# Sequences of information backflow in local dephasing channels with spectral gaps

## TL;DR

This paper investigates how spectral gaps in structured reservoirs cause periodic and controllable sequences of information backflow in local dephasing channels, revealing long-term non-Markovian dynamics.

## Contribution

It analytically characterizes the regularity and timing of information backflow intervals caused by spectral gaps in structured reservoirs.

## Key findings

- Spectral gaps induce infinite sequences of information backflow intervals.
- Backflow intervals become regular and tend to a fixed length over long times.
- Reservoir engineering can control non-Markovian dynamics and recoherence.

## Abstract

The flow of quantum information in local dephasing channels is analyzed over short and long times in case the structured reservoirs of frequency modes exhibit a spectral gap in the density of modes over low frequencies. The presence of the low-frequency gap with upper cut-off frequency $\omega_g$ produces over the time scale $1/\omega_g$ an infinite sequence of time intervals over which information backflow appears. Such time intervals are generally irregular but, under certain conditions, exhibit the following bounds: the $n$th backflow has certainly started at the instant $\pi \left(1+2(n-1)\right)/\omega_g$, and certainly ended at the instant $2\pi n/\omega_g$, for every $n=1,2,\ldots$. The intervals become regular over long times, tend to the asymptotic length $\pi/\omega_g$ as supremum value, and are described analytically in terms of the structure of the spectral density near the cut-off frequency. Consequently, engineering structured reservoirs of frequency modes with low-frequency spectral gaps produces in local dephasing channels regular and controllable sequences of information backflow and recoherence over long times, along with non-Markovian evolution.