Coherence, squeezing and entanglement -- an example of peaceful coexistence

TL;DR

This paper explores a unified, kernel-based definition of bosonic coherent states, including squeezed and entangled states, demonstrating their properties and relationships through holomorphic Hermite polynomials and limit procedures.

Contribution

It introduces a general, kernel-based framework for coherent, squeezed, and entangled states, unifying their description and analyzing their interrelations.

Findings

Unified kernel-based definition encompasses various coherent states.

Holomorphic Hermite polynomials facilitate analysis of state properties.

Limit procedures enable disentangling of complex states.

Abstract

After exhaustive inspection of bosonic coherent states appearing in physical literature two of us, Horzela and Szafraniec, came in 2012 to the reasonably general definition which relies exclusively on reproducing kernels. The basic feature of coherent states, which is the resolution of the identity, is preserved though it now achieves advantageous form of the Segal-Bargmann transform. It turns out that the aforesaid definition is not only extremely economical but also puts under a common umbrella typical coherent states as well as those which are squeezed and entangled. We examine the case here on the groundwork of holomorphic Hermite polynomials in one and two variables. An interesting side of this story is how some limit procedure allows disentangling.