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The ALPHA-g experiment at CERN recently made the first direct observation of the effect of gravity on the motion of antimatter [1]. The result – that antihydrogen falls towards the Earth – is consistent with Einstein’s Weak Equivalence Principle.
In ALPHA-g, antihydrogen is produced by combining antiproton and positron plasmas, each confined in Penning-Malmberg traps. Antihydrogen is subsequently confined in an Ioffe-Pritchard magnetic trap with its axis aligned parallel to the Earth's gravitational field; an octupole provides radial confinement and two solenoids (one above and one below the trapping region), provide axial confinement. The gravitational potential adds to the magnetic potential; when the magnetic fields from the upper and lower solenoids are equal, the gravitational potential results in an up-down asymmetry in the total potential.
An imposed difference in magnetic field in the upper and lower solenoids, known as a bias, is delicately adjusted over a range of values. At each value of the magnetic bias, the magnetic fields of the solenoids are ramped down slowly compared to the antiatom motion, releasing the antihydrogen, and leading to annihilations on the walls of the apparatus which are detected by a position and time sensitive detector. If the imposed bias cancels the gravitational potential, antihydrogen escapes upwards or downwards with equal probability.
Determining the downward, $p_{\text{dn}}$, escape probability from observed annihilations is non-trivial because the efficiency with which antihydrogen annihilations are detected in the upper and lower regions may be different, some small fraction of antihydrogen escaping downwards may be detected in the upper region (and vice versa) and the precise number of trapped antihydrogen atoms is unknown. In addition, cosmic rays passing through the apparatus lead to a background annihilation rate which may also be up-down asymmetric.
A Bayesian method is employed to determine $p_{\text{dn}}$. The likelihood analysis assumes annihilations detected in the upper and lower regions are independently Poisson distributed, with Poisson mean expressed in terms of the relative detector efficiency, the efficiencies with which annihilations are detected in the incorrect region, the cosmic background annihilation rates, and $p_{\text{dn}}$. We solve for the posterior $p_{\text{dn}}$ using the Markov-Chain Monte-Carlo integration package, Stan [2].
Further, we determine the gravitational acceleration of antihydrogen and a statistical error by modifying the likelihood analysis described above to include results from simulations of the experimental procedure. In the modified analysis, $p_{\text{dn}}$ is replaced by the simulated probability of downward escape, which is a function of the antihydrogen gravitational acceleration.
Future increased precision measurements of antimatter gravity will involve transferring the trapped antiatoms to shallower confining potentials. Adiabatic cooling [3] during magnetic transfer will reduce antiatom loss and further increase sensitivity to gravity.
[1] Anderson, E.K., Baker, C.J., Bertsche, W. et al. Observation of the effect of gravity on the motion of antimatter. Nature 621, 716–722 (2023). https://doi.org/10.1038/s41586-023-06527-1
[2] Stan Development Team. 2023. Stan Modeling Language Users Guide and Reference Manual, 2.31. https://mc-stan.org
[3] D. Hodgkinson, On the Dynamics of Adiabatically Cooled Antihydrogen in an Octupole-Based Ioffe-Pritchard Magnetic Trap, Ph.D. thesis, The University of Manchester (2022).
