A Mass-Energy United Test of the Equivalence Principle

The equivalence principle (EP) is one of the basic assumptions of general relativity. Almost all new theories[1] that attempt to unify gravity with the standard model[2] require the EP be broken. Experimental tests of EP provide opportunities for verification of different theoretical models and emergence of new physics. Traditional mass tests[3-9] of EP have achieved the precision of 10-15 level[3]. Tests with quantum properties including spin[10,11], superposition[12], quantum statistics[10] and internal state[4,13], have been performed, and entanglement[14] test was also proposed. Energy is another very important property and is related to mass by the mass-energy equivalence (MEE). However, mass-energy united tests of EP have never been carried out. Here, we achieve for the first time the united EP test covering energy interval from micro-eV to giga-eV by a mass and internal energy specified atom interferometer (AI). The AI was realized by taking advantage of the Four-Wave Double-diffraction Raman transition (4WDR) method[7] for specified internal energy states, and by extending 4WDR to include excited states. The Eötvös parameters of the four paired combinations (87Rb|F＝1>-85Rb|F＝2>, 87Rb|F＝2>-85Rb|F＝2>, 87Rb|F＝1>-85Rb|F＝3> and 87Rb|F＝2>-85Rb|F＝3>) were measured to be η1=(1.5±3.2)×10-10, η2=(-0.6 ±3.7)×10-10, η3=(-2.5±4.1)×10-10 and η4=(-2.7±3.6)×10-10, respectively. The violation parameters of mass and internal energy are constrained to η0 = (-0.8±1.4)×10-10 and β = (-0.6±6.9)×105. This work opens a door for united tests of EP and MEE in large energy range with quantum systems.