Technique to measure the gravitational mass of ultracold matter and its implications for antimatter studies

Measuring the effect of gravity on antimatter is a longstanding problem in physics that has significant implications for our understanding of the fundamental nature of the universe. Here, we present a technique to measure the gravitational mass of atoms, motivated by a recent measurement of antimatter atoms at CERN [Nature (London) 621, 716 (2023)]. We demonstrate our technique on cold atoms by measuring the fraction of atoms that survive in the trap after gradually softening a quadrupole magnetic trap in a gravitational potential. We compare our measurements with a Monte Carlo simulation to extract the value of the gravitational acceleration. The difference between the accepted value for g, the local acceleration due to gravity, and the measured value is (-1.9 +/- 12stat +/- 40syst) x 10-4g. We demonstrate the importance of various design parameters in the experiment setup and estimate their contribution to the achievable accuracy in future experiments. Our method demonstrates simplicity, precision, and reliability, facilitating future precision studies of the gravitational force on antimatter. It can also be used to precisely calibrate atom traps based on the known gravitational attraction of ordinary matter to Earth.