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The comparison between the noncommutative length scale $\sqrt{\theta}$ andthe length variation $\delta L=h L$, detected in the GW detectors indicate thatthere is a strong possibility to detect the noncommutative structure of spacein the GW detector set up. We therefore explore how the response of a bardetector gets affected due to the presence of noncommutative structure of spacekeeping terms upto second order in the gravitational wave perturbation ($h$) inthe Hamiltonian. Interestingly, the second order term in $h$ shows a transitionbetween the ground state and one of the perturbed second excited states thatwas absent when the calculation was restricted only to first order in $h$.

Signatures of noncommutativity in bar detectors of gravitational waves