Gravitationally-Induced Photon Entanglement in an FLRW Cosmological Background

Abstract

In order to detect the quantum nature of gravity, the quantum gravity induced entanglement of masses(QGEM) has been proposed both in flat and curved spacetime. In this paper we propose an analogous QGEM protocol using photons produced in astronomical processes as the quantum systems. Unlike massive particles, the gravitational interaction between photons-intrinsically relativistic particles-simultaneously satisfies both the event and system localities. So it can provide a clear test of whether the gravitational mediator must be nonclassical based on the Local Operations and Classical Communication (LOCC) principle. Although the gravitationally induced entanglement between massless relativistic photons is extremely small, our quantitative calculations clarify the characteristic features of the entanglement induced by the photon's own gravitational field in astronomical process and may inspire other photon entanglement experiments.

Figures (5)

• Figure 1: Diagram of photon trajectory. All four superposition states move parallel along the Z-axis and we have plotted here only the spacetime trajectory of the state $\left|{RL}\right\rangle_{12}$ we need to consider. In the first order approximation, we just have to think about the unperturbed trajectory of the two photons. In Minkowski spacetime due to the self-stability of the gravitational field of light radiation, the exact trajectory of the second photon inside the light cone of metric perturbation remains a straight line with unit velocity along z-axis.
• Figure 2: Phase change ${\Delta {\phi}}$ as a function of z.
• Figure 3: Contour plot of phase change ${\Delta \phi}$ as a function of azimuthal angle $\varphi$ and polar angle $\theta$ with spatial separation fixed at ${d_{{\rm{mean}}}}$. Assume the photon pair is emitted at $z = 1100$. ${\Delta \phi}$ has been measured in units of $- {w_{1\gamma }}{w_{2\gamma }}$.
• Figure 4: The distribution of 2000 sample points of the four independent random variables. The horizontal axis denotes the sampled random variables and the vertical axis denotes probability density (PD). The red curve shows the probability density function from which the samples were drawn.
• Figure 5: Histogram of Monte Carlo–simulated entanglement phase. Both photons are assumed emitted at $z=1100$. The horizontal axis represents the logarithm of absolute entanglement phase and the vertical axis represents the probability density per bin.