Phase-Dependent Photon Emission Rates in Quantum Gravity-Induced Entangled States

TL;DR

This work investigates how gravity-induced entanglement in the QGEM setup affects spontaneous photon emission rates. Using first-order time-dependent perturbation theory, it derives photon emission amplitudes and the total rate $R(\delta\phi,k,d)$ for an entangled two-spin state, showing explicit dependence on the entanglement phase $\delta\phi$ and inter-particle separation through $kd$. In the limits $d\to 0$ and $d\to\infty$, the rate approaches entanglement-insensitive asymptotes, while at finite $d$ the rate can be suppressed or enhanced by $\delta\phi$, implying a nuanced but not universal link between emission rates and entanglement. The results suggest photon emission rates could serve as an indirect entanglement probe in QGEM experiments under certain conditions and motivate extensions to higher-order processes, more-body entanglement, and curved spacetime scenarios.

Abstract

Quantum entanglement, as one of the fundamental concepts in quantum mechanics, has garnered significant attention over the past few decades for its extraordinary nonlocality. With the advancement of quantum technology, quantum entanglement holds promising application for exploring fundamental physical theories. The experimental scheme of Quantum Gravity Induced Entanglement of Masses (QGEM) was proposed to investigate the quantum effects of gravity based on the Local Operations and Classical Communication (LOCC) theory. In this study, we analyze the quantum properties of the entangled final states generated in the QGEM scheme. Our findings reveal that the photon emission rates (transition rates) are closely related to the degree of entanglement. Specifically, the transition rate decreases as the degree of entanglement increases when the distance between particle pairs is small, then it gradually approaches an asymptotic value that is independent of entanglement as the distance increases. We then discuss the possibility of using photon emission rates to detect quantum entanglement with these results.

Figures (3)

• Figure 1: Schematic diagram of particle pair transitions. In the numerical calculation, we set the particle spin quantum number to $\frac{1}{2}$. $R$ stands for photon emission rate measured in ${R_0}$, $kd$ for spatial distance between two particles multiplied by the photon wave number $k$, $\delta \phi$ for entanglement phase.
• Figure 2: The photon emission rate difference of each entangled state as a function of particle distance. The horizontal axis, $kd$, is the distance between particle pairs multiplied by the photon wave number. The vertical axis, transition rate difference $dR$, is calculated as: ${\rm{dR = }}{{\rm{R}}_{\delta \phi = 0}} - {{\rm{R}}_{\delta \phi }}$.
• Figure 3: The photon emission rates of five non-entangled states: (1) $\left| { \uparrow \uparrow } \right\rangle$, (2) $\left| { \uparrow \downarrow } \right\rangle$, (3) $\frac{1}{{\sqrt 2 }}\left( {\left| { \uparrow \downarrow } \right\rangle + \left| { \downarrow \downarrow } \right\rangle } \right)$, (4) $\frac{1}{{\sqrt 2 }}\left( {\left| { \uparrow \uparrow } \right\rangle + \left| { \downarrow \uparrow } \right\rangle } \right)$, (5) ${\left| { \downarrow \downarrow } \right\rangle }$. $R$ stands for photon emission rate measured in ${R_0}$, $kd$ for spatial distance between two particles multiplied by the photon wave number $k$.