Virtual Detector Theory of Free-Particle Wave Packets

TL;DR

This paper introduces a virtual detector approach to analyze free-particle wave packets, demonstrating its equivalence to Fourier transforms in the asymptotic limit and exploring effects of laser fields.

Contribution

It applies the virtual detector method to free-particle wave packets, providing analytical expressions and establishing its equivalence to Fourier transforms in the large-time limit.

Findings

Virtual detector method yields the same momentum distribution as Fourier transform asymptotically.

Analytical expressions for detection in real and momentum space are derived.

Laser fields influence the detection process, extending the method's applicability.

Abstract

We apply a recently emerging "virtual detector" method to general free-particle wave packets. We discuss what is actually detected by a virtual detector and give analytical expressions in both the real space and the momentum space. We prove that in the asymptotic limit when the time difference between wave packet creation and detection is large, resembling real detection processes, the obtained differential momentum distribution is equivalent to Fourier transforming the free-particle wave packets. We further consider the situation with the presence of laser fields.