Nonequilibrium Quantum Fluctuation Forces

Abstract

We study all known and as yet unknown forces between neutral atoms and neutral atoms and surfaces. The forces arise from mutual influences mediated by an attending electromagnetic field and not from direct interaction. We allow as dynamical variables the center of mass motion of the atom (or surface Chapter 5), its internal degrees of freedom, modeled as a three dimensional harmonic oscillator (the internal degrees of freedom of the surface in chapter 4), and the quantum field treated relativistically.

We adopt the methods of nonequilibrium quantum field theory (NEqQFT) to study the problem of fluctuation forces beginning from first principles. NEqQFT provides a fully dynamical description of systems far from equilibrium having the advantage of being the

synthesis of quantum field theory and nonequilibrium statistical mechanics. The integration of these two paradigms is necessary for a complete study of fluctuation forces; quantum field theory for providing effects such as retardation and quantum field fluctuations, and nonequilbrium statistical mechanics for treating processes involving quantum dissipation and noises. By embarking from first principles we avoid wrong or only partially correct results from inconsistent theories that can be generated from assumptions made at lower levels of accuracy.

In thermodynamic equilibrium we reproduce all the effects and forces known in the last century, such as Casimir-Polder-- between neutral

atoms, Lifshitz-- between an atom and a surface and Casimir between surfaces (and the generalization of these forces to nonequilibrium stationary-states). More noteworthy is the discovery of the existence of a new type of interatomic force which we call the `entanglement force', originating from the quantum correlations of the internal degrees of freedom of entangled atoms.

Fluctuation phenomena associated with quantum fields is a new frontier of future research in atom-field interaction. With NEqQFT we have derived Langevin equations which account for fluctuations of an atom's trajectory about its semi-classical value. These quantum field-induced perturbations of the atom's position could lead to measurable results such as the damping of the center-of-mass oscillations of a trapped Bose-Einstein condensate near a surface or backaction cooling of moving mirror by radiative pressure and quantum viscosity discussed respectively in Chapter 3 and 5 of this thesis.

The methods introduced in this thesis for treating atom-field interactions or mirror-field interactions go beyond previous work by

providing a fully dynamical description of these forces valid for arbitrary atom and surface motion, indeed the inclusion of self consistent backactions are necessary for the study of phenomena such as quantum decoherence and entanglement dynamics, including non-Markovian processes which invariably will appear

when backaction is taken into consideration(especially for strong fields, low temperatures, or fast response).