Noncommutative quantum mechanics of simple matter systems interacting with circularly polarized gravitational waves

The response of a test particle, both for the free case and under the harmonic oscillator potential, to circularly polarized gravitational waves is investigated in a noncommutative quantum mechanical setting. The system is quantized following the prescription in Saha and Gangopadhyay (Phys Lett B 681: 96, 2009). An algebraic technique is then employed to solve the Hamiltonian of the system. The solutions, in both cases, show signatures of the coordinate noncommutativity. In the harmonic oscillator case, this NC effect plays a key role in altering the resonance point at which the system couples maximally with the GW. This feature, if observed in an experimental setting, will serve to determine the scale of spatial NC parameter. The applicability of our treatement and the relevance of our results to resonant bar detectors of GW are discussed.