The project of quantum spacetime phenomenology focuses on searching pragmatically for the Planck-scale quantum features of spacetime. Among these features is the existence of a characteristic length scale commonly addressed by effective approaches to quantum gravity (QG). This characteristic length scale could be simply realized, for instance, by generalizing the standard Heisenberg uncertainty principle to a generalized uncertainty principle (GUP). While it is usually expected that phenomena belonging to the realm of QG are essentially probable solely at the so-called Planck energy, here we show how a GUP proposal containing the most general modification of coordinate representation of the momentum operator could be probed by a cold atomic ensemble recoil experiment (CARE) as a low-energy quantum system. This proposed atomic interferometer setup has advantages over the conventional architectures owing to the enclosure in a high-finesse optical cavity that is supported by a new class of low-power-consumption integrated devices known as micro-electro-opto-mechanical systems. In the framework of a top-down-inspired bottom-up QG phenomenological viewpoint and by taking into account the measurement accuracy realized for the fine structure constant from the rubidium (87Rb) CARE, we set some constraints as upper bounds on the characteristic parameters of the underlying GUP. In the case of superposition of the possible GUP modification terms, we managed to set a tight constraint of 0.999 978 < λ0 < 1.000 02 for the dimensionless characteristic parameter. Our study shows that the best playground to test QG approaches is not merely high-energy physics, but a table-top nanosystem assembly as well.
