Spectral signatures of the Markovian to Non-Markovian transition in open quantum systems

TL;DR

This work addresses how memory effects in open quantum systems manifest as Markovian to non-Markovian transitions in molecular aggregates. It develops a Laplace-domain hierarchy of equations (HOPS) to compute the linear absorption spectrum F(ω) = Re[lim_{ε→0} ∑_{nm} μ_n μ_m ilde{C}_{nm}(s)], connecting spectral features to bath-induced memory through dissipation γ, aggregate-bath coupling g, and intra-aggregate dipole-dipole interactions V. Key contributions include analytic limiting-case results for linear and ring geometries, and a systematic mapping of spectral signatures—peak splitting, merging, and shifts—to non-