Probing Planck-scale spacetime by cavity opto-atomic 87Rb interferometry

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 ( Rb-87) 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 < lambda(0) < 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.