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The existence of a minimal measurable length as a characteristic length inthe Planck scale is one of the main features of quantum gravity and has beenwidely explored in the context. Various different deformations of spacetimehave been employed successfully for the purpose. However, polymer quantizationapproach is a relatively new and dynamic field towards the quantum gravityphenomenology, which emerges from the symmetric sector of the loop quantumgravity. In this article, we extend the standard ideas of polymer quantizationto find a new and tighter bound on the polymer deformation parameter. Ourprotocol relies on an opto-mechanical experimental setup that was originallyproposed in Ref.\cite{ref:Igor} to explore some interesting phenomena byembedding the minimal length into the standard canonical commutation relation.We extend this scheme to probe the \emph{polymer length} deformed canonicalcommutation relation of the center of mass mode of a mechanical oscillator witha mass around the Planck scale. The method utilizes the novelty of exchangingthe relevant mechanical information with a high intensity optical pulse insidean optical cavity. We also demonstrate that our proposal is within the reach ofthe current technologies and, thus, it could uncover a decent realization ofquantum gravitational phenomena thorough a simple table-top experiment.

A new bound on polymer quantization via an opto-mechanical setup