Equations of motion approach to decoherence and current noise in ballistic interferometers coupled to a quantum bath

Abstract

We present a technique for treating many particles moving inside a ballistic interferometer, under the influence of a quantum-mechanical environment (phonons, photons, Nyquist noise etc.). Our approach is based on solving the coupled Heisenberg equations of motion of the many-particle system and the bath and is inspired by the quantum Langevin method known for the Caldeira Leggett model. It allows to study decoherence and the influence of the bath on other properties of the interferometer. As a first application, we treat a fermionic Mach-Zehnder interferometer. In particular, we discuss the dephasing rate and present full analytical expressions for the leading corrections to the current noise, brought about by the coupling to the quantum bath.