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arXiv:2012.12903 · Physical review. D/Physical review. D.

Decoherence from general relativity

Itamar J. Allali, Mark P. Hertzberg

Published May 24, 2021• 15 citations
arXivHTMLPDF

Abstract

It is of great interest to explore matter in nontrivial quantum arrangements, including Schr\"odinger catlike states. Such states are sensitive to decoherence from their environment. Recently, in Allali and Hertzberg [Gravitational decoherence of dark matter, J. Cosmol. Astropart. Phys. 07 (2020) 056] we computed the rate of decoherence of a piece of superposed matter that primarily interacts only gravitationally, a dark-matter-Schr\"odinger-cat state (DMSCS), within the nonrelativistic approximation. In this work we improve this to a general relativistic analysis. We first derive a single particle relativistic Schr\"odinger equation for a probe particle that passes through the DMSCS; the interaction is provided by the weak field metric of general relativity from the source. For a static DMSCS we find a neat generalization of our previous results. We then turn to the interesting new case of a time dependent DMSCS, which can be provided by a coherently oscillating axion field leading to superposed time dependent oscillations in the metric: a truly quantum-general relativistic phenomenon. We use scattering theory to derive the decoherence rate in all these cases. When the DMSCS is in a superposition of distinct density profiles, we find that the decoherence rate can be appreciable. We then consider the novel special case in which the density is not in a superposition, but the phase of its field oscillation is; this is a property that cannot be decohered within the nonrelativistic framework. We find that if the probe particle and/or the DMSCS's velocity dispersion is slow, then the rate of decoherence of the phase is exponentially suppressed. However, if both the probe and the DMSCS's velocity dispersion are relativistic, then the phase can decohere more rapidly. As applications, we find that diffuse galactic axions with superposed phases are robust against decoherence, while dense boson stars and regions near black hole horizons are not, and we discuss implications for experiment.

