Constraining the generalized uncertainty principle with the atomic weak-equivalence-principle test

Various models of quantum gravity imply the Planck-scale modifications of Heisenberg's uncertainty principle into a so-called generalized uncertainty principle (GUP). The GUP effects on high-energy physics, cosmology, and astrophysics have been extensively studied. Here, we focus on the weak-equivalence-principle (WEP) violation induced by the GUP. Results from the WEP test with the ${}^{85}\mathrm{Rb}-{}^{87}\mathrm{Rb}$ dual-species atom interferometer are used to set upper bounds on parameters in two GUP proposals. A ${10}^{45}$-level bound on the Kempf-Mangano-Mann proposal and a ${10}^{27}$-level bound on Maggiore's proposal, which are consistent with bounds from other experiments, are obtained. All these bounds have huge room for improvement in the future.

Figure 1

Schematic diagrams for a $\pi /2-\pi -\pi /2$ Raman atom interferometer. (a) Diagram for Raman transitions, which happen between two hyperfine ground states $|g\rangle$ and $|e\rangle$. Laser beams are detuned by $\mathrm{\Delta }$ from the optical resonance $|c\rangle$. The atomic population is resonantly transferred between $|g\rangle$ and $|e\rangle$ when the frequency difference ${\omega }_1-{\omega }_2$ is close to ${\omega }_{\mathrm{hfs}}$. (b) Diagram for paths of an atom in the interferometer, where Raman $\pi /2$ pulses are applied at points A and D and Raman $\pi$ pulses are applied at points B and C.