Non-Markovian giant-atom dynamics in a disordered lattice

Abstract

While ideal lattice models have been widely used to study giant-atom systems, fabrication-induced defects inevitably introduce disorder in realistic platforms. Here, we study non-Markovian dynamics of a giant atom coupled to a discrete photonic lattice with on-site frequency disorder. Using time-domain and spectral analyses, we show that the overall population-decay envelope and global photon-transport patterns remain robust against moderate lattice disorder, while the quantified non-Markovian memory can be significantly enhanced within the explored disorder range. We characterize the memory using a normalized geometrical non-Markovianity measure tailored to delayed giant-atom feedback and demonstrate how the coupling-point separation and the disorder strength serve as complementary parameters that shape the delay timescale and the complexity of coherent-feedback interference. Spectral analysis reveals that scattering-band transport is relatively insensitive to disorder, whereas disorder-sensitive bound-state branches and localization features reshape revival windows and promote information backflow. Our results establish a disorder-aware framework for understanding and engineering non-Markovian feedback effects of giant atoms in structured reservoirs.

Figures (5)

• Figure 1: Schematic configuration for a discrete lattice coupled to a giant atom at the $m$ site and $n$ site.
• Figure 2: (a) Evolution of the excited-state population $|C_e(t)|^2$ and (c) non-Markovianity measure $N$ for a giant atom with coupling points at $m=99$ site and $n=102$ site. (b) Evolution of the excited-state population $|C_e(t)|^2$ and (d) non-Markovianity measure $N$ for a giant atom with coupling points at $m=83$ site and $n=118$ site. The red, purple, and green solid curves correspond to disorder parameters $\delta=0$, $\delta \in [-0.005,0.005]$, and $\delta \in [-0.02,0.02]$, respectively. The insets in (a) and (b) show enlarged views that allow the three curves to be distinguished more clearly. Other parameters are $\omega_{0}=2J$, $\omega_{e}=2J$, and $g_{m}=g_{n}=0.35J$.
• Figure 3: (a) and (c) Evolution of the excited-state population $|C_e(t)|^2$ in an ordered lattice ($\delta = 0$) for different coupling-point separations $|m - n|$. (b) and (d) Evolution of $|C_e(t)|^2$ in a disordered lattice with $\delta \in [-0.02,0.02]$ for different $|m - n|$. (e) and (g) Evolution of the photon population at site $j$ in an ordered lattice ($\delta = 0$). (f),(h) Time evolution of the photon population at site $j$ in a disordered lattice with $\delta \in [-0.02,0.02]$. The coupling points are $m=99$ and $n=102$ in (e) and (f), while they are $m=83$ and $n=118$ in (g) and (h). Other parameters are the same as in Fig. \ref{['F2']}.
• Figure 4: (a) and (b) Dynamical evolution of the photon state in the ordered lattice ($\delta = 0$). (c) and (d) Dynamical evolution of the photon state in the disordered lattice ($\delta \in [-0.02,0.02]$). Here, $m=99$ and $n=102$ in (a) and (c), and $m=83$ and $n=118$ in (b) and (d). Other parameters are the same as in Fig. \ref{['F2']}.
• Figure 5: (a) and (b) Energy spectrum as a function of detuning $\Delta = \omega_{0} - \omega_{e}$. (c) and (d) Energy spectrum as a function of hopping strength $J$. (e) and (f) Energy spectrum as a function of coupling strength $g$. (g) and (h) Energy spectrum as a function of coupling strength $g$ with $\omega_{0} = 2J$ and $\omega_{e} = 5J$. Here, $\delta = 0$ for (a), (c), (e), and (g), and $\delta \in [-0.02,0.02]$ for (b), (d), (f), and (h). Here, $m=99$ and $n=102$, and other parameters are the same as in Fig. \ref{['F2']}.