Gravitational Decoherence of Dark Matter

TL;DR

This paper investigates how gravitational interactions can cause decoherence in light dark matter, potentially affecting its quantum properties in galactic and terrestrial environments, with implications for understanding dark matter's quantum nature.

Contribution

It provides a detailed calculation of gravitational decoherence rates for light dark matter, highlighting conditions under which dark matter behaves classically or quantum mechanically.

Findings

Decoherence rate exceeds Hubble rate for DM masses below 5×10⁻⁷ eV in the galaxy.

Decoherence rate surpasses classical coherence rate for DM masses below 10⁻⁶ eV on Earth.

Dark matter Bose-Einstein condensates decohere rapidly, behaving classically.

Abstract

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 $m_a \lesssim 5 \times 10^{-7}$eV and in earth based experiments it is higher than the classical field coherence rate for $m_a \lesssim 10^{-6}$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.