Abstract
The existence of a minimal measurable length as a characteristic length in the Planck scale is one of the main features of quantum gravity and has been widely explored in the context. Various different deformations of spacetime have been employed successfully for the purpose. However, polymer quantization approach is a relatively new and dynamic field towards the quantum gravity phenomenology, which emerges from the symmetric sector of the loop quantum gravity. In this article, we extend the standard ideas of polymer quantization to find a new and tighter bound on the polymer deformation parameter. Our protocol relies on an opto-mechanical experimental setup that was originally proposed to explore some interesting phenomena by embedding the minimal length into the standard canonical commutation relation. We extend this scheme to probe the polymer length deformed canonical commutation relation of the center of mass mode of a mechanical oscillator with a mass around the Planck scale. The method utilizes the novelty of exchanging the relevant mechanical information with a high intensity optical pulse inside an optical cavity. We also demonstrate that our proposal is within the reach of the current technologies and, thus, it could uncover a decent realization of quantum gravitational phenomena thorough a simple table-top experiment.
Highlights
After more than 70 years of focusing on the theoretical and mathematical aspects of the theory of quantum gravity (QG), in recent decades we have encountered some serious proposals on the project of the QG phenomenology[1]
We have explored a detailed and elegant procedure to understand the effects of the modified commutation relation thorough polymer quantization in laboratory
We obtained a new bound on the deformation parameter μ0, which may lead us towards an advanced understanding of the polymer quantization as well as the problem of quantum gravity
Summary
The existence of a minimal measurable length as a characteristic length in the Planck scale is one of the main features of quantum gravity and has been widely explored in the context. Our protocol relies on an opto-mechanical experimental setup that was originally proposed to explore some interesting phenomena by embedding the minimal length into the standard canonical commutation relation. Given that gravity is not an ordinary force, but a property of space-time, we can deal with an effective framework of QG by considering a fundamental and minimal characteristic length for the geometry of space-time that is probed by a moving quantum particle Within such context the standard Heisenberg uncertainty principle and relativistic dispersion relation are replaced by the generalized uncertainty principle (GUP)[11–18] and the modified dispersion relation (MDR)[19,20], respectively, where. It has been demonstrated that polymer quantization and GUP have the same physical consiquences[27] Within this scheme, one implements the Weyl algebra[21,22] by preserving the standard canonical form of the commutation relations such that the momentum operator becomes ill-defined. From (4) we compute the deviation in the average value of the field operator with c1 ≈ 1 and follow the similar steps as in[32,36] to obtain the deviation of the optical phase as
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