Squeezing: from numerical to conceptual problems

TL;DR

This paper explores new methods for quantum state squeezing using external fields, providing exactly solvable models and revealing connections to algebraic structures, thus broadening understanding beyond traditional state-focused approaches.

Contribution

It introduces exactly solvable cases of quantum squeezing via external fields and links the problem to Toeplitz algebra, offering new analytical tools and perspectives.

Findings

Explicit solutions for external field-driven squeezing

Connection between squeezing and Toeplitz algebra

Potential implications for fundamental quantum theory

Abstract

In the studies of the squeezing it is customary to focus more attention on the particular squeezed states and their evolution than on the dynamical operations that could squeeze simultaneously some wider families of quantum states, independently of their initial shape. We look for new steps in this direction, carried out by softly acting external fields which might produce the squeezing of the canonical observables $q,p$ of charged particles. The works on these problems collect so many valuable results that the question is whether something more is indeed something more in our knowledge. Yet we decided to present some exactly solvable cases of the problem which appear in the symmetric evolution intervals permitting to find explicitly the time dependence of the external fields needed to generate the required evolution operators. Curiously, our results are interrelated with a simple anti-commuting algebra of Toeplitz which describes the problem more easily than the frequently used Ermakov--Milne invariants. Some trending topics, as well as some fundamental problems in quantum theory, might also be involved.