The Schrödinger-Newton equation, a theoretical framework connecting quantum mechanics with classical gravity, predicts that gravity may induce measurable deviations in low-frequency mechanical systems—an intriguing hypothesis at the frontier of fundamental physics. In this study, we developed and operated an advanced optomechanical platform to investigate these effects. The system integrates an optical cavity with finesse over 3.5 × 10 5 and a torsion pendulum with an ultralow eigenfrequency of 0.6 mHz, achieving a high mechanical quality factor exceeding 5 × 10 4 . We collected data for three months and reached a sensitivity of 0.3 μ rad / Hz at the Schrödinger-Newton frequency of 2.5 mHz where deviations from the standard quantum mechanics may occur. While no evidence supporting semiclassical gravity was found, we identify key challenges in such tests and propose new experimental approaches to advance this line of inquiry. This work demonstrates the potential of precision optomechanics to probe the interplay between quantum mechanics and gravity.
The Schrödinger-Newton equation, a theoretical framework connecting quantum mechanics with classical gravity, predicts that gravity may induce measurable deviations in low-frequency mechanical systems—an intriguing hypothesis at the frontier of fundamental physics. In this study, we developed and operated an advanced optomechanical platform to investigate these effects. The system integrates an optical cavity with finesse over 3.5 × 10 5 and a torsion pendulum with an ultralow eigenfrequency of 0.6 mHz, achieving a high mechanical quality factor exceeding 5 × 10 4 . We collected data for three months and reached a sensitivity of 0.3 μ rad / Hz at the Schrödinger-Newton frequency of 2.5 mHz where deviations from the standard quantum mechanics may occur. While no evidence supporting semiclassical gravity was found, we identify key challenges in such tests and propose new experimental approaches to advance this line of inquiry. This work demonstrates the potential of precision optomechanics to probe the interplay between quantum mechanics and gravity.
The interplay between gravity and quantum mechanics remains a central open problem in modern physics. In this talk, I will discuss how a fundamentally classical, local gravitational interaction necessarily induces a diffusive modification of quantum dynamics. This diffusion leads to measurable noise even in the classical regime and provides a novel, experimentally accessible signature that does not require macroscopic quantum superpositions. I will derive a lower bound on the gravitational noise required to prevent entanglement generation and outline an experimental proposal based on torsion pendulums to test this bound. Next, I will consider the Schrödinger-Newton equation—a paradigmatic model of semiclassical gravity—which predicts nonlinear, self-induced gravitational effects. I will show how a periodic modulation of the trap frequency in levitated mechanical oscillators can amplify these otherwise negligible deviations by up to six orders of magnitude. The protocol remains feasible within current technologies and opens new pathways to experimentally test the SN dynamics through precise monitoring of the system’s position variance.
An interesting idea, dating back to Feynman [Report from Chapel Hill Conference, edited by C. M. DeWitt and D. Rickles (1957)], argues that quantum mechanics may break down for large masses if one entertains the possibility that gravity can be ``classical,'' thereby leading to predictions different from conventional low-energy quantum gravity. Despite the technical difficulty in testing such deviations, a large number of experimental proposals have been put forward due to the high level of fundamental interest. Here, we consider the Schr\"odinger-Newton (SN) theory and the correlated worldline (CWL) theory, and show that they can be distinguished from conventional quantum mechanics, as well as each other, by performing pulsed optomechanics experiments. For CWL specifically we develop a framework resembling the commonly used ``Heisenberg-picture'' treatment of coupled oscillators, allowing one to perform simple calculations for such systems without delving into the deeper path-integral formalism. We find that discriminating between the theories will be very difficult until experimental control over low frequency quantum optomechanical systems is pushed much further. However, the predicted departures of SN and CWL from quantum mechanics occur at the same scale, so both alternative models could in principle be probed by a single experiment.
