Gravitational and other shifts of whispering gallery and gravitational state interference patterns of light neutral particles

TL;DR

The paper develops a general framework to optimize and model whispering-gallery states and gravitational quantum states across neutrons, hydrogen, antihydrogen, muonium, and positronium, enabling precise measurements of gravity-related shifts and fundamental constants. It introduces parameter-optimization, statistical-sensitivity estimation, and Schrödinger-based interference modeling, then applies these methods to propose feasible experiments for neutrons, H, antiH, Mu, and Ps. The work provides concrete schemes to measure the gravitational constant G, constrain the neutron electric charge, and test antimatter gravity, while highlighting the advantages of WGS/GQS across a wide velocity and lifetime spectrum. Overall, it demonstrates that WGS/GQS interferometry can achieve high sensitivity for gravity and QR-related phenomena in diverse particles, offering a roadmap for future high-precision tests of fundamental physics.

Abstract

We discuss small shifts in the interference patterns of gravitational and whispering gallery quantum states that can be observed with neutrons, atoms, antiatoms, muonium, positronium, and other particles. A gravitational shift of interference patterns of neutron gravitational and whispering-gallery states can be easily observed with cold, very cold, or ultracold neutrons. The developed methods can be used for observing/searching for other shifts in fundamental neutron physics experiments, for instance, for measuring the gravitational constant or constraining the neutron electric charge. A series of such measurements will be made with neutrons at the PF1B/PF2/D17 facilities at the ILL. A peculiar feature of analogous atomic (anti-atomic) experiments is the much smaller effective critical energies of the materials of mirrors for (anti)atoms. We evaluated parameters that make a measurement of the hydrogen and antihydrogen whispering-gallery states and their gravitational shifts feasible. A series of such measurements will be made with hydrogen and deuterium atoms by the GRASIAN collaboration in Vienna and Turku. Such a measurement with antihydrogen atoms may be of interest for the GBAR experiment, the ASACUSA experiment, which is producing a beam of slow antihydrogen atoms, and other experiments at CERN, which study the gravitational properties of antimatter. Quantum reflection of muonium and positronium from material surfaces opens the possibility of observing whispering-galley states, although such measurements remain experimentally challenging. Because of small masses of muonium and positronium, the effective critical energies of the mirror materials are much higher for them than the effective critical energies for hydrogen and other atoms. The observation of gravitational shifts of such states is particularly demanding because of the extremely short lifetimes of these systems.

Figures (13)

• Figure 1: An angularly collimated white neutron beam arrives to the entrance of a concave cylindrical mirror at a small grazing angle to the surface. Some neutrons are trapped in WGS and continue following the surface towards the exit of the mirror. Due to WGS, an interference pattern is observed when measuring simultaneously longitudinal and tangential components of neutron velocities. The longitudinal component of velocity (neutron wavelength) is measured using the time-of-flight technique. The tangential component of velocity (the angle of escape from the mirror edge) is measured in a position-sensitive detector installed at a distance from the exit of the mirror (the figure is copied from ref. Rauch2010).
• Figure 2: A schematic of a neutron GQS experiment. A collimated beam of neutrons enters the system through a chopper, placed a distance $D_C$ away from the entrance of the mirror, which enables the measurement of the neutrons' velocity by the time of flight (ToF) method. The beam then enters the mirror absorber/scatterer system. Lower energy GQS can pass through the initial section where an absorber/scatterer of length $L$ is placed a height $\Delta H$ above the mirror, while higher GQS are rejected. The lower GQS then propagate along the surface and interfere with each other until reaching the end of the mirror, which has a total length $L$. The exiting beam enters a free fall region where a time and position sensitive detection system is placed a distance $D_F$ from the exit of the mirror. The position of the neutrons on the detector is denoted as $X$.
• Figure 3: A simulation of the interference pattern generated by propagating VCNs through a mirror-absorber/scatterer system of length $L_{GQS}^{VCN} = 30~\text{cm}$. The height of the absorber/scatterer is set to $\Delta H_{GQS}^{VCN}=40~\mu \text{m}$ and the absorber/scatterer is assumed to be very efficient. After exiting the mirror, neutrons enter a free fall region of length $D_{GQS}^{VCN} =7~\text{m}$. The velocities presented in the simulation correspond to the peak in the VCN spectrum at the PF2/VCN instrument. Note that a much richer interference pattern can be produced if a position-sensitive detector with better resolution is available or slower neutrons are used.
• Figure 4: A schematic of the UCN GQS experiment in reduced gravity to measure $q_{\text{n}}$ or $G$. An incoming UCN beam enters a mirror absorber/scatterer system which is oriented such that the Earth's gravitational field is pointed nearly normal to the plane of the page. The value of the remaining gravity is defined by the projection of the gravity vector to the plane of the page. GQS with reduced gravity are populated and generate interference patterns which then enter a storage volume where an additional force is exerted on the outgoing beam, either gravitational from a large mass or electric from electrodes, both are generically indicated by $\vec{a}$. After some time in the volume, the beam leaves and reaches a detector to record the interference pattern. An element to shape and analyze the neutron's velocity may also be advantageous, depending on the available UCN spectrum. The optical system for shaping the GQS in reduced gravity can consist of one or more systems of the mirror and the absorber/scatterer (if the characteristic size of the interference structures on the detector is larger than the size of one slit, or, alternatively, if the slits are oriented in a way to direct the beams to the same spot in the position-sensitive detector).
• Figure 5: Simulations of the expected interference pattern for UCN $G$ and $q_{\text{n}}$ measurements. A mirror absorber/scatterer system of length $L_{GQS^{reduced}}^{UCN}=1$ m is used for calculations with the absorber/scatterer height of $\Delta H_{GQS^{reduced}}^{UCN}=700$$\mu$m. The system oriented so that the slit between the mirror and absorber/scatterer is nearly vertical, as described in the text. The exiting wave packet is propagated for $D_{GQS^{reduced}}^{UCN}=40$ m, corresponding to the $T_{GQS^{reduced}}^{UCN}=20$ s observation time for $V_{GQS^{reduced}}^{UCN}=2$ m/s UCNs. The effect of a gravitational field from a test mass, or the electric field of electrodes, was included with the presence of a uniform field that allows the exiting wave packet to "fall." The left plot shows the pattern without the effect of an external force and the right has an applied acceleration of $a = 2.7\times10^{-6} g$. This is 10 times higher than the proposed additional acceleration to improve the visibility the pattern's shift to more negative positions.