Prospects for detecting entanglement-induced modifications of the atomic light shift with twin atom interferometers

Through adiabatic elimination of the atom–field Hamiltonian we show that, to second order in the dispersive regime, the light shift depends only on the mean photon number. Residual contributions that involve anomalous correlators appear at higher order or when counter-rotating terms and multi-level structure are retained.

With cavity parameters currently compatible with atom interferometry these residual terms yield phases of order 10^{-11}–10^{-10} rad or smaller, below practical detection thresholds. We identify the technological advances (stronger atom–cavity coupling with clean spatial modes, scattering control, and phase metrology at the 10^{-9} rad level) that could render the effect measurable. A twin-atom-interferometer architecture is proposed as the natural platform once those advances are realized.