Several theories that attempt to unify quantum theory and gravitational theory assume that space has an observable limiting resolution related to the Planck length, denoted by \(\sqrt{{\beta }_{0}}{L}_{p}\) . Quantum mechanically, this concept derives a generalized uncertainty principle (GUP) and the corresponding modified commutator. The prediction and observation of GUP-induced new physics, as well as the quantitative measurement of the value of β0, may provide substantial support for the establishment of quantum gravity theory. Here, we develop a quantum framework to probe GUP at low energies, exploiting interference-induced bright-dark modes in an optomechanical system. The nonlinearity induced by GUP will be amplified by the bright mode dynamics, and then be quantitatively read out by the noise spectrum of the dark mode. The measurement limit resolution of the scheme is not constrained by the quality factor of the oscillator. Under experimentally achievable parameters, the measurement resolution has been shown to reach β0,lim ~ 1023.3 for nanogram-mass oscillator, which is 10 orders of magnitude lower than the electroweak level.
