Do atoms in internal-energy superpositions obey the equivalence principle?
In plain words
Since energy has mass, an atom in a quantum superposition of two energy levels has no single definite mass. Whether it still falls exactly like a normal atom is a question that classical physics cannot pose.
Precise statement
In the quantum formulation of the equivalence principle (Zych and Brukner, arXiv 1502.00971), the internal mass-energy operator $M = m_0 + H_{\int}/c^2$ may couple to gravity through operators $M_g$ and $M_i$ that differ off-diagonally. Bound the off-diagonal violation parameters for atoms prepared in coherent superpositions of hyperfine or optical clock states at better than $10^{-12}$, improving on the about $10^{-9}$ bound of Rosi et al 2017.
What would settle it
An atom interferometer with test atoms in clock-state superpositions measuring the differential acceleration with sub-$10^{-12}$ precision.
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