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Physica Scripta

The Search for Quantum Gravity Using Matter Interferometers

R. Bingham

Published Jan 1, 2005• 5 citations
Publisher

Abstract

One of the biggest unsolved problems in fundamental physics is the unification of quantum mechanics and gravity. One of the consequences of unification could be the existence of "incoherent conformal waves" in gravitational fields due to quantum mechanical zero-point fluctuations. Recent theories have demonstrated that these fluctuations change the first order correlation function of matterwaves. A spacecraft mission called Hyper is being designed to conduct matterwave experiments in space. An order of magnitude improvement may be gained by going into orbit reducing the effects of environmental interactions. Such experiments could put constraints on the upper bands of measurements of decoherence of a matterwave interferometer due to quantum fluctuations.

DOI
10.1238/physica.topical.116a00132

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Robustness is a critical challenge for matter-wave interferometers. In real experiments, various sources of classical noises arise from mechanical vibrations, seismic motions, inertial forces, tidal forces, magnetic field fluctuations and so on. These noises can disturb the spin and spatial degrees of freedom of the test mass, resulting in witness loss of the interferometer. While spin decoherence is relatively well understood and can be formulated by the Bloch-Redfield master equation, the impact on spatial degrees of freedom still requires systematic investigation. This thesis therefore aims to explore witness loss in an SGI induced by stochastic noises acting on spatial degrees of freedom. As investigated by this thesis, the witness gets lost via several mechanisms: (i) Dephasing. The spatial phase is fluctuated by stochastic noise, resulting in a random phase factor eiδϕ, whose ensemble average contributes a decay factor e−Γ to the spin density matrix and leads to a loss of witness. As is demonstrated by the thesis, this decay factor is a linear response to the external noise, with a transfer function as the Fourier transform of the unperturbed classical trajectories. (ii) Humpty-Dumpty problem. The classical trajectories are also disturbed by stochastic noise, resulting in a non-closure problem of the interferometer, known as the Humpty-Dumpty problem. The resulting witness loss is usually characterized by the contrast of the final states ⟨ψ1|ψ2⟩, which equals the phase-space distance |α1 − α2|2 when the test mass is in coherent states. (iii) Position localization decoherence. Due to the randomness of the noise, the spatial wavefunction of the test mass is thus also stochastic, of which the ensemble average experiences decoherence characterized by the power spectrum density of external noise. However, as illustrated by this thesis, this type of decoherence does not affect spin-based witnesses in most practical scenarios. The general theoretical framework is mainly constructed in chapter 3 of this thesis. The subsequent chapters analyze several representative noise sources: (i) Gravitational and electrostatic noise. Molecules in the surrounding gas move randomly due to thermal motion, generating stochastic gravitational accelerations and electrostatic forces that can be expanded in multipole series. Since the random motion follows Maxwell’s distribution and approximately has a cylindrical symmetry, the resulting noise power spectrum density takes the form of Bessel functions. (ii) Inertial acceleration noise. The mechanical support of the experimental apparatus is always fluctuated by vibrational noise, resulting in random inertial force on the test mass. In practice, dephasing can be mitigated through destructive interference by introducing appropriate coupling between different directional components. (iii) Inertial torsion noise. In suspended experiments, the experimental apparatus is fluctuated by torsional noise, leading to another inertial noise on the test mass. The power spectrum density of the inertial torsion noise is formulated by the selfconvolution of the original noise, resulting in the peak frequencies that are doubled. Taken together, these analyses build a comprehensive picture of how stochastic noise affects the spatial dynamics of an SGI and leads to the loss of spin-based witnesses. Future work may include more realistic noise sources such as magnetic noise and trap-potential noise. These insights will be valuable for future experimental implementations, particularly in precision sensing for quantum gravity, where preserving coherence and maintaining reliable witness signals are essential.

