Response of simple quantum systems to different polarizations of gravitational waves in noncommutative phase-space

TL;DR

This paper investigates how simple quantum systems like free particles and harmonic oscillators respond to polarized gravitational waves within a noncommutative phase-space, revealing resonance behaviors that could inform future detection of noncommutative effects.

Contribution

It introduces the response analysis of quantum systems to gravitational waves in a noncommutative phase-space, highlighting potential observable effects and relevance to current GW detectors.

Findings

Resonance behavior observed in quantum systems under GW influence.

Noncommutative parameters influence the response magnitude.

Relevance to existing resonant bar GW detectors.

Abstract

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.