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Chinese Physics Letters

Quantum Interference by Entangled Trajectories

Feng Xu, Lifei Wang, Xiaodong Cui

Published Aug 1, 2015• 2 citations
Publisher

Abstract

The quantum interference pattern in the double-slit experiment is qualitatively reproduced by using the entangled trajectory molecular dynamics method and compared with previous works. We compare entangled trajectory and classical trajectory with the same initial state in the phase space to show quantum effect in the evolution of trajectories. It is involved with breakdown in the statistical independence of the trajectories. Although our result does not agree well with exact quantum calculation in quantitatively with loss of part of interference pattern peaks, we can offer a reasonable explanation by analyzing quantum interference of two Gaussian wave packets in the phase space.

DOI
10.1088/0256-307x/32/8/080304

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The quantum interference pattern in the double-slit experiment is qualitatively reproduced by using the entangled trajectory molecular dynamics method and compared with previous works. We compare entangled trajectory and classical trajectory with the same initial state in the phase space to show quantum effect in the evolution of trajectories. It is involved with breakdown in the statistical independence of the trajectories. Although our result does not agree well with exact quantum calculation in quantitatively with loss of part of interference pattern peaks, we can offer a reasonable explanation by analyzing quantum interference of two Gaussian wave packets in the phase space.
In this paper, we describe a new method for simulating quantum processes using classical-like molecular dynamics. The approach is based on solving the quantum Liouville equation in the Wigner representation using ensembles of classical trajectories in phase space. The nonlocality of quantum mechanics is incorporated in the trajectory representation as nonclassical interactions between the members of the ensemble, leading to an entanglement of their evolution. The statistical independence of the individual trajectories making up an ensemble in the classical limit is lost when quantum effects are included, and the entire state of the system must be propagated as a unified whole. We develop the formalism and its numerical implementation, and illustrate its application on two model problems of quantum mechanical tunneling: escape from a metastable well and wave packet penetration of the Eckhart barrier.
Abstract We provide a semiclassical description of the double-slit experiment given by the momentous quantum mechanics. This formulation allows the study of quantum systems by an effective augmented Hamiltonian. The use of canonical variables enables us to comprise all the quantum information into a finite system of equations. We show the evolution of individual particles and their semiclassical trajectories, and how their collective behavior seems to reproduce the well-known quantum interference pattern. We are able to follow the individual evolution of each particle and its interaction with the effective quantum potential, showing that, contrary to the non-crossing rule present in Bohmian mechanics, particle trajectories actually cross each other in our description. By discussing the quantum-effective potential obtained, we mention possible extensions and applications to other areas.
Abstract In Copenhagen’s interpretation, a self-interference mechanism is assumed for a wave function to split and to pass through the slits simultaneously, then recombine and collapse to generate a dot signal on a detector. Its use of a single wave function to describe a whole ensemble without accounting for a particle’s individuality is incomplete. To better understand the single-electron double-slit interference, we use a wave-packet trajectory approach to track each electron’s dynamics and calculate the time-dependent interference intensity. We analyze the self-interference and cross-interference mechanisms to illustrate how an electron’s coherence length affects the self-interference and how it dictates the wave packet overlaps between adjacent electrons for the cross-interference mechanism to be effective. To circumvent a conflicting dilemma between the electron’s indivisibility and its wave-packet split while passing through the slits, we consider an alternate mechanism involving slit-induced quantized momentum. This mechanism preserves the electron’s indivisibility and avoids the illusive split, recombination and mysterious collapse of a single particle’s wave function.
Quantum tunneling effects of Gaussian wave packet in one- and two-dimensional double well potentials are investigated using quantum Liouville equation for time evolution of Wigner distribution in phase space. It is shown that a trajectory-based solution of this problem can be constructed by the entangled trajectory ensemble simulating the evolving quantum state. Quantum effects arise in this approach as a breakdown of the statistical independence of the trajectory ensemble. © 2014 Wiley Periodicals, Inc.
Based on a proposed classical explanation, the quantum mechanical "decay of the wave packet" is shown to simply result from sub-quantum diffusion with a specific diffusivity varying in time due to a particle's changing thermal environment. The exact quantum mechanical intensity distribution, as well as the corresponding trajectory distribution and the velocity field of a Gaussian wave packet are therewith computed. We utilize no quantum mechanics, but only familiar simulation techniques for diffusion, e.g., finite differences or coupled map lattices (CML).
We investigate quantum dynamics in a double-well system subject to time-dependent perturbation with some incommensurate frequencies using entangled trajectory molecular dynamics method. We first compare time evolution of energy of the driven system with two mode perturbation under classical dynamics with one under quantum dynamics, it is found that quantum dynamics obeys Ehrenfest's theorem and it shows our results obtain from entangled trajectory molecular dynamics method are correct and accurate. Quantum coherence suppresses trajectory which initial energy is higher than barrier to get over it, this process is named coherent destruction of tunneling (CDT). We show this interesting phenomenon through showing entangled trajectory and corresponding classical trajectory in phase space and discuss their energy fluctuation with time. Furthermore, we discuss quantum dynamics with different frequency mode perturbation from the perspective of autocorrelation evolution, classical chaos brings remarkable influence on quantum-mechanical phenomena.