Regular patterns in the information flow of local dephasing channels

Abstract

Consider local dephasing processes of a qubit that interacts with a structured reservoir of frequency modes or a thermal bath, with Ohmic-like spectral density (SD). It is known that non-Markovian evolution appears uniquely above a temperature-dependent critical value of the Ohmicity parameter and non-Markovianity can be induced by properly engineering the external environment. In the same scenario, we find regular patterns in the flow of quantum information: Alternate directions appear in correspondence with periodic intervals of the Ohmicity parameter ${\ensuremath{\alpha}}_{0}$. The information flows back into the system over long times at zero temperature for $2+4n<{\ensuremath{\alpha}}_{0}<4+4n$, where $n=0,1,2,...,$ and at nonvanishing temperatures for $3+4n<{\ensuremath{\alpha}}_{0}<5+4n$. Under special conditions, backflow of information appears also for nonvanishing, even natural values of the Ohmicity parameter, at zero temperature, and for odd natural values at nonvanishing temperatures. Otherwise, the long-time information flows into the environment. In the transition from vanishing to arbitrary nonvanishing temperature, the long-time backflow of information is stable for $3+4n<{\ensuremath{\alpha}}_{0}<4+4n$, while it is reversed for $2+4n<{\ensuremath{\alpha}}_{0}<3+4n$ and $4+4n<{\ensuremath{\alpha}}_{0}<5+4n$. The patterns in the information flow are not altered if the low-frequency Ohmic-like profiles of the SDs are perturbed with additional factors that consist in arbitrary powers of logarithmic forms. Consequently, the flow of information can be controlled, directed, and reversed over long times by engineering a wide variety of reservoirs that includes and continuously departs from the Ohmic-like structure at low frequencies. Non-Markovianity and recoherence appear according to the same rules along with the backflow of information.