Phase-space representation of diffraction in time: Analytic results

TL;DR

This paper analytically characterizes the phase-space structure of diffraction-in-time fringes for smooth time gratings, providing explicit formulas for the Husimi distribution in Lorentzian slit scenarios, including a simple model for double-slit interference.

Contribution

It introduces an analytic description of the phase-space structure of diffraction-in-time fringes for smooth time gratings, including explicit formulas for the Husimi distribution.

Findings

Derived an analytic expression for the Husimi distribution in time gratings.

Provided a simple formula for interference fringes in double-slit diffraction.

Accurately captured phase-space fringe positions with analytical results.

Abstract

Diffraction in time manifests itself as the appearance of probability-density fringes when a matter wave passes through an opaque screen with abrupt temporal variations of transmission properties. Here we analytically describe the phase-space structure of diffraction-in-time fringes for a class of smooth time gratings. More precisely, we obtain an analytic expression for the Husimi distribution representing the state of the system in the case of time gratings comprising a succession of Lorentzian-like slits. In particular, for a double-slit scenario, we derive a simple and intuitive expression that accurately captures the position of interference fringes in phase space.