Quantum field theory for multipolar composite bosons with mass defect and relativistic corrections

Atomic high-precision measurements have become a competitive and essential technique for tests of fundamental physics, the Standard Model, and our theory of gravity. It is therefore self-evident that such measurements call for a consistent relativistic description of atoms that eventually originates from quantum field theories like quantum electrodynamics. Most quantum-metrological approaches even postulate effective field-theoretical treatments to describe a precision enhancement through techniques like squeezing. However, a consistent derivation of interacting atomic quantum gases from an elementary quantum field theory that includes both the internal structure as well as the center of mass of atoms, has not yet been addressed. We present such an effective quantum field theory for interacting, spin-carrying, and possibly charged ensembles of atoms composed of nucleus and electron that form composite bosons called cobosons, where the interaction with light is included in a multipolar description. Relativistic corrections to the energy of a single coboson, light-matter interaction, and the scattering potential between cobosons arise in a consistent and natural manner. In particular, we obtain a relativistic coupling between the coboson's center-of-mass motion and internal structure encoded by the mass defect, together with an ion spin-orbit coupling. We use these results to derive modified bound-state energies including the motion of ions, modified scattering potentials, a relativistic extension of the Gross-Pitaevskii equation, and the mass defect applicable to atomic clocks or quantum-clock interferometry. Our theory does not only combine and generalize aspects of effective field theories, quantum optics, scattering theory, and ultracold quantum gases, but it also bridges the gap between quantum electrodynamics and effective field theories for ultracold quantum gases.