X iv : q ua nt - p h / 97 10 06 1 v 1 2 7 O ct 1 99 7 Coherence and Fluctuations in the Interaction between Moving Atoms and a Quantum Field ∗

Mesoscopic physics deals with three fundamental issues: quantum coherence, fluctuations and correlations. Here we analyze these issues for atom optics, using a simplified model of an assembly of atoms (or detectors, which are particles with some internal degree of freedom) moving in arbitrary trajectories in a quantum field. Employing the influence functional formalism, we study the self-consistent effect of the field on the atoms, and their mutual interactions via coupling to the field. We derive the coupled Langevin equations for the atom assemblage and analyze the relation of dissipative dynamics of the atoms (detectors) with the correlation and fluctuations of the quantum field. This provides a useful theoretical framework for analysing the coherent properties of atom-field systems. ∗Invited talk by B. L. Hu at the International Conference on Quantum Coherence, Northeastern University, Boston, July 11-13, 1997. To appear in the Proceedings edited by J. Swain and A. Widom (World Scientific, Singapore, 1998). 1 1 Mesoscopic Physics in Condensed Matter, Atom Optics, and Cosmology To practitioners in condensed matter physics, mesoscopia refers to rather specific problems where, for example, the sample size is comparable to the probing scale (nanometers), or the interaction time is comparable to the time of measurement (femtoseconds), or that the electron wavefunction is correlated over the sample thus changing its transport properties fundamentally, or that the fluctuation pattern is reproducible and sample specific. In atom/radiation optics, it is the regime where coherent atom-field interaction, correlations of field, or the effect of boundaries become important. In cosmology, it is the epoch when quantum fluctuations of fields mediate phase transitions, reheat the universe or seed the galaxies. They are described by semiclassical gravity and unified theories from the Planck to the GUT scales. Here we work with a generalized definition of mesoscopia proposed by one of us (see [1], where a general discussion of the conceptual unity among these disciplines can be found), i.e., the quantum / classical, micro / macro interface. It also entails coherent / decoherent, stochastic / deterministic dynamics, and discrete / continuum correspondences. As pointed out in [1], mesoscopia deals with three fundamental issues: quantum coherence, fluctuations and correlations. All mesoscopic processes involve one or more of these aspects. Many current research directions in early universe cosmology and black hole physics also involve these aspects in a fundamental way. The focus of this talk is however exclusively on atom / radiation optics, which deals with the coherent interaction of atoms and radiation. We will consider the interaction of an atom with a quantum field and examine the coherence, correlation and fluctuations of such a system in a fully non-equilibrium, relativistic fieldtheoretical treatment [2] . This situation is of basic interest because quantum fields possess zero-point fluctuations which manifest as random forces on an atom. The coherence of the vacuum state also enters in an essential way in the description of atom-field interactions. Here, we shall use a simplified model of an atom, that of a particle with an internal oscillator degree of freedom – call it a detector, moving along an arbitrary trajectory. In fact, to make the correlation aspects even more manifest, we consider an assembly of n such detectors coupled to a quantum field, and study their interaction with the field and their mutual interactions via coupling to the field. This type of problem has been treated before when the atoms (or detectors) are stationary. In [4], for example, there is a discussion of Langevin equations for an arbitrary number of homogenously broadened three-level atoms. Such a treatment, however, holds for atoms fixed in space, and does not consider arbitrary states of motion of the atoms themselves. On the other hand, nowhere is the role of fluctuations of the vacuum more explicit than in the motion of a uniformly accelerated atom or detector. In the frame moving with such a detector, fluctuations of different modes of the vacuum combine so as to appear as therThis treatment is more than necessary for atom optics which deals with slowly moving atoms, and perhaps more befitting for fast moving charged particles in strong fields (plasma physics), but the consistency of backreaction makes such a demand, and it is safer to take the finite temperature, nonrelativistic, far-field, slow motion limits from the final result than as simplifying conditions ab initio. See [3].