Squeezed states for Frenkel-like two-fermion composite bosons

TL;DR

This paper explores the quantum squeezing properties of Frenkel-like composite bosons formed by fermion pairs, revealing how their fermionic structure influences quadrature uncertainties and squeezing limits.

Contribution

It introduces a new framework for defining and analyzing squeezed states of composite bosons, accounting for Pauli blocking and non-canonical algebra, with explicit expressions and numerical illustrations.

Findings

Fermionic structure modifies the Heisenberg uncertainty bound.

Squeezing can fall below the canonical bosonic limit without violating uncertainty.

Finite-dimensional models illustrate constraints on attainable squeezing.

Abstract

We investigate squeezed states of composite bosons (cobosons) formed by pairs of spin-$1/2$ fermions, with emphasis on Frenkel-like cobosons. While squeezing for standard bosonic modes is well established, its extension to cobosons requires accounting for Pauli blocking and the resulting non-canonical commutation algebra. Building on earlier constructions of coboson coherent states, we define squeezed cobosons as eigenstates of a Bogoliubov transformed coboson operator and derive explicit expressions for the associated quadrature variances. We show that the underlying fermionic structure leads to state-dependent modifications of the Heisenberg--Robertson uncertainty bound, which may fall below the canonical bosonic limit without implying any violation of uncertainty principles. Numerical results based on finite-dimensional matrix representations illustrate how these effects constrain the attainable squeezing. Our framework is relevant to composite boson systems such as tightly bound electron-hole pairs and provides a physically transparent setting to probe compositeness through observable quadrature fluctuations.