  The detection of low frequency gravitational waves (LFGWs) astronomy has
marked an advent of new era in the domain of astrophysics and general
relativity. Using the framework of interaction between GWs and a point
two-particles like detector, within linearized gravity approach, we propose a
toy detector model whose quantum state is being investigated at a low-frequency
of GWs. The detector is in simultaneous interaction with GWs and an external
time-dependent (tuneable) two-dimensional harmonic potential. We observe that
the interaction with low frequency GWs naturally provides adiabatic
approximation in the calculation, and thereby can lead to a quantal geometric
phase in the quantum states of the detector. Moreover this can be controlled by
tuning the frequency of the external harmonic potential trap. We argue that
such geometric phase detection may serve as a manifestation of the footprint of
GWs. More importantly, our theoretical model may be capable of providing a
layout for the detection of very small frequency GWs through Berry phase.
