Exact Born Approximation for the Spin-Boson Model

Abstract

Within the lowest-order Born approximation, we present an exact calculation of the time dynamics of the spin-boson model in the Ohmic regime. We observe non-Markovian effects at zero temperature that scale with the system-bath coupling strength and cause qualitative changes in the evolution of coherence at intermediate times of order of the oscillation period. These changes could significantly affect the performance of these systems as qubits. In the biased case, we find a prompt loss of coherence at these intermediate times, whose decay rate is set by $\sqrtα$, where $α$ is the coupling strength to the environment. These calculations indicate precision experimental tests that could confirm or refute the validity of the spin-boson model in a variety of systems.