•Apr 8, 2026•0 citations
One of the biggest unsolved problems in fundamental physics is the unification of quantum mechanics and gravity. One of the consequences of unification could be the existence of "incoherent conformal waves" in gravitational fields due to quantum mechanical zero-point fluctuations. Recent theories have demonstrated that these fluctuations change the first order correlation function of matterwaves. A spacecraft mission called Hyper is being designed to conduct matterwave experiments in space. An order of magnitude improvement may be gained by going into orbit reducing the effects of environmental interactions. Such experiments could put constraints on the upper bands of measurements of decoherence of a matterwave interferometer due to quantum fluctuations.
One of the biggest unsolved problems in fundamental physics is the unification of quantum mechanics and general relativity. The lack of experimental guidance makes the issue particularly evasive. Recent models of decoherence demonstrated that conformal fluctuations of spacetime can change the correlation function of matter-waves. Latest progress on conformal decomposition in canonical gravity makes it possible for these decoherence models to be developed without freezing any degrees of freedom for general relativity. The new approach allows the roles of the conformal field and (spin-2) gravitational waves to be identified in the Brownian motion principle based on which Planck scale physics could be accessed. A spacecraft mission called Hyper was proposed to conduct matter-wave experiments in space. Orders of magnitude improvement may be gained by going into orbit reducing the effects of environmental interactions. Such experiments could put constraints on the upper bounds of measurements of decoherence of a matter-wave interferometer due to quantum fluctuations of spacetime.
One of the biggest unsolved problems in physics is the unification of quantum mechanics and general relativity. The lack of experimental guidance has made the issue extremely evasive, though various attempts have been made to relate the loss of matter wave coherence to quantum spacetime fluctuations. We present a new approach to the gravitational decoherence near the Planck scale, made possible by recently discovered conformal structure of canonical gravity. This leads to a gravitational analogue of the Brownian motion whose correlation length is given by the Planck length up to a scaling factor. With input from recent matter wave experiments, we show that the minimum value of this factor to be well within the expected range for quantum gravity theories. This suggests that the sensitivities of advanced matter wave interferometers may be approaching the fundamental level due to quantum spacetime fluctuations and that investigating Planck scale physics using matter wave interferometry may become a reality in the near future. Physics on the large scale is based on Einstein’s theory of general relativity (GR), which interprets gravity as the curvature of spacetime. Despite its tremendous success as an isolated
One of the biggest unsolved problems in physics is the unification of quantum mechanics and general relativity. The lack of experimental guidance has made the issue extremely evasive, though various attempts have been made to relate the loss of matter wave coherence to quantum spacetime fluctuations. We present a new approach to the gravitational decoherence near the Planck scale, made possible by the recently discovered conformal structure of canonical gravity. This leads to a gravitational analogue of Brownian motion whose correlation length is given by the Planck length up to a scaling factor. With input from recent matter wave experiments, we show the minimum value of this factor to be well within the expected range for quantum gravity theories. This suggests that the sensitivities of advanced matter wave interferometers may be approaching the fundamental level due to quantum spacetime fluctuations, and that investigating Planck scale physics using matter wave interferometry may become a reality in the near future.
One of the biggest problems faced by those attempting to combine quantum theory and general relativity is the experimental inaccessibility of the unification scale. In this paper, we show how incoherent conformal waves in the gravitational field, which may be produced by quantum mechanical zero–point fluctuations, interact with the wave packets of massive particles. The result of this interaction is to produce decoherence within the wave packets which could be accessible in experiments at the atomic scale.Using a simple nonlinear model for the coherence properties of the gravitational field, we derive an equation for the evolution of the density matrix of such a wave packet. Following the primary state diffusion programme, the most promising source of space–time fluctuations for experimental detection is these zero–point energy fluctuations. According to our model, the absence of intrinsic irremovable decoherence in matter interferometry experiments puts bounds on some of the parameters of quantum gravity theories. Current experiments give λ >18, where λtPlanck is an effective cut–off for the validity of low–energy quantum gravity theories.
The quantum nature of gravity is one of physics' greatest unsolved problems, with existing experimental proposals facing formidable challenges in maintaining spatial superpositions of massive objects against decoherence. We propose a fundamentally different approach that bypasses these difficulties. The central insight is that a quantum gravitational field can imprint a gauge-invariant phase on a particle's wavefunction even along an open trajectory, arising from the quantum backreaction of the source. This phase, which manifests prior to the final recombination stage of an interferometer and cannot be generated by a classical gravitational field, provides an operationally direct witness to the quantumness of gravity. Our experimental design uses a single photon whose accumulated gravitational phase due to the Earth is transferred via absorption to auxiliary atoms near the end of the interferometer sequence, preserving the open-path character essential for the test. We scale the interferometer to yield a detectable phase of order 10−310^{-3}10−3 rad and show how non-local correlation measurements on the atoms can access this gauge-invariant signature. Leveraging established quantum optical and atomic techniques, this proposal offers a feasible path to distinguish quantum from classical gravity. A positive result would provide the first experimental evidence for the quantum nature of gravitational fields, with profound implications for quantum gravity theories.
