Partially coherent matter wave and its evolution

TL;DR

This paper develops a theoretical framework for understanding the evolution of partially coherent matter waves using an extended ABCD matrix formalism and provides analytical solutions and numerical examples.

Contribution

It extends the ABCD matrix formalism to partially coherent matter waves and derives a new law for their evolution, offering a clearer analytical approach.

Findings

Derived a new ABCD law for PCMW evolution

Obtained analytical solutions for the correlation function

Numerically demonstrated propagation in a gravitational field

Abstract

The evolution and propagation of a partially coherent matter wave (PCMW) is investigated theoretically by the correlation function method. The ABCD matrix formalism previously used for a fully coherent matter wave is extended to the PCMW domain. A new ABCD law is derived, using a tensor method to describe the evolution of a PCMW. An analytical solution of the first-order correlation function is obtained that makes the propagation and evolution of a PCMW very simple and clear. As an example, the propagation of a PCMW in a gravitational field is calculated numerically.