DOI
10.1103/physrevd.103.104053

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It is of great interest to explore matter in nontrivial quantum arrangements, including Schr"odinger catlike states. Such states are sensitive to decoherence from their environment. Recently, in Allali and Hertzberg [Gravitational decoherence of dark matter, J. Cosmol. Astropart. Phys. 07 (2020) 056] we computed the rate of decoherence of a piece of superposed matter that primarily interacts only gravitationally, a dark-matter-Schr"odinger-cat state (DMSCS), within the nonrelativistic approximation. In this work we improve this to a general relativistic analysis. We first derive a single particle relativistic Schr"odinger equation for a probe particle that passes through the DMSCS; the interaction is provided by the weak field metric of general relativity from the source. For a static DMSCS we find a neat generalization of our previous results. We then turn to the interesting new case of a time dependent DMSCS, which can be provided by a coherently oscillating axion field leading to superposed time dependent oscillations in the metric: a truly quantum-general relativistic phenomenon. We use scattering theory to derive the decoherence rate in all these cases. When the DMSCS is in a superposition of distinct density profiles, we find that the decoherence rate can be appreciable. We then consider the novel special case in which the density is not in a superposition, but the phase of its field oscillation is; this is a property that cannot be decohered within the nonrelativistic framework. We find that if the probe particle and/or the DMSCS's velocity dispersion is slow, then the rate of decoherence of the phase is exponentially suppressed. However, if both the probe and the DMSCS's velocity dispersion are relativistic, then the phase can decohere more rapidly. As applications, we find that diffuse galactic axions with superposed phases are robust against decoherence, while dense boson stars and regions near black hole horizons are not, and we discuss implications for experiment.
Quantum mechanics allows for states in macroscopic superpositions, but they ordinarily undergo rapid decoherence due to interactions with their environment. A system that only interacts gravitationally, such as an arrangement of dark matter (DM), may exhibit slow decoherence. In this Letter, we compute the decoherence rate of a quantum object within general relativity, focusing on superposed metric oscillations; a rare quantum general relativistic result. For axion DM in a superposition of the field's phase, we find that DM in the Milky Way is robust against decoherence, while a spatial superposition is not. This novel phase behavior may impact direct detection experiments.
Decoherence describes the tendency of quantum sub-systems to dynamically lose their quantum character. This happens when the quantum sub-system of interest interacts and becomes entangled with an environment that is traced out. For ordinary macroscopic systems, electromagnetic and other interactions cause rapid decoherence. However, dark matter (DM) may have the unique possibility of exhibiting naturally prolonged macroscopic quantum properties due to its weak coupling to its environment, particularly if it only interacts gravitationally. In this work, we compute the rate of decoherence for light DM in the galaxy, where a local density has its mass, size, and location in a quantum superposition. The decoherence is via the gravitational interaction of the DM overdensity with its environment, provided by ordinary matter. We focus on relatively robust configurations: DM perturbations that involve an overdensity followed by an underdensity, with no monopole, such that it is only observable at relatively close distances. We use non-relativistic scattering theory with a Newtonian potential generated by the overdensity to determine how a probe particle scatters off of it and thereby becomes entangled. As an application, we consider light scalar DM, including axions. In the galactic halo, we use diffuse hydrogen as the environment, while near the earth, we use air as the environment. For an overdensity whose size is the typical DM de Broglie wavelength, we find that the decoherence rate in the halo is higher than the present Hubble rate for DM masses m a ≲ 5 × 10 −7 eV and in earth based experiments it is higher than the classical field coherence rate for m a ≲ 10 −6 eV . When spreading of the states occurs, the rates can become much faster, as we quantify. Also, we establish that DM BECs decohere very rapidly and so are very well described by classical field theory.
Quantum mechanics allows for states in macroscopic superpositions, but they ordinarily undergo rapid decoherence due to interactions with their environment. A system that only interacts gravitationally, such as an arrangement of dark matter (DM), may exhibit slow decoherence. In this letter, we compute the decoherence rate of a quantum object in general relativity. For axion DM in a superposition of the field's phase, we find that DM in the Milky Way is robust against decoherence, while a spatial superposition is not. This novel phase behavior may be relevant to direct detection experiments.
A new frontier in the search for dark matter (DM) is based on the idea of detecting the decoherence caused by DM scattering against a mesoscopic superposition of normal matter. Such superpositions are uniquely sensitive to very small momentum transfers from new particles and forces, especially DM with a mass below 100 MeV. Here we investigate what sorts of dark sectors are inaccessible with existing methods but would induce noticeable decoherence in the next generation of matter interferometers. We show that very soft but medium range ($0.1\text{ }\mathrm{nm}--1\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$) elastic interactions between nuclei and DM are particularly suitable. We construct toy models for such interactions, discuss existing constraints, and delineate the expected sensitivity of forthcoming experiments. The first hints of DM in these devices would appear as small variations in the anomalous decoherence rate with a period of one sidereal day. This is a generic signature of interstellar sources of decoherence, clearly distinguishing it from terrestrial backgrounds. The OTIMA experiment under development in Vienna will begin to probe Earth-thermalizing DM once sidereal variations in the background decoherence rate are pushed below one part in a hundred for superposed 5-nm gold nanoparticles. The proposals by Bateman et al. and Geraci et al. could be similarly sensitive although they would require at least a month of data taking. DM that is absorbed or elastically reflected by the Earth, and so avoids a greenhouse density enhancement, would not be detectable by those three experiments. On the other hand, the aggressive proposals of the MAQRO collaboration and Pino et al. would immediately open up many orders of magnitude in DM mass, interaction range, and coupling strength, regardless of how DM behaves in bulk matter.
We give a first principles derivation of a master equation for the evolution of a quantum matter field in a linearly perturbed Minkowski spacetime, based solely on quantum field theory and general relativity. We make no additional assumptions nor introduce extra ingredients, as is often done in alternative quantum theories. When the quantum matter field is projected to a one-particle state, the master equation for a non-relativistic quantum particle in a weak gravitational field predicts decoherence in the energy basis , in contrast to most existing theories of gravitational decoherence. We point out the gauge nature of time and space reparameterizations in matter–gravity couplings, and warn that 'intrinsic' decoherence or alternative quantum theories invoking stochastic dynamics arising from temporal or spatial fluctuations violate this fundamental symmetry of classical general relativity. Interestingly we find that the decoherence rate depends on extra parameters other than the Planck scale, an important feature of gravitational decoherence. This is similar to the dependence of the decoherence rate of a quantum Brownian particle to the temperature and spectral density of the environment it interacts with. The corresponding features when gravity acts as an environment in decohering quantum objects are what we call the ' textures' of spacetime . We point out the marked difference between the case when gravity is represented as a background spacetime versus the case when gravity acts like a thermodynamic bath to quantum particles. This points to the possibility of using gravitational decoherence measurements to discern whether gravity is intrinsically elemental or emergent.
In a previous work [L. Asprea, G. Gasbarri, and A. Bassi, Gravitational decoherence: A general nonrelativistic model, Phys. Rev. D 103, 104041 (2021).] we derived a quantum master equation for the dynamics of a scalar bosonic particle interacting with a weak, stochastic and classical gravitational field. As standard matter is made of fermions, such an equation should be suitably extended to describe more relevant experimental situations. Here we derive a nonrelativistic model for the gravitational decoherence of spin 1/2 particles. We enrich the treatment by also considering a coupling with an external classical electromagnetic field. We comment on the differences with the scalar bosonic model and we describe the regimes in which they become negligible.