Matter-wave interferometry is a striking quantum phenomenon that differs fundamentally from classical mechanics. In the quantum regime, matter behaves like a wave and can exist in spatial superpositions, allowing a single quantum object to move along multiple trajectories simultaneously. Similar to optical interferometers, such quantum matter systems act as interferometers themselves, with the differential phase that encodes information about external forces experienced during their evolution. This makes matter-wave interferometry a powerful platform for quantum sensing across various applications: (i) One of the most direct applications is precision measurement. Atomic interferometers can measure local acceleration and have already been implemented in devices such as accelerometers, seismometers, gravimeters, and gradiometers. (ii) Atomic interferometers are proposed as complementary tools for future gravitational-wave observatories, including ongoing projects MIGA, MAGIS-100, AION and ZAIGA. (iii) Matter-wave interferometry also offers a promising platform for probing quantum aspects of gravity. Numerous tabletop proposals aim to test quantum gravity models, investigate collapse mechanisms, study gravity-induced decoherence, and search for gravity-mediated quantum entanglement. The Stern-Gerlach interferometer (SGI) is a type of matter-wave interferometer that manipulates spatial superpositions using magnetic-field gradients. The witness of an SGI can be designed via its spin, enabling more precise measurements of the differential phase. Recent developments in atomic chip technology have enabled the generation of highly controlled magnetic fields on compact platforms, allowing for precise manipulation of spin states and making SGIs experimentally realizable. Robustness is a critical challenge for matter-wave interferometers. In real experiments, various sources of classical noises arise from mechanical vibrations, seismic motions, inertial forces, tidal forces, magnetic field fluctuations and so on. These noises can disturb the spin and spatial degrees of freedom of the test mass, resulting in witness loss of the interferometer. While spin decoherence is relatively well understood and can be formulated by the Bloch-Redfield master equation, the impact on spatial degrees of freedom still requires systematic investigation. This thesis therefore aims to explore witness loss in an SGI induced by stochastic noises acting on spatial degrees of freedom. As investigated by this thesis, the witness gets lost via several mechanisms: (i) Dephasing. The spatial phase is fluctuated by stochastic noise, resulting in a random phase factor eiδϕ, whose ensemble average contributes a decay factor e−Γ to the spin density matrix and leads to a loss of witness. As is demonstrated by the thesis, this decay factor is a linear response to the external noise, with a transfer function as the Fourier transform of the unperturbed classical trajectories. (ii) Humpty-Dumpty problem. The classical trajectories are also disturbed by stochastic noise, resulting in a non-closure problem of the interferometer, known as the Humpty-Dumpty problem. The resulting witness loss is usually characterized by the contrast of the final states ⟨ψ1|ψ2⟩, which equals the phase-space distance |α1 − α2|2 when the test mass is in coherent states. (iii) Position localization decoherence. Due to the randomness of the noise, the spatial wavefunction of the test mass is thus also stochastic, of which the ensemble average experiences decoherence characterized by the power spectrum density of external noise. However, as illustrated by this thesis, this type of decoherence does not affect spin-based witnesses in most practical scenarios. The general theoretical framework is mainly constructed in chapter 3 of this thesis. The subsequent chapters analyze several representative noise sources: (i) Gravitational and electrostatic noise. Molecules in the surrounding gas move randomly due to thermal motion, generating stochastic gravitational accelerations and electrostatic forces that can be expanded in multipole series. Since the random motion follows Maxwell’s distribution and approximately has a cylindrical symmetry, the resulting noise power spectrum density takes the form of Bessel functions. (ii) Inertial acceleration noise. The mechanical support of the experimental apparatus is always fluctuated by vibrational noise, resulting in random inertial force on the test mass. In practice, dephasing can be mitigated through destructive interference by introducing appropriate coupling between different directional components. (iii) Inertial torsion noise. In suspended experiments, the experimental apparatus is fluctuated by torsional noise, leading to another inertial noise on the test mass. The power spectrum density of the inertial torsion noise is formulated by the selfconvolution of the original noise, resulting in the peak frequencies that are doubled. Taken together, these analyses build a comprehensive picture of how stochastic noise affects the spatial dynamics of an SGI and leads to the loss of spin-based witnesses. Future work may include more realistic noise sources such as magnetic noise and trap-potential noise. These insights will be valuable for future experimental implementations, particularly in precision sensing for quantum gravity, where preserving coherence and maintaining reliable witness signals are essential.