Generalized Uncertainty Principle and Analogue of Quantum Gravity in Optics

TL;DR

This paper applies the concept of the generalized uncertainty principle from quantum gravity to optics, predicting a minimal spatial or temporal scale for ultra-focused beams and short pulses, with potential practical and theoretical implications.

Contribution

It introduces a novel application of G-UP in optics, deriving a generalized Schrödinger equation and identifying maximally localized states for ultra-focused beams.

Findings

Existence of a minimal spatial or temporal scale for optical pulses

Nonlinearity enhances the system's ability to reach maximal localization

Potential for experimental tests of fundamental physical theories in optics

Abstract

The design of optical systems capable of processing and manipulating ultra-short pulses and ultra-focused beams is highly challenging with far reaching fundamental technological applications. One key obstacle routinely encountered while implementing sub-wavelength optical schemes is how to overcome the limitations set by standard Fourier optics. A strategy to overcome these difficulties is to utilize the concept of generalized uncertainty principle (G-UP) that has been originally developed to study quantum gravity. In this paper we propose to use the concept of G-UP within the framework of optics to show that the generalized Schrodinger equation describing short pulses and ultra-focused beams predicts the existence of a minimal spatial or temporal scale which in turn implies the existence of maximally localized states. Using a Gaussian wavepacket with complex phase, we derive the corresponding generalized uncertainty relation and its maximally localized states. We numerically show that the presence of nonlinearity helps the system to reach its maximal localization. Our results may trigger further theoretical and experimental tests for practical applications and analogues of fundamental physical theories.