Executive Summary : | Quantum gravity predicts departures from classical relativity at energy scales far beyond the current experimental capacity. This project proposes an alternative theoretical route for probing noncommutative signatures of space-time through a table-top interferometry experiment. The scheme relies on the utilization of a weak impulsive force using a coherent light mode in the cavity and weak short-pulsed light-matter interactions for the detection of the signature of quantum gravity. The guiding line is the mathematical similarity of the Hamiltonian of an oscillator in noncommutative space and the Hamiltonian of a charged particle inside a magnetic field. The optomechanical scheme provides the signature of quantum gravity by the phase-shift of the pulse. However, the problem is that the arm's length of the interferometer needs to be a few kilometers and the mechanism of extracting individual θ or η from the product θη is not known. The project aims to develop the optomechanical scheme so that the arm length can be brought into a suitable limit for a table-top experiment, along with a formalism of extraction of noncommutative parameters individually. In practical situations, time-dependent interactions may occur due to interaction with the environment. Studying the general time-dependent situation with the Lewis-Riesenfeld phase space invariant method will open a new regime in optomechanical setup. This multidisciplinary research aims to probe the non-commutativity of space-time structure with the formalism of quantum information through a quantum optomechanical scheme. |