Shaping Dynamics Through Memory: A Study of Reservoir Profiles in Open Quantum Systems

TL;DR

This work analyzes how three representative reservoir memory profiles—Lorentzian, Gaussian, and Uniform—shape the non-Markovian dynamics of a single-mode waveguide coupled to an environment. By solving the system with a memory-kernel formalism and computing transmission, transparency, and information backflow via the BLP measure, the authors reveal distinct memory-induced transport signatures: Uniform reservoirs exhibit the strongest non-Markovian revivals, Lorentzian reservoirs resemble single pseudo-modes and tend toward Markovian decay, while Gaussian reservoirs provide an intermediate, controllable regime. The study connects spectral density features to observable transport properties and demonstrates a memory-hierarchy useful for reservoir engineering in photonic systems. These insights have implications for designing devices that leverage or suppress memory effects to control light transport and coherence.

Abstract

In this work, we investigate how different reservoir memory profiles influence the dynamical evolution of a single waveguide coupled to an external environment. We compare three representative memory kernels: Lorentzian, Gaussian and Uniform, highlighting their distinct spatial correlations and their impact on system behavior. We compute the transmission amplitude, transparency properties, as well as long-time behavior of the system under each memory model. To quantify deviations from Markovian dynamics, we employ a non-Markovianity measure based on information backflow, allowing a direct comparison between the structured reservoirs and the Markovian limit. Our results reveal clear signatures of memoryless-induced modifications in the transmission spectrum and demonstrate how specific reservoir profiles enhance or suppress non-Markovian effects.

Figures (5)

• Figure 1: G-waveguide coupled to an environment by a parameter $\alpha$ that can exhibit different mode distributions with a fixed width $\gamma$.
• Figure 2: Transmission with $\gamma=2\alpha$ for three reservoirs highlighted with a solid line and the Hermitian situation where $\gamma=0$ with a dashed line.
• Figure 3: function $|f|$ on a logarithmic scale with $\gamma = 10\alpha$ for each reservoir, with the addition of points indicating Markovian decays for comparative purposes.
• Figure 4: Transmission to the three registers as a function of $\gamma/\alpha$ with $\alpha z=\pi/4,\,\pi/2,\,3\pi/4,\,\pi$.
• Figure 5: BLP measurement curves for comparative evaluation of memory between three reservoirs.