Generalized uncertainty principle in resonant detectors of gravitational waves

Abstract

With the direct detection of gravitational waves by advanced LIGO detector, a new "window" to quantum gravity phenomenology has been opened. At present, these detectors achieve the sensitivity to detect the length variation ($\delta L$), $\mathcal{O}\approx 10^{-17}-10^{-21}$ meter. Recently a more stringent upperbound on the dimensionless parameter ${\beta }_0$, bearing the effect of generalized uncertainty principle has been given which corresponds to the intermediate length scale $l_{im}=\sqrt{{\beta }_0}{l}_{pl}\sim 10^{-23}m$. Hence the flavour of the generalized uncertainty principle can be realised by observing the response of the vibrations of phonon modes in such resonant detectors in the near future. In this paper, therefore, we calculate the resonant frequencies and transition rates induced by the incoming gravitational waves on these detectors in the generalized uncertainty principle framework. It is observed that the effects of the generalized uncertainty principle bears its signature in both the time independent and dependent part of the gravitational wave-harmonic oscillator Hamiltonian. We also make an upper bound estimate of the GUP parameter.

12 pages Latex, thoroughly revised

References in corpus (8)

• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• Advanced Virgo: a 2nd generation interferometric gravitational wave detector
• Universality of Quantum Gravity Corrections
• GUP parameter from quantum corrections to the Newtonian potential
• Constraining the generalized uncertainty principle with the gravitational wave event GW150914
• Implication for the core collapse supernova rate from 21 years of data of the Large Volume Detector
• Noncommutative quantum mechanics of a harmonic oscillator under linearized gravitational waves
• Path integral action of a particle with the generalized uncertainty principle and correspondence with noncommutativity

Cited by in corpus (2)

• Path integral action for a resonant detector of gravitational waves in the generalized uncertainty principle framework
• Minimal length implications on the Hartree-Fock theory