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.
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.
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.
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).
This chapter discusses how Bohmian mechanics can help us to understand and model the behavior of novel electron device prototypes at the nanometer and picosecond scales. It shows that how Bohmian mechanics can help us in the understanding and designing the upcoming electron device prototypes. The chapter also discusses how Bohmian mechanics can help us to study many-particle quantum electron transport phenomena in nanoelectronic devices and an important advantage of Bohmian mechanics: its ability to treat many-particle systems. It explains the birth of the electronics and its evolution towards nanoelectronics. The chapter also shows that the Bohmian perspective provides useful tools when dealing with the continuous measurement of the electrical current in nanodevices. The former appears at nonzero temperature, where the thermal agitation causes the occupation of energy states to fluctuate. The practical expressions for the computation of the current fluctuations within Bohmian mechanics are quite simple.
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.
Bohmian mechanics, also referred to as the de Broglie-Bohm pilot-wave theory, represents a deterministic and nonlocal interpretation of quantum mechanics. Central to this framework is a description of quantum motion in terms of particle trajectories, whose reconciliation with relativity remains a fundamental challenge. Although relativistic guidance laws have been proposed, their predicted dynamics has remained experimentally untested. Here we use weak measurements in a single-photon interferometer to jointly reconstruct the photon energy and momentum weak values and the associated relativistic velocity field. The reconstructed average trajectories agree with theoretical predictions. Near destructive interference, the flow exhibits local reconstructed velocities exceeding the speed of light and negative values of the effective squared-mass parameter. Our results establish an experimental basis for investigating the physical meaning of quantum trajectories and their role in describing motion in relativistic spacetime.
The use of Bohmian mechanics as a practical tool for modeling non-relativistic quantum phenomena of matter provides clear evidence of its success, not only as a way to interpret the foundations of quantum mechanics, but also as a computational framework. In the literature, it is frequently argued that such a realistic view-based on deterministic trajectories cannot account for phenomena involving the "creation" and "annihilation" of photons. In this paper, by revisiting and rehabilitating earlier proposals, we show how quantum optics can be modeled using Bohmian trajectories for electrons in physical space, together with well-defined electromagnetic fields evolving in time. By paying special attention to an experiment demonstrating partition noise for photons, and to how the Born rule emerges in this context, the paper pursues two main goals. First, it vindicates the pedagogical use of this simple Bohmian framework to compute, understand, and visualize quantum electrodynamics phenomena. Second, given that measurements are ultimately indicated on matter pointers, it clarifies what it means to measure photon or electromagnetic-field properties, even when they are considered non-ontic elements.