Noncommutative quantum mechanics of a harmonic oscillator under linearized gravitational waves

Abstract

We consider the quantum dynamics of a harmonic oscillator in noncommutative space under the influence of linearized gravitational waves (GWs) in the long-wavelength and low-velocity limit. Following the prescription in Saha and Gangopadhyay [Phys. Lett. B 681, 96 (2009)PYLBAJ0370-269310.1016/j.physletb. 2009.09.063] we quantize the system. The Hamiltonian of the system is solved by using standard algebraic iterative methods. The solution shows signatures of the coordinate noncommutativity via alterations in the oscillation frequency of the harmonic oscillator system from its commutative counterpart. Moreover, it is found that the response of the harmonic oscillator to periodic GWs, when their frequencies match, will oscillate with a time scale imposed by the noncommutative parameter. We expect this noncommutative signature to show up as some noise source in the GW detection experiments since the recent phenomenological upper bounds set on the spatial noncommutative parameter imply a length scale comparable to the length variations due to the passage of gravitational waves, detectable in the present-day GW detectors. © 2011 The American Physical Society.