Various theories of quantum gravity predict the existence of a minimum length scale, which implies the Planck-scale modifications of the Heisenberg uncertainty principle to a so-called generalized uncertainty principle (GUP). Previous studies of the GUP focused on its implications for high-energy physics, cosmology, and astrophysics. Here the application of the GUP to low-energy quantum systems, and particularly cold atoms, is studied. Results from the ${}^{87}\mathrm{Rb}$ atom recoil experiment are used to set upper bounds on parameters in three different GUP proposals. A ${10}^{14}$-level bound on the Ali-Das-Vagenas proposal is found, which is the second best bound so far. A ${10}^{26}$-level bound on Maggiore's proposal is obtained, which turns out to be the best available bound on it.

• Received 13 December 2015

DOI:https://doi.org/10.1103/PhysRevA.94.013607