Extended virtual detector theory including quantum interferences

Xu, Rui-Hua; Xu, Wei; Eberly, J. H.

doi:10.48550/arxiv.2003.05051

Cited by 1 publication

(1 citation statement)

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“…The instantaneous classical momentum of the probability fluid may then be calculated and binned into a final spectrum. Such a result allows for the creation of a semi-classical model, with one region treated quantum mechanically and the other treated classically with phase integration [5]. The proof [6] that this equates to measuring the true momentum distribution requires that the measurement time tends towards infinity, leading to the requirement of a strong momentum-spatial correlation.…”

Section: Introductionmentioning

confidence: 99%

A Coherent Bi-Directional Virtual Detector for the 1-D Schrödinger Equation

Mann¹,

Rosenzweig²

2022

Preprint

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The virtual detector is a commonly utilized technique to measure the properties of a wavefunction in simulation. One type of virtual detector measures the probability density and current at a set position over time, permitting an instantaneous measurement of momentum at a boundary. This may be used as the boundary condition between a quantum and a classical simulation. However, as a tool for measuring spectra, it possesses several problems stemming from its incoherent nature. Another form of virtual detector measures the wavefunction's complex value at a set position in real space over time and Fourier analyzes it to produce an energy spectrum. The spectra it produces are exact provided that the wavefunction propagated through the detector in one direction. Otherwise it will produce a spectrum that includes interference between forward and backward propagating wavepackets. Here we propose a virtual detector which maintains all the benefits of this coherent virtual detector while also being able to resolve the direction of propagation and mitigate nonphysical interference by use of a second measurement point. We show that, in the continuum limit, this bi-directional virtual detector can reproduce an equivalent wavefunction assuming a globally constant potential. It is therefore equivalent to the exact spectrum.

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Section: Introductionmentioning

confidence: 99%