Loss of quantum coherence in a system coupled to a zero-temperature environment

We the influence of a zero-temperature environment on a coherent quantum system. First, we calculate the reduced density operator of the system in the framework of the well-known, exactly solvable model of an oscillator coupled to a bath of harmonic oscillators. Then, we propose the sketch of an Aharonov - Bohm-like interferometer showing, through interference measurements, the decrease of the coherence length of the system due to the interaction with the environment, even in the zero temperature limit.