Nonequilibrium forces between neutral atoms mediated by a quantum field

We study forces between two neutral atoms, modeled as three-dimensional harmonic oscillators, arising from mutual influences mediated by an electromagnetic field but not from their direct interactions. We allow as dynamical variables the center-of-mass motion of the atom, its internal degrees of freedom, and the quantum field treated relativistically. We adopt the method of nonequilibrium quantum field theory which can provide a first-principles, systematic, and unified description including the intrinsic and induced dipole fluctuations. The inclusion of self-consistent back-actions makes possible a fully dynamical description of these forces valid for general atom motion. In thermal equilibrium we recover the known forces-London, van der Waals, and Casimir-Polder-between neutral atoms in the long-time limit. We also reproduce a recently reported force between atoms when the system is out of thermal equilibrium at late times. More noteworthy is the discovery of the existence of a type of ( or identification of the source of some known) interatomic force which we call the "entanglement force," originating from the quantum correlations of the internal degrees of freedom of entangled atoms.