Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1612.06310 · Physical review. D/Physical review. D.

Measurable signatures of quantum mechanics in a classical spacetime

Bassam Helou, Jun Luo, Hsien‐Chi Yeh, Cheng-gang Shao, Bram J. J. Slagmolen, David E. McClelland, Yanbei Chen

Published Aug 9, 2017• 17 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevd.96.044008

Related papers

Optomechanical tests of a Schrödinger-Newton equation for gravitational quantum mechanics

Ching Chuan Gan, Craig M. Savage, Sabina Scully

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.

arXiv:1512.04183•Physical review. D/Physical review. D.•Jun 20, 2016•27 citations

Macroscopic Quantum Mechanics in a Classical Spacetime

Huan Yang, Haixing Miao, Da-Shin Lee +2 more

We apply the many-particle Schrödinger-Newton equation, which describes the coevolution of a many-particle quantum wave function and a classical space-time geometry, to macroscopic mechanical objects. By averaging over motions of the objects' internal degrees of freedom, we obtain an effective Schrödinger-Newton equation for their centers of mass, which can be monitored and manipulated at quantum levels by state-of-the-art optomechanics experiments. For a single macroscopic object moving quantum mechanically within a harmonic potential well, its quantum uncertainty is found to evolve at a frequency different from its classical eigenfrequency-with a difference that depends on the internal structure of the object-and can be observable using current technology. For several objects, the Schrödinger-Newton equation predicts semiclassical motions just like Newtonian physics, yet quantum uncertainty cannot be transferred from one object to another.

arXiv:1210.0457•Physical Review Letters•Apr 22, 2013•138 citations

Testing Alternative Theories of Quantum Mechanics with Optomechanics, and Effective Modes for Gaussian Linear Optomechanics

Bassam Helou

Optomechanics has made great strides in theory and experiments over the past decade, which culminated in the first direct detection of gravitational waves in 2015 by LIGO. This thesis explores how optomechanics can be used to test fundamental physics other than the theory of general relativity. Our emphasis will be on falsifiable theories (ultimately, only experiments can decide whether a theory is correct) that address two outstanding issues in quantum mechanics: the measurement problem, and reconciling quantum mechanics with the theory of general relativity. In particular, we show that the space experiment LISA pathfinder places aggressive bounds on two objective collapse models, which are non-linear stochastic modifications of the Schroedinger equation that can resolve the measurement problem. Moreover, we show that state-of-the-art torsion pendulum experiments can test the Schroedinger-Newton theory, which is the non-relativistic limit of a non-linear theory combining quantum mechanics with a fundamentally classical spacetime. Along the way, we propose how to resolve two major difficulties with determining the predictions of non-linear quantum mechanics in an actual experiment. First, we cannot use the density matrix formalism in non-linear quantum mechanics and so we have to suggest and justify a particular ensemble for the thermal bath. Separating out quantum and classical fluctuations helped us propose a reasonable ensemble. Second, most researchers believe that deterministic non-linear quantum mechanics must violate the no-signaling condition. We show this isn't necessarily the case because different interpretations of quantum mechanics make different predictions in non-linear quantum mechanics. We propose an interpretation, the causal-conditional prescription, that doesn't violate causality by noticing that once we fix an initial state, the evolution of a system under many non-linear theories is equivalent to evolution under a linear Hamiltonian with feedback. The mapping allows us to leverage the tools of quantum control, and it tells us that if the non-linear parameters of a non-linear Hamiltonian respond causally (i.e. with an appropriate delay) to measurement results, then the theory can be made causal. We also contribute to the theory of quantum optomechanics. We introduce two new bases that one can view environment modes with. In linear optomechanics a system interacts with an infinite number of bath modes. We show that the interaction can be reduced to one with finite degrees of freedom. Moreover, at any particular time, the system is correlated with only a finite number of bath modes. We show that if we make the assumption that we can measure any commuting environment modes, then this basis allows us to understand the one-shot quantum Cramer-Rao bound in a simple way, and allows us to sweep large parameter regimes and so find promising optomechanics topologies for quantum state preparation tasks that we can then analyze without the assumption of being able to measure any observable of the environment. We also use this basis to show that when we are interested in the conditional dynamics of a test mass, we can only adiabatically eliminate a lossy cavity when we measure the optomechanical system at a slow enough rate. Finally, we develop an analytic filter for obtaining the state of a generic optomechanical system that interacts linearly with its environment and is driven by Gaussian states, and where the outgoing light is measured with a non-linear photon-counting measurement. We hope that our work will help researchers explore optomechanics topologies that make use of photon counters.

•Mar 27, 2019•2 citations

Tomography of a Macroscopic Quantum State influenced by Classical Self-Gravity

Wenjie Zhong, Yubao Liu, Yanbei Chen +2 more

Macroscopic optomechanical systems offer a promising testbed for distinguishing whether gravity acts as a quantum interaction or as a classical field. Schrodinger-Newton (SN) theory is the nonrelativistic limit of semi-classical gravity where quantum matter couples to classical gravity. Based on SN theory, this work investigates how classical self-gravity affects continuous quantum state tomography of a macroscopic mechanical oscillator monitored by variable-angle homodyne detection. In the Schrodinger-Newton (SN) theory, the measurement record arises from a different conditional test mass dynamics from that in quantum-gravity (QG)/standard quantum mechanics, consequently, applying the QG-optimised reconstruction map introduces an additional state-dependent contribution. We show that this contribution makes the reconstructed covariance depend on the chosen set of tomography angles and can drive the SN covariance--after QG filtering--outside the standard Gaussian-covariance domain set by the Heisenberg uncertainty principle. We quantify the resulting QG-SN distinguishability via the Hellinger distance and analyse its dependence on measurement strength and temperature. We then formulate the same issue in the broader setting of nonlinear quantum mechanics: when the system's conditional dynamics during the readout process depends on the state being inferred, the tomographic map acquires nonlinear, model-dependent corrections to the usual Radon or Gaussian reconstruction map.

