Detectability of post-Newtonian classical and quantum gravity via quantum clock interferometry

TL;DR

This work tackles the challenge of probing quantum gravity effects in the post Newtonian regime by proposing two quantum clock based schemes that isolate frame-dragging signatures in a symmetric geometry. It develops a consistent canonical path integral framework for quantum clocks in nonstatic spacetimes, derives the gravitomagnetic proper-time difference, and analyzes both a clock interferometry visibility test and a gravity induced entanglement (GIE) test. The paper also extends the quantum equivalence principle to nonstatic and quantum superposed geometries, showing how the proposed experiments could distinguish competing quantum gravity models, though the predicted effects are currently extremely small. Together these results establish a rigorous theoretical foundation and a clear path for future experiments to explore post-Newtonian quantum gravitational phenomena.

Abstract

Understanding physical phenomena at the intersection of quantum mechanics and general relativity remains a major challenge in modern physics. While various experimental approaches have been proposed to probe quantum systems in curved spacetime, most focus on the Newtonian regime, leaving post-Newtonian effects such as frame dragging largely unexplored. In this study, we propose and theoretically analyze an experimental scheme to investigate how post-Newtonian gravity affects quantum systems. We consider two setups: (i) a quantum clock interferometry setup designed to detect the gravitational field of a rotating mass, and (ii) a scheme exploring whether such effects could be used to generate gravity-induced entanglement. Due to the symmetry of the configuration, the proposed setup is insensitive to Newtonian gravitational contributions but remains sensitive to the frame-dragging effect. Furthermore, our scheme allows for testing whether the observed gravity-induced entanglement is consistent with the quantum equivalence principle. While the predicted effects appear too small to detect with current technology, our scheme offers a starting point for future experiments probing post-Newtonian quantum gravitational effects.

Figures (6)

• Figure 1: Schematic diagram of the proposed experiment. An atom is placed in a superposition of two parallel paths using a beam splitter and mirrors. After propagating along both paths, it is recombined to produce an interference pattern, which will be observed as a function of the width of the interferometer, $w$. A rotating massive object is located at the center of the interferometer, with its rotation axis perpendicular to the plane of the interferometer arms. While traversing each path, the atom interacts with the gravitational field generated by this object. The difference of gravitational effects between the two paths appears as a proper-time difference. Due to the symmetry of the setup, the Newtonian contributions of the gravitational field cancels out, and the remaining proper-time difference arises purely from frame-dragging. This results in the gravitomagnetic clock effect, making the observed interference pattern a direct signature of post-Newtonian gravity.
• Figure 2: The paths for which the proper time difference is evaluated.
• Figure 3: The interference pattern predicted from Eqs. (\ref{['eq:alphadfn']}) and (\ref{['eq:PrL']}) is shown. The vertical axis represents the probability that the detector at the left port clicks, and the horizontal axis denotes the width of the interferometer $w'$ (see Eq. (\ref{['eq:dfnwp']})). The blue and orange lines correspond to $\Delta E = 0$ and $\Delta E = \bar{E}/24$, respectively.
• Figure 4: The amount of entanglement predicted from Eqs. (\ref{['eq:ESPC']}) and (\ref{['eq:ESP']}) is shown. The horizontal axis denotes the width of the interferometer $w$. The blue line represents the entanglement for the case of $\Delta E = 0$, while the orange and green lines correspond to $\mathcal{E}^{S|PC}$ and $\mathcal{E}^{S|P}$, respectively, for $\Delta E = \bar{E}/24$.
• Figure 5: The interference pattern predicted from Eqs. (\ref{['eq:visQEP']}) and (\ref{['eq:PrLQEP']}) is shown. The vertical axis represents the probability that the detector at the left port clicks, and the horizontal axis denotes the width of the interferometer $w'$. The energy eigenvalues are chosen to be $E_g'=E_g$, $E_e'=E_e$ and $\Delta E'=\Delta E=\bar{E}/24$. The blue and orange lines correspond to $\theta = 0$ and $\theta = \pi/6$, respectively.