  Owing to the extreme smallness of any noncommutative scale that may exist in
nature, both in the spatial and momentum sector of the quantum phase-space, a
credible possibility of their detection lies in the present day gravitational
wave detector set-ups, which effectively detects the relative length-scale
variations ${\cal{O}}\left[10^{-23} \right]$. With this motivation, we have
considered how a free particle and harmonic oscillator in a quantum domain will
respond to linearly and circularly polarized gravitational waves if the given
phase-space has a noncommutative structure. The results show resonance
behaviour in the responses of both free particle and HO systems to GW with both
kind of polarizations. We critically analyze all the responses, and their
implications in possible detection of noncommutativity. We use the currently
available upper-bound estimates on various noncommutative parameters to
anticipate the relative size of various response terms. We also argue how the
quantum harmonic oscillator system we considered here can be very relevant in
context of the resonant bar detectors of GW which are already operational
currently.
