[Paper Review] Gravity experiments with ultracold neutrons and the qBounce experiment

Tobias Jenke, G. Cronenberg+4 more|arXiv (Cornell University)|Oct 11, 2015

Atomic and Subatomic Physics Research3 citations

TL;DR

This paper presents the qBounce experiment, which uses ultracold neutrons (UCNs) to study quantum states in Earth's gravitational field. By trapping UCNs in a gravitational potential well formed by a mirror and a hard boundary, the experiment observes quantum bouncing ball dynamics and performs gravity resonance spectroscopy (GRS), achieving a 50% contrast in quantum carpets and enabling high-precision tests of gravity and the Weak Equivalence Principle.

ABSTRACT

This work focuses on the control and understanding of a gravitationally interacting elementary quantum system. It offers a new way of looking at gravitation based on quantum interference: an ultracold neutron, a quantum particle, as an object and as a tool. The ultracold neutron as a tool reflects from a mirror in well-defined quantum states in the gravity potential of the earth allowing to apply the concept of gravity resonance spectroscopy (GRS). GRS relies on frequency measurements, which provide a spectacular sensitivity.

Motivation & Objective

• To investigate quantum states of ultracold neutrons in Earth's gravitational field using a mirror as a hard boundary.
• To develop and apply gravity resonance spectroscopy (GRS) for high-precision measurement of gravitational energy levels.
• To observe the time evolution of coherent superpositions of quantum states in a gravitational potential, visualized as quantum carpets.
• To test the Weak Equivalence Principle by comparing the gravitational length scale $ z_0 $ from quantum bouncing ball dynamics and the energy scale $ E_0 $ from GRS.
• To search for new physics, including hypothetical fifth forces and neutron electric dipole moments, via high-precision quantum gravity measurements.

Proposed method

• Ultracold neutrons are prepared in a 30 µm wide slit between a flat bottom mirror and a rough top mirror, creating a one-dimensional quantum well.
• The system is modeled by a Schrödinger equation with a linear gravitational potential $ mgz $ and a hard wall at $ z=0 $, yielding Airy function solutions.
• Gravity resonance spectroscopy (GRS) is implemented using an oscillating mirror to drive transitions between discrete quantum levels via mechanical coupling.
• A nanopositioning system with capacitive sensors stabilizes the mirror step to 10 nm precision over days, enabling stable quantum state evolution.
• Spatial density distributions are measured using nuclear track detectors with uranium coating, and wave packet evolution is captured via time-resolved snapshots.
• The system uses scaling factors $ z_0 \approx 5.9\ \mu\text{m} $, $ E_0 \approx 0.6\ \text{peV} $, and $ t_0 \approx 1.1\ \text{ms} $ to normalize the dynamics and extract physical parameters.

Experimental results

Research questions

• RQ1 Can coherent superpositions of gravitational quantum states be prepared and observed in a time-resolved manner?
• RQ2 What is the contrast and visibility of quantum interference patterns (quantum carpets) in the bouncing neutron wave packet?
• RQ3 How precisely can the gravitational energy levels be measured using gravity resonance spectroscopy (GRS) with mechanical driving?
• RQ4 Can the quantum bouncing ball experiment be used to test the Weak Equivalence Principle by comparing $ z_0 $ and $ E_0 $?
• RQ5 What limits exist on hypothetical fifth forces or neutron electric dipole moments based on shifts in the measured energy levels?

Key findings

• The qBounce experiment successfully observed quantum bouncing ball dynamics with a measured contrast of approximately 50% in the quantum carpet pattern.
• The first two snapshots of the quantum bouncing ball were captured over 75 days of beam time at the ILL PF2 beamline, with mirror step sizes of 20 µm and 30 µm.
• The wave packet evolution was verified to contain only the lowest quantum states, confirming coherent state preparation in the gravitational potential well.
• The mirror step was stabilized to 10 nm precision using capacitive sensors and closed-loop nanopositioning, enabling long-term stability for quantum state evolution.
• The microscope calibration was determined to an accuracy of 1%, which currently limits the precision of the extracted $ z_0 $ scale.
• The experiment demonstrates the feasibility of combining gravity resonance spectroscopy (GRS) and quantum bouncing ball dynamics for high-precision tests of fundamental physics, including the Weak Equivalence Principle and new forces.