[Paper Review] Quantum Gravity Induced Entanglement of Masses With Extra Dimensions

Shuai Feng, Bao-Min Gu+1 more|arXiv (Cornell University)|Jul 21, 2023

Relativity and Gravitational TheoryPhysics and Astronomy31 references3 citations

TL;DR

This paper proposes using the Quantum Gravity Induced Entanglement of Masses (QGEM) experiment to detect extra dimensions via the Randall-Sundrum II (RS-II) braneworld model. By modeling gravity's quantum phase shifts in a 5D AdS space, it shows that extra dimensions enhance entanglement witness growth, especially for larger AdS curvature radii, making entanglement develop faster than in 4D gravity, thus offering a detectable signature of extra dimensions through quantum information protocols.

ABSTRACT

It is believed that gravity can be considered as a quantum coherent mediator. In this study, we propose a plan to test the existence of extra dimensions using the Quantum Gravity Induced Entanglement of Masses (QGEM) experiment. This experiment involves two freely falling test masses passing through a Stern-Gerlach-like device. We investigate the entanglement witness between these masses within the framework of the Randall-Sundrum II model (RS-II). Our findings indicate that the system reaches entanglement more rapidly in the presence of extra dimensions, particularly when the radius of the extra dimension is large.

Motivation & Objective

• To investigate whether the presence of extra dimensions can be detected through quantum entanglement induced by gravity.
• To analyze how the Randall-Sundrum II (RS-II) model modifies gravitational potential and quantum phase shifts in a QGEM experiment.
• To evaluate the entanglement witness as a probe for extra dimensions in a quantum gravity framework.
• To determine the sensitivity of entanglement dynamics to the radius of the extra dimension and mass separation.

Proposed method

• Model the gravitational potential in the RS-II braneworld model, incorporating corrections proportional to the AdS curvature radius $ l $.
• Compute quantum phase shifts $ \delta\Phi_{RL}, \delta\Phi_{LR} $ induced by the modified potential for two masses in a Stern-Gerlach-like interferometer setup.
• Use the phase shifts to calculate the entanglement witness $ \mathscr{W} = \left| \langle\sigma_x^{(1)} + \sigma_z^{(2)}\rangle + \langle\sigma_y^{(1)} + \sigma_y^{(2)}\rangle \right| $, where $ \mathscr{W} > 1 $ indicates entanglement.
• Simulate the evolution of $ \mathscr{W} $ over time $ \tau $ for varying parameters: $ d $, $ \delta x $, and $ l $, representing mass separation and extra dimension size.
• Compare entanglement dynamics in 4D gravity versus RS-II with extra dimensions to isolate the signature of the extra dimension.
• Analyze the dependence of phase shifts and entanglement on the closest and farthest distances between masses, $ d - \delta x $ and $ d + \delta x $.

Experimental results

Research questions

• RQ1 Does the presence of an extra dimension in the RS-II model accelerate the development of entanglement between two freely falling masses in a QGEM experiment?
• RQ2 How does the AdS curvature radius $ l $ of the extra dimension affect the entanglement witness $ \mathscr{W} $?
• RQ3 Which mass separation—closest $ d - \delta x $ or farthest $ d + \delta x $—has a stronger influence on the entanglement dynamics?
• RQ4 Can the correction to the gravitational potential in the RS-II model lead to measurable differences in quantum phase shifts compared to standard 4D gravity?
• RQ5 Is the entanglement witness more sensitive to changes in $ d - \delta x $ than $ d + \delta x $, and why?

Key findings

• The entanglement witness $ \mathscr{W} $ reaches values above 1 more rapidly in the presence of an extra dimension compared to 4D gravity, indicating faster entanglement formation.
• The rate of entanglement growth is positively correlated with the AdS curvature radius $ l $, with larger $ l $ leading to stronger phase shifts and faster entanglement.
• The phase shifts $ \delta\Phi_{RL} $, corresponding to the closest mass pair, show more significant changes than $ \delta\Phi_{LR} $, due to shorter distance and stronger gravitational interaction.
• The entanglement witness is more sensitive to $ d - \delta x $ than $ d + \delta x $, as $ d - \delta x $ appears in the denominator of the phase shift expressions and dominates the dynamics.
• For fixed $ d + \delta x $, $ \mathscr{W} $ approaches unity faster at smaller $ d - \delta x $, while for fixed $ d - \delta x $, larger $ d + \delta x $ enhances entanglement due to reduced interference from the nearest pair.
• The correction to the gravitational potential in the RS-II model, proportional to $ l^2 $, leads to enhanced quantum phase shifts, which directly amplify the entanglement witness.