Abstract
The comparison between the noncommutative length scale √θ and the length variation δL = hL, detected in the GW detectors, indicates that there is a strong possibility to detect the noncommutative structure of space in the GW detector setup. Therefore, we explore how the response of a bar detector gets affected due to the presence of a noncommutative structure of space keeping terms up to the second order in a gravitational wave perturbation (h) in the Hamiltonian. Interestingly, the second-order term in h shows a transition between the ground state and one of the perturbed second excited states that was absent, when the calculation was restricted only to the first order in h.
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