Resonant-bar detectors of gravitational wave as possible probe of the noncommutative structure of space

We report the plausibility of using quantum mechanical transitions, induced by the combined effect of Gravitational wave (GW) and noncommutative (NC) structure of space, among the states of a 2-dimensional harmonic oscillator, to probe the spatial NC geometry. The phonon modes excited by the passing GW within the resonant bar-detector are formally identical to forced harmonic oscillator and they represent a length variation of roughly the same order of magnitude as the characteristic length-scale of spatial noncommutativity estimated from the phenomenological upper bound of the NC parameter. This motivates our present work. We employ various GW wave-forms that are typically expected from possible astronomical sources. We find that the transition probablities are quite sensitive to the nature of polarization of the GW. We also elaborate on the particular type of sources of GW, radiation from which can induce transitions that can be used as effective probe of the spatial noncommutative structure.