We show that optomechanical systems can test the Schr\"odinger-Newton equation of gravitational quantum mechanics due to Yang et al. Phys. Rev. Lett. 110, 170401 (2013). This equation is motivated by semiclassical gravity, a widely used theory of interacting gravitational and quantum fields. From the many-body Schr\"odinger-Newton equation follows an approximate equation for the center-of-mass dynamics of macroscopic objects. This predicts a distinctive double-peaked signature in the output optical quadrature power spectral density of certain optomechanical systems. Since the Schr\"odinger-Newton equation lacks free parameters, these will allow its experimental confirmation or refutation.
We propose an optomechanics experiment that can search for signatures of a fundamentally classical theory of gravity and in particular of the many-body Schr\"odinger-Newton (SN) equation, which governs the evolution of a crystal under a self-gravitational field. The SN equation predicts that the dynamics of a macroscopic mechanical oscillator's center-of-mass wave function differ from the predictions of standard quantum mechanics [H. Yang, H. Miao, D.-S. Lee, B. Helou, and Y. Chen, Phys. Rev. Lett. 110, 170401 (2013)]. This difference is largest for low-frequency oscillators, and for materials, such as tungsten or osmium, with small quantum fluctuations of the constituent atoms around their lattice equilibrium sites. Light probes the motion of these oscillators and is eventually measured in order to extract valuable information on the pendulum's dynamics. Due to the nonlinearity contained in the SN equation, we analyze the fluctuations of measurement results differently than standard quantum mechanics. We revisit how to model a thermal bath, and the wave-function collapse postulate, resulting in two prescriptions for analyzing the quantum measurement of the light. We demonstrate that both predict features, in the outgoing light's phase fluctuations' spectrum, which are separate from classical thermal fluctuations and quantum shot noise, and which can be clearly resolved with state of the art technology.
The semiclassical gravity sourced by the quantum expectation value of the matter's energy-momentum tensor will change the evolution of the quantum state of matter, which can be described by the Schr\"odinger-Newton (SN) equation. Understanding the phenomenology of the SN equation is important for experimentally testing the quantumness of gravity. In the SN theory, semiclassical gravity contributes a gravitational potential term depending on the matter's quantum state. This state-dependent potential introduces the complexity of the quantum state evolution and measurement in SN theory, which is different for different quantum measurement prescriptions. Previous theoretical investigations on the SN-theory phenomenology in the optomechanical experimental platform were carried out under the so-called post/preselection prescription. This work will focus on the phenomenology of SN theory under the causal-conditional prescription, which fits the standard intuition of the continuous quantum measurement process. We found that under the causal-conditional prescription, the quantum state of the test mass mirrors is conditionally prepared by the continuous projection of the outgoing light field in an optomechanical system. Hence a quantum-trajectory-dependent gravitational potential is created, which significantly changes the system evolution. This work provides an extensive analysis of this new picture of system evolution, and shows that various experimentally measurable signatures predicted by SN theory under causal-conditional prescription cannot be distinguished from that predicted by quantum gravity unless a very extreme experimental parameter region is assumed. Therefore, our new understanding of SN phenomenology provides an important caution toward the experimental verification of quantum gravity.
Quantum mechanics and general relativity are the foundational pillars of modern physics, yet experimental tests that combine the two frameworks remain rare. Measuring optical phase shifts of massless photons in a gravitational potential provides a unique quantum platform to probe gravity beyond Newtonian descriptions, but laboratory-based interferometers have not yet reached the sensitivity needed to access this regime. Here, we report the realization of a 50-km table-top Mach-Zehnder fiber interferometer operating at the single-photon level, achieving a phase sensitivity of 4.42×10−6 rad root-mean-square (RMS) within the frequency range of 0.01 Hz to 5 Hz. We demonstrate that this sensitivity is sufficient to resolve a phase-shift signal of (6.18±0.44)×10−5 rad RMS at 0.1 Hz, associated with a modulated gravity-induced signal. Our results establish a milestone for quantum sensing with large-scale optical interferometry, demonstrating the capability to detect gravitational redshifts in a local laboratory, thereby paving the way for testing quantum phenomena within general relativistic frameworks.