Analysis of Landau-Zener tunneling with an Ohmic reservoir and a noise source

Abstract

To determine the possibility of single-electron operation in electronic devices, we investigated the Landau-Zener (LZ) tunneling process with dissipation. This work presents an analytical formula and detailed numerical results for dynamical tunneling phenomena with an Ohmic reservoir and a noise source. First, we calculated the transient and final density matrices of a single-electron system coupled to a reservoir at zero temperature, and then noted the rigid tunneling process and a noticeable decoherence of the tunneling. The rigidity of the LZ tunneling suggests that we can suppress errors in single-electron operations. However, our analytical and numerical results clarified the fact that noise strongly affects the tunneling process. When half of the noise spectrum bandwidth ${\ensuremath{\omega}}_{\mathrm{max}}$ is larger than the gap of the adiabatic potential, thermal excitation by the noise source considerably increases the tunneling probability. On the other hand, our numerical results found that the noise effect is proportional to ${\ensuremath{\omega}}_{\mathrm{max}}^{3}$ when ${\ensuremath{\omega}}_{\mathrm{max}}$ is smaller than the gap. Then we can accurately operate single electrons if the noise source has a sufficiently narrow band.