Critical Phenomenon of a Consistent q-Deformed Squeezed State

TL;DR

This paper explores a novel q-deformed squeezed state exhibiting a critical phenomenon where one quadrature's variance approaches zero while the conjugate remains finite, challenging traditional uncertainty principles.

Contribution

It introduces a new class of q-deformed squeezed states demonstrating a critical behavior and potential experimental implications, expanding understanding of quantum uncertainties.

Findings

Observation of strong squeezing at large amplitudes

Identification of a critical point where uncertainty relation is violated

Potential experimental evidence for q-deformed quantum effects

Abstract

Within a self-consistent framework of q-deformed Heisenberg algebra and its equivalent framework of q-deformed boson commutation relations, which relate to the under-cutting phenomenon of Heisenberg's minimal uncertainty relation, special q-deformed squeezed states are constructed. Besides the similar local maximum squeezing as the one in the undeformed case, new strong squeezing appears when the amplitude of the related coherent state increases to large values. A critical phenomenon appears at a large value of the amplitude: the variance of one component of the quadrature of the light field approaches zero, but the variance of the corresponding conjugate quantity remains finite, which is a surprising deviation from Heisenberg's uncertainty relation. The qualitative character exposed by this q-squeezed state may provide some evidence about q-deformed effects in current experiments.