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Photon-graviton polarization entanglement induced by a classical electromagnetic wave

Alessandro Ferreri

TL;DR

The paper investigates photon–graviton pair production driven by a classical electromagnetic beam in flat spacetime, treating gravity as a quantum field and the EM field as a classical drive plus fluctuations. Using a perturbative quantum-field-theoretic framework with a TT-quantized graviton, it derives the interaction Hamiltonians and tracks the time evolution of the combined state. For linear polarization, the process yields a Bell-type photon–graviton entangled state with a heralding photon that is maximally mixed in polarization, while circular polarization introduces coherence in the heralded photon and a different Bell composition. The study assesses experimental prospects for observing heralding photons, noting substantial lab challenges but highlighting potential observations in cosmological phenomena and the utility of heralded photons as signatures of quantum gravity.

Abstract

We study the photon-graviton pair production induced by the propagation of a classical electromagnetic (EM) wave in a Minkowskian spacetime. In our model, the gravitational field is described in terms of the quantized graviton field, whereas the electromagnetic field is split into a classical drive (a linearly or circularly polarized electromagnetic wave) and a quantum fluctuation field. We analyze the time evolution of the quantum state showing that, among other outcomes, the propagation of the EM wave can generate Bell states in the photon-graviton polarization basis. We finally discuss the possibility to observe entangled photons in artificial and natural scenarios.

Photon-graviton polarization entanglement induced by a classical electromagnetic wave

TL;DR

The paper investigates photon–graviton pair production driven by a classical electromagnetic beam in flat spacetime, treating gravity as a quantum field and the EM field as a classical drive plus fluctuations. Using a perturbative quantum-field-theoretic framework with a TT-quantized graviton, it derives the interaction Hamiltonians and tracks the time evolution of the combined state. For linear polarization, the process yields a Bell-type photon–graviton entangled state with a heralding photon that is maximally mixed in polarization, while circular polarization introduces coherence in the heralded photon and a different Bell composition. The study assesses experimental prospects for observing heralding photons, noting substantial lab challenges but highlighting potential observations in cosmological phenomena and the utility of heralded photons as signatures of quantum gravity.

Abstract

We study the photon-graviton pair production induced by the propagation of a classical electromagnetic (EM) wave in a Minkowskian spacetime. In our model, the gravitational field is described in terms of the quantized graviton field, whereas the electromagnetic field is split into a classical drive (a linearly or circularly polarized electromagnetic wave) and a quantum fluctuation field. We analyze the time evolution of the quantum state showing that, among other outcomes, the propagation of the EM wave can generate Bell states in the photon-graviton polarization basis. We finally discuss the possibility to observe entangled photons in artificial and natural scenarios.
Paper Structure (15 sections, 84 equations, 1 figure)

This paper contains 15 sections, 84 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Theoretical model
  3. Photon-graviton entanglement
  4. Linearly polarized EM wave
  5. Calculations of $\hat{H}_{\mathcal{E}_0^2}$ and $\hat{H}_{\mathcal{E}_0}$
  6. Time evolution of the state
  7. Circularly polarized EM wave
  8. Can we observe heralding photons?
  9. Transition probability
  10. Discussion
  11. Conclusions
  12. Acknowledgment
  13. Hamiltonian and time evolution operator
  14. Time integrals of $\hat{H}_{\kappa}(t)$ and $\hat{H}_{\mathcal{E}_0}^{(\textrm{I})}(t)$
  15. Normalization of $\lvert\Psi(t)\rangle$ and calculation of the transition probability amplitude

Figures (1)

  • Figure 1: Pictorial representation of the scenario of interest: an intense classical electromagnetic beam propagates in the spacetime region between an emitter and an observer. Among other effects, we expect that the beam stimulates the vacua of both the quantum electromagnetic and the gravitational (graviton) fields, generating photon-graviton pairs.