Various physical effects resulting from environmental decoherence are discussed in the algebraic framework. An example of dynamical de-quantization of a quantum particle is considered.
According to a usual reading, decoherence is a process resulting from the interaction between a small system and its large environment where information and energy are dissipated. The particular models treated in the literature on the subject reinforce this idea since, in general, the behavior of a particle immersed in a large "bath" composed by many particles is studied. The aim of this letter is to warn against this usual simplified reading. By means of the analysis of a well-known model, we will show that decoherence may occur in a system interacting with an environment consisting of only one particle.
We recall the classical picture about the decoherence effects induced on a quantum sub-system by the interaction with a macroscopic environment. We discuss the need of a rigorous treatment, in mathematically reasonable models, of the dynamical process bringing the system in an entangled state with the environment. We consider a simple system consisting of two particles interacting via a two-body potential and we discuss a rigorous derivation of the asymptotic wave function of the system in the limit of small mass ratio. We apply the result to the explicit computation of the decoherence effect induced on the heavy particle, in concrete examples of quantum evolution.
We discuss the various manifestations of quantum decoherence in the forms of dephasing, entanglement with the environment, and revelation of "which-path" information. As a specific example, we consider an electron interference experiment. The coupling of the coherent electrons to the quantized electromagnetic field illustrates all of these versions of decoherence. This decoherence has two equivalent interpretations, in terms of photon emission or in terms of Aharonov-Bohm phase fluctuations. We consider the case when the coherent electrons are coupled to photons in a squeezed vacuum state. The time-averaged result is increased decoherence. However, if only electrons which are emitted during selected periods are counted, the decoherence can be suppressed below the level for the photon vacuum. This is the phenomenon of recoherence. This effect is closely related to the quantum violations of the weak energy condition, and is restricted by similar inequalities. We give some estimates of the magnitude of the recoherence effect and discuss prospects for observing it in an electron interferometry experiment.