Starting with the interaction of interacting field and a two level atom we observe that the atom-interacting field system acquires a space parameter dependent Berry phase after the phase parameter slowly changes and ultimately returns to its initial form.
Motivated by work [Phys. Rev. Lett. 89, 220404 (2002)] for detecting the vacuum-induced Berry phases with two-mode Jaynes-Cummings models (JCMs), we show here that, for a parameter-dependent single-mode JCM, certain atom-field states also acquired photon-number-dependent Berry phases after the parameter slowly changed and eventually returned to its initial value. This geometric effect related to the field quantization still exists, even if the field is kept in its vacuum state. Specifically, a feasible Ramsey interference experiment with a cavity quantum electrodynamics system is designed to detect the vacuum-induced Berry phase.
We consider the scattering of an atom by a sequence of two near-resonant standing light waves, each formed by two running waves with slightly different wave vectors. Due to opposite detunings of the two standing waves, within the rotating wave approximation, the adiabatic approximation applied to the atomic center-of-mass motion, and a smooth turning on and off of the interaction, the dynamical phase cancels out and the final state of the atom differs from the initial one only by the sum of the two Berry phases accumulated in the two interaction regions. This phase depends on the position of the atom in a way such that the wave packet emerging from the scattering region will focus, which constitutes a method to observe the Berry phase without resorting to interferometric methods.