Quantum Field Theory for Multipolar Composite Bosons with Mass Defect and Relativistic Corrections

Abstract

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 a subspace effective 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. 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. Published by the American Physical Society 2024

Finite pulse-time effects in long-baseline quantum clock interferometry

“…Specifically, we refer to the works of Sonnleitner et al 74 and Schwartz et al 75,76 for systems with quantized COM motion, respectively, without and with gravity. A field theoretical derivation has recently been performed by Aßmann et al 77 Moreover, Perche et al 78,79 contain a discussion under which conditions and by which guiding principles, effective models for composite systems can be constructed in curved spacetime. Extensions examining the coupling of Dirac particles to gravitational backgrounds have recently also been discussed, 78,80,81 yielding overall sensible but in the details slightly differing results in the weak-field limit.…”

“…( 4), since the mass eigenstates are identical to the internal energy eigenstates except for an energy shift. The details of this interaction Hamiltonian can be quite complicated 74,76,77 when all corrections from the mass defect are included. However, to leading order, it consists of the standard electric or magnetic dipole transitions described by…”

“…for an atom with internal structure interacting with an external electromagnetic field. While our introduction here can only serve as a sketch, motivated by mass energy equivalence, it turns out that the derivation of the intern-extern coupling can be made fairly rigorous, 47,[75][76][77]83,84,86 however, with serious gains in the theoretical complexity of the model depending on the setting as well as the starting point. Nevertheless, the basic premises and leading order results do not change significantly.…”