Behavior of the AB-like geometric phase under quantized gravitational wave backgrounds

Determine whether the Aharonov–Bohm–like geometric phase arising from cyclic displacement in the Hamiltonian parameter space of a mesoscopic optomechanical mirror subjected to low-frequency gravitational waves and radiation pressure persists or exhibits new features when the gravitational wave background is quantized (i.e., gravitons), and characterize any resulting modifications to the interferometric phase measurable in the proposed Ramsey-type scheme.

Background

The paper proposes a mesoscopic optomechanical framework in which low-frequency gravitational waves, together with radiation pressure and trap modulation, induce two distinct quantum geometric phases in a mechanical mirror: a Berry phase and an Aharonov–Bohm–like (AB-like) phase. The AB-like phase is generated by cyclic displacement in the Hamiltonian’s parameter space and has no classical analogue. A Ramsey-type interferometric protocol is outlined to isolate and measure this geometric phase.

While all derivations are performed for classical gravitational wave backgrounds, the authors identify a key unresolved issue: the fate of the AB-like phase when the gravitational field itself is quantized. Establishing the behavior of this phase in a graviton background would clarify its robustness and potentially reveal genuinely quantum-gravitational signatures accessible in mesoscopic interferometry.