that one can teil the difference between radiation from a laser and that from a black body on the basis of their fluctuating Signals: The wave contribution to the fluctuations is entirely absent for a laser; it is merely small for a black body. Noise measurements are now a routine technique in quantum optics, and Roy Glauber's quantum mechanical theory of photon statistics is textbook material. Because electrons share the particle—wave duality with photons, one might expect fluctuations in the electrical current to play a similar diagnostic role. Current fluctuations due to the discreteness of the electrical charge are known as shot noise. Although the first observations of shot noise date from work on vacuum tubes in the 1920s,