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Symmetry

Peculiarities of Electron Wave Packet Dynamics in Planar Nanostructures in the Presence of Magnetic and Electric Fields

Darya Starodubtseva, Olga V. Tikhonova

Published Oct 20, 2022• 0 citations

Abstract

Currently, spatially localized electron densities and currents are considered to be candidates for use in the encoding of quantum information. For this reason, the control of their temporal dynamics is an important task. In this work, the spatiotemporal evolution of an electron wave packet in planar nanostructure in the presence of transverse magnetic and lateral electric fields is investigated by direct analytical solution of the non-stationary Schrödinger equation. Methods to control and manage the dynamics of the spatially localized electron density distribution are developed. The production of photon-like quantum states of electrons opens up opportunities for applications similar to quantum optical and quantum information technologies but implemented with charge carriers. Quantum control of the trajectory of the electron wave packet, accompanied by dramatic suppression of its spreading, is demonstrated. This study discovered methods to manage spatially localized electron behavior in a nanostructure that allows a controllable charge quantum transfer and gives rise to new prospects for quantum nanoelectronics technology.

DOI: 10.3390/sym14102215

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Currently, spatially localized electron densities and currents are considered to be candidates for use in the encoding of quantum information. For this reason, the control of their temporal dynamics is an important task. In this work, the spatiotemporal evolution of an electron wave packet in planar nanostructure in the presence of transverse magnetic and lateral electric fields is investigated by direct analytical solution of the non-stationary Schrödinger equation. Methods to control and manage the dynamics of the spatially localized electron density distribution are developed. The production of photon-like quantum states of electrons opens up opportunities for applications similar to quantum optical and quantum information technologies but implemented with charge carriers. Quantum control of the trajectory of the electron wave packet, accompanied by dramatic suppression of its spreading, is demonstrated. This study discovered methods to manage spatially localized electron behavior in a nanostructure that allows a controllable charge quantum transfer and gives rise to new prospects for quantum nanoelectronics technology.

Quantum hydrodynamic equations are used to describe motion of single electron. The initial and boundary conditions are formulated from the analytic formula for the electron packet in a free space. The numerical integration of equations for the free packet is performed. Then, we investigated the wave packet propagation through the back-ground positive charge, when the electric field is self-consistent. Moreover, we studied the influence of the external harmonic electric fields on the properties of the motion. The purpose of the present work consists in study of the spatial-temporal processes including packets when the quantum wave effects are essential.

We study the phenomenon of wave-packet revivals of Bloch electrons and explore how to control them by a magnetic field for quantum-information transfer. It is shown that the single electron system can be modulated into a linear dispersion regime by the ``quantized'' flux and then an electronic wave packet with the components localized in this regime can be transferred without spreading. This feature can be utilized to perform the high-fidelity transfer of quantum information encoded in the polarization of the spin. Beyond the linear approximation, the relocalization and self-interference occur as the interesting phenomena of quantum coherence.

Quantum lattices are pivotal in the burgeoning fields of quantum materials and information science. Novel experimental techniques allow the preparation and monitoring of wave packet dynamics on quantum lattices with high spatiotemporal resolution. We present an analytical study of wave packet diffusivity and diffusion length on tight-binding quantum lattices subject to stochastic noise. Our analysis reveals the crucial role of spatial coherence and predicts a set of novel phenomena: (1) noise can enhance the transient diffusivity and diffusion length of spatially extended initial states; (2) standing or traveling initial states, with large momentum, spread faster than a localized initial state and exhibit a noise-induced peak in the transient diffusivity; (3) the differences in the diffusivity or diffusion length of extended and localized initial states have a universal dependence on initial width. These predictions suggest the possibility of controlling the wave packet dynamics by spatial manipulations, which will have implications for materials science and quantum technologies.

We have modeled the transmission of an electron wave packet through a resonant tunneling semiconductor nanostructure by solving the time-dependent Schr\"odinger equation using the finite-difference method. We have found in all cases that the passage of the electron wave packet through the tunneling barrier is accompanied by a propagation delay relative to the propagation of an undisturbed wave packet. Tunneling transport is shown to be causal, and no evidence of superluminal behavior is seen, either for resonant or for off-resonant tunneling. In the case of off-resonant tunneling, the peak of the transmitted wave packet is observed to exit a double resonant tunneling barrier before the peak of the incident wave packet enters the structure. However, these two peaks are not directly related, and the appearance of a well-formed peak in the transmitted intensity is shown to be a result of the transient behavior of the tunneling event.

Abstract The peculiarities of the excitation in planar nanostructures induced by a nonclassical field under the impact of cross phase modulation are analyzed. The possibility to controllably enhance a certain excitation channel by varying field frequency detuning from resonance is demonstrated. The effect of formation of entangled two mode field states similar to the Schrodinger’s cat state under the influence of the cross-phase modulation is revealed. The influence of the correlated two mode squeezed vacuum field state is studied and the effect of enhancement of even excitation channels due to photon correlations in the field modes is found. The obtained results open new prospects to control the hybrid electron-photon systems and to develop a fully quantum photon-matter interface on the basis of the 2D nanomaterials.