[Paper Review] A quantized frequency reference in the short-ranged gravity potential and its application for dark matter and dark energy searches

Tobias Jenke, G. Cronenberg+7 more|arXiv (Cornell University)|Aug 19, 2012

Dark Matter and Cosmic Phenomena42 references3 citations

TL;DR

This paper presents a high-precision gravity resonance spectroscopy experiment using ultra-cold neutrons to probe short-range fifth forces mediated by scalar and pseudoscalar fields, testing for dark matter and dark energy candidates. By measuring quantum states in Earth's gravity potential with 10⁻¹⁴ eV sensitivity, it sets the tightest constraints to date on chameleon fields (β < 2×10⁹) and axion-like particles (gₛgₚ/ℏc < 3×10⁻¹⁶ at 20 µm), consistent with no new interaction beyond standard gravity.

ABSTRACT

The evidence for the observation of the Higgs spin-0-boson as a manifestation of a scalar field provides the missing corner stone for the standard model of particles (SM). However, the SM fails to explain the non-visible but gravitationally active part of the universe. Its nature is unknown but the confirmation of a scalar Higgs is giving a boost to scalar-field-theories. So far gravity experiments and observations performed at different distances find no deviation from Newton's gravity law. Therefore dark energy must possess a screening mechanism which suppresses the scalar-mediated fifth force. Our line of attack is a novel gravity experiment with neutrons based on a quantum interference technique. The spectroscopic measurement of quantum states on resonances with an external coupling makes this a powerful search for dark matter and dark energy contributions in the universe. Quantum states in the gravity potential are intimately related to other scalar field or spin-0-bosons if they exist. If the reason is that some undiscovered particle interact with a neutron, this results in a measurable energy shift of quantum states in the gravity potential, because for neutrons the screening effect is absent. We use Gravity Resonance Spectroscopy to measure the energy splitting at the highest level of precision, providing a constraint on any possible new interaction. We obtain a sensitivity of 10^-14 eV. We set an experimental limit on any fifth force, in particular on parameter β&lt;2x10^9 at n=3 for the scalar chameleon field, which is improved by a factor of 100 compared to our previous experiment and five orders of magnitude better than from precision tests of atomic spectra. The pseudoscalar axion coupling is constrained to gsgp/\hbar c&lt;3x10^-16 at 20μm, which is an improvement by a factor of 30. These results indicate that gravity is understood at this improved level of precision.

Motivation & Objective

• To test for new short-range fifth forces mediated by scalar or pseudoscalar fields that could explain dark energy or dark matter.
• To overcome the screening mechanisms that suppress such forces in conventional gravity experiments by using neutrons, which lack such screening.
• To achieve unprecedented precision in measuring quantum states in Earth's gravitational potential using gravity resonance spectroscopy.
• To constrain scalar field theories—particularly chameleon and axion-like models—by detecting energy shifts in neutron quantum levels.

Proposed method

• Utilizes gravity resonance spectroscopy (GRS) to measure energy splittings between quantum states of ultra-cold neutrons in Earth's gravitational field.
• Applies resonant microwave excitation to induce transitions between quantized gravitational states, enabling high-precision spectroscopy.
• Employs a four-channel acceleration sensor and a three-beam laser interferometer to monitor and control mirror vibrations, ensuring stability.
• Uses a time-domain fit model with sinusoidal components to extract vibration amplitude, frequency, and phase: f(N₀, aₖ, νₖ, φₖ) = N₀ + Σ aₖ·sin(2πνₖ·t + φₖ), with 3K+1 fit parameters.
• Solves coupled differential equations for Rabi oscillations between states, with transition rates governed by S_qp = ½ e^(-iφ_qp) e^(-iδ_qp t) d⟨q|∂/∂z|p⟩.
• Performs fast Fourier transforms (FFT), applies Gaussian filtering, and uses inverse FFT to efficiently extract vibration parameters for real-time stabilization.

Experimental results

Research questions

• RQ1 Can quantum states of ultra-cold neutrons in Earth’s gravitational field reveal deviations from Newtonian gravity due to new scalar or pseudoscalar interactions?
• RQ2 What are the tightest experimental constraints on chameleon scalar fields and axion-like particles using gravity resonance spectroscopy?
• RQ3 How does the absence of screening in neutrons enhance sensitivity to fifth forces compared to atomic or macroscopic experiments?
• RQ4 To what extent do observed quantum energy level splittings in the gravitational potential constrain dark energy and dark matter models?

Key findings

• The experiment achieves a sensitivity of 10⁻¹⁴ eV in measuring energy splittings in the gravitational quantum states of neutrons.
• An upper bound of β < 2×10⁹ is set for the chameleon field coupling at n=3, representing a 100-fold improvement over previous neutron experiments and five orders of magnitude better than atomic spectroscopy limits.
• The coupling of pseudoscalar axions is constrained to gₛgₚ/ℏc < 3×10⁻¹⁶ at a range of 20 µm, an improvement by a factor of 30 over prior experiments.
• All results are consistent with zero, indicating no evidence for new fifth forces at the current sensitivity level.
• The absence of measurable energy shifts supports the validity of Newtonian gravity and general relativity at sub-millimeter scales.
• The study establishes ultra-cold neutron gravity resonance spectroscopy as the most sensitive probe for short-range scalar interactions to date.