Squeezing effect induced by minimal length uncertainty

TL;DR

This paper investigates how minimal length uncertainty, related to gravitational effects, causes a squeezing effect in the quantum harmonic oscillator's position and momentum, with potential implications for electrons in strong magnetic fields.

Contribution

It provides analytical solutions for the deformed harmonic oscillator dynamics considering minimal length uncertainty, revealing a novel squeezing effect not previously characterized.

Findings

Squeezing effect occurs in both position and momentum due to minimal length uncertainty

The effect is very small in realistic systems like electrons in strong magnetic fields

Analytical solutions avoid approximations that neglect higher order terms

Abstract

In this work, the dynamics of the deformed one-dimensional harmonic oscillator with minimal length uncertainty is examined and the analytical solutions for time evolution of position and momentum operators are presented in which the rough approximation that neglects the higher order terms in BakerHausdor lemma is avoided. Based on these analytical solutions the uncertainties for position and momentum operators are calculated in a coherent state, and an unexpected squeezing effect in both coordinate and momentum directions is found in comparison with ordinary harmonic oscillator. Obviously such a squeezing effect is induced by the minimal length uncertainty (gravitational effects). Our results are applied to the electrons trapped in strong magnetic fields to examine the degree of the existing squeezing effect in a real system, which shows the squeezing degree induced by minimal length uncertainty is very small.