quant-pharXiv:2607.06967•Jul 9, 2026•0 citations

Semiclassical gravity phenomenology under the causal-conditional quantum measurement prescription

Yubao Liu, Haixing Miao, Yanbei Chen +1 more

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.

arXiv:2207.05966•Physical review. D/Physical review. D.•Jan 5, 2023•14 citations

Testing quantum gravity using pulsed optomechanical systems

Jordan Wilson-Gerow, Yanbei Chen, Philip C. E. Stamp

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.

arXiv:2311.02033•Physical review. D/Physical review. D.•Mar 26, 2024•7 citations
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.
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 apply the many-particle Schrödinger-Newton equation, which describes the coevolution of a many-particle quantum wave function and a classical space-time geometry, to macroscopic mechanical objects. By averaging over motions of the objects' internal degrees of freedom, we obtain an effective Schrödinger-Newton equation for their centers of mass, which can be monitored and manipulated at quantum levels by state-of-the-art optomechanics experiments. For a single macroscopic object moving quantum mechanically within a harmonic potential well, its quantum uncertainty is found to evolve at a frequency different from its classical eigenfrequency-with a difference that depends on the internal structure of the object-and can be observable using current technology. For several objects, the Schrödinger-Newton equation predicts semiclassical motions just like Newtonian physics, yet quantum uncertainty cannot be transferred from one object to another.
Optomechanics has made great strides in theory and experiments over the past decade, which culminated in the first direct detection of gravitational waves in 2015 by LIGO. This thesis explores how optomechanics can be used to test fundamental physics other than the theory of general relativity. Our emphasis will be on falsifiable theories (ultimately, only experiments can decide whether a theory is correct) that address two outstanding issues in quantum mechanics: the measurement problem, and reconciling quantum mechanics with the theory of general relativity. In particular, we show that the space experiment LISA pathfinder places aggressive bounds on two objective collapse models, which are non-linear stochastic modifications of the Schroedinger equation that can resolve the measurement problem. Moreover, we show that state-of-the-art torsion pendulum experiments can test the Schroedinger-Newton theory, which is the non-relativistic limit of a non-linear theory combining quantum mechanics with a fundamentally classical spacetime. Along the way, we propose how to resolve two major difficulties with determining the predictions of non-linear quantum mechanics in an actual experiment. First, we cannot use the density matrix formalism in non-linear quantum mechanics and so we have to suggest and justify a particular ensemble for the thermal bath. Separating out quantum and classical fluctuations helped us propose a reasonable ensemble. Second, most researchers believe that deterministic non-linear quantum mechanics must violate the no-signaling condition. We show this isn't necessarily the case because different interpretations of quantum mechanics make different predictions in non-linear quantum mechanics. We propose an interpretation, the causal-conditional prescription, that doesn't violate causality by noticing that once we fix an initial state, the evolution of a system under many non-linear theories is equivalent to evolution under a linear Hamiltonian with feedback. The mapping allows us to leverage the tools of quantum control, and it tells us that if the non-linear parameters of a non-linear Hamiltonian respond causally (i.e. with an appropriate delay) to measurement results, then the theory can be made causal. We also contribute to the theory of quantum optomechanics. We introduce two new bases that one can view environment modes with. In linear optomechanics a system interacts with an infinite number of bath modes. We show that the interaction can be reduced to one with finite degrees of freedom. Moreover, at any particular time, the system is correlated with only a finite number of bath modes. We show that if we make the assumption that we can measure any commuting environment modes, then this basis allows us to understand the one-shot quantum Cramer-Rao bound in a simple way, and allows us to sweep large parameter regimes and so find promising optomechanics topologies for quantum state preparation tasks that we can then analyze without the assumption of being able to measure any observable of the environment. We also use this basis to show that when we are interested in the conditional dynamics of a test mass, we can only adiabatically eliminate a lossy cavity when we measure the optomechanical system at a slow enough rate. Finally, we develop an analytic filter for obtaining the state of a generic optomechanical system that interacts linearly with its environment and is driven by Gaussian states, and where the outgoing light is measured with a non-linear photon-counting measurement. We hope that our work will help researchers explore optomechanics topologies that make use of photon counters.
Macroscopic optomechanical systems offer a promising testbed for distinguishing whether gravity acts as a quantum interaction or as a classical field. Schrodinger-Newton (SN) theory is the nonrelativistic limit of semi-classical gravity where quantum matter couples to classical gravity. Based on SN theory, this work investigates how classical self-gravity affects continuous quantum state tomography of a macroscopic mechanical oscillator monitored by variable-angle homodyne detection. In the Schrodinger-Newton (SN) theory, the measurement record arises from a different conditional test mass dynamics from that in quantum-gravity (QG)/standard quantum mechanics, consequently, applying the QG-optimised reconstruction map introduces an additional state-dependent contribution. We show that this contribution makes the reconstructed covariance depend on the chosen set of tomography angles and can drive the SN covariance--after QG filtering--outside the standard Gaussian-covariance domain set by the Heisenberg uncertainty principle. We quantify the resulting QG-SN distinguishability via the Hellinger distance and analyse its dependence on measurement strength and temperature. We then formulate the same issue in the broader setting of nonlinear quantum mechanics: when the system's conditional dynamics during the readout process depends on the state being inferred, the tomographic map acquires nonlinear, model-dependent corrections to the usual Radon or Gaussian reconstruction map.
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.
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.