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Nonlinear Ringdowns as Sources and Detectors of Quantum Gravitational Waves

Thiago Guerreiro

TL;DR

The paper proposes that nonlinearities in black hole ringdowns, especially second-harmonic generation, can produce gravitational waves in non-classical states and, crucially, that these nonlinearities can function as strongly coupled detectors of quantum gravitational radiation. By deriving the effective three-wave mixing Hamiltonian $H_I = \kappa a^2 b^{\dagger} + \kappa^{*} a^{\dagger 2} b$ and analyzing the coupled dynamics of the fundamental and second-harmonic GW modes, it shows that non-classical features (squeezing, sub-Poissonian statistics, and entanglement) can in principle be generated and read out via interferometric readout. The work connects the GW sector to quantum optics concepts through an optogravitational coupling to an optical cavity, enabling estimation of GW correlations via the optical covariance matrix and entanglement witnesses, though direct detection remains experimentally challenging due to the small gravity–matter coupling. Overall, the paper argues that BH ringdowns could serve as both sources and detectors of quantum gravitational states, offering a potentially new route to probe the quantum nature of gravity through BH spectroscopy and nonlinear GW dynamics.

Abstract

Is gravity quantum mechanical? If so, we argue that nonlinear effects in black hole ringdowns - notably second harmonic generation - generates gravitational waves in non-classical states. While quantum features of these states such as sub-Poissonian statistics or entanglement could in principle be measured at interferometric detectors, the tiny coupling of gravity to matter makes this extremely challenging. Drawing on ideas from quantum optics, we instead propose that the nonlinearities in ringdowns could be used as strongly coupled detectors of quantum gravitational radiation, potentially offering a new route to probing the quantum nature of gravity.

Nonlinear Ringdowns as Sources and Detectors of Quantum Gravitational Waves

TL;DR

The paper proposes that nonlinearities in black hole ringdowns, especially second-harmonic generation, can produce gravitational waves in non-classical states and, crucially, that these nonlinearities can function as strongly coupled detectors of quantum gravitational radiation. By deriving the effective three-wave mixing Hamiltonian and analyzing the coupled dynamics of the fundamental and second-harmonic GW modes, it shows that non-classical features (squeezing, sub-Poissonian statistics, and entanglement) can in principle be generated and read out via interferometric readout. The work connects the GW sector to quantum optics concepts through an optogravitational coupling to an optical cavity, enabling estimation of GW correlations via the optical covariance matrix and entanglement witnesses, though direct detection remains experimentally challenging due to the small gravity–matter coupling. Overall, the paper argues that BH ringdowns could serve as both sources and detectors of quantum gravitational states, offering a potentially new route to probe the quantum nature of gravity through BH spectroscopy and nonlinear GW dynamics.

Abstract

Is gravity quantum mechanical? If so, we argue that nonlinear effects in black hole ringdowns - notably second harmonic generation - generates gravitational waves in non-classical states. While quantum features of these states such as sub-Poissonian statistics or entanglement could in principle be measured at interferometric detectors, the tiny coupling of gravity to matter makes this extremely challenging. Drawing on ideas from quantum optics, we instead propose that the nonlinearities in ringdowns could be used as strongly coupled detectors of quantum gravitational radiation, potentially offering a new route to probing the quantum nature of gravity.

Paper Structure

This paper contains 15 sections, 77 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Second harmonics in ringdowns
  3. Hamiltonian
  4. Equations of motion
  5. Signatures on interferometers
  6. Ringdown nonlinearities as detectors
  7. Discussion
  8. Energy conservation and frequency doubling
  9. Frequency doubling equations
  10. Interaction between GW modes and cavity
  11. Hamiltonian
  12. Multimode vacuum corrections and few-mode Hamiltonian
  13. Few mode Hamiltonian
  14. Optical density matrix
  15. Parent mode quadrature in frequency doubling

Figures (1)

  • Figure 1: Concept for a gravitational wave entanglement witness. A nonlinear ringing black hole produces entangled GW states in modes $a$ and $b$ via the interaction Hamiltonian $H_{I}$. The GWs subsequently interact with an ensemble of optical modes $c$ via the optogravitational Hamiltonian $H_{O}$. Information on quantum features of the waves, notably field quadrature correlation functions, get imprinted on the optical ensemble's state.