Simulation of tunneling in the quantum tomography approach

TL;DR

This paper introduces a novel quantum simulation method using quantum tomography, enabling efficient analysis of nonstationary tunneling phenomena and exciton ionization without direct tomogram calculation.

Contribution

The paper presents a new trajectory-based quantum tomography method for simulating nonstationary quantum processes, avoiding direct computation of the quantum tomogram.

Findings

Calculated tunneling time and probability for wave packets.

Analyzed exciton ionization due to barrier scattering.

Demonstrated method's effectiveness in nonstationary tunneling scenarios.

Abstract

The new method for the simulation of nonstationary quantum processes is proposed. The method is based on the tomography representation of quantum mechanics, {\it i.e.}, the state of the system is described by the {\it nonnegative} function (quantum tomogram). In the framework of the method one uses the ensemble of trajectories in the tomographic space to represent evolution of the system (therefore direct calculation of the quantum tomogram is avoided). To illustrate the method we consider the problem of nonstationary tunneling of a wave packet. Different characteristics of tunneling, such as tunneling time, evolution of spatial and momentum distributions, tunneling probability are calculated in the quantum tomography approach. Tunneling of a wave packet of composite particle, exciton, is also considered; exciton ionization due to the scattering on the barrier is analyzed.