General framework for quantifying entanglement production in ultracold molecular collisions and chemical reactions

TL;DR

This paper introduces a comprehensive theoretical framework to quantify and control various forms of entanglement produced in ultracold molecular collisions and reactions, highlighting the role of scattering matrices and magnetic Feshbach resonances.

Contribution

It develops a general method to quantify entanglement from scattering matrices and identifies new hybrid entangled states in molecular collisions.

Findings

Entanglement arises from coupling of motional and internal degrees of freedom.

The framework applies to ultracold and cold collision regimes.

Entanglement can be controlled via magnetic Feshbach resonances.

Abstract

Entanglement, a defining feature of quantum mechanics, arises naturally from interactions between molecular systems. Yet the precise nature and quantification of entanglement in the products of molecular collisions and reactions remain largely unexplored. Here, we show that coupling between the external (motional) and internal degrees of freedom of the colliding molecules generates diverse forms of product-state entanglement: discrete-discrete, continuum-continuum, and hybrid discrete-continuum. We develop a general theoretical framework to quantify these entanglement forms directly from scattering S-matrix elements and identify a novel class of entangled states-multimode hybrid cat states, that exhibit multimode discrete-continuum entanglement. Although applicable at arbitrary collision energies, the formalism is illustrated in the ultracold and cold regimes for inelastic Rb+SrF and Rb+Sr$^+$ collisions, as well as the chemical reaction F+HD $\rightarrow$ HF+D, DF+H. We demonstrate that entanglement can be efficiently controlled near magnetic Feshbach resonances, paving the way for precise magnetic control of product-state entanglement generation in ultracold molecular collisions.