Quantum Dynamics of Spins Coupled by Electrons in 1D Channel

We develop a unified theoretical description of the induced interaction and quantum noise in a system of two spins (qubits) coupled via a quasi-one-dimensional electron gas in the Luttinger liquid regime. Our results allow evaluation of the degree of coherence in quantum dynamics driven by the induced indirect exchange interaction of localized magnetic moments due to conduction electrons, in channel geometries recently experimentally studied for qubit control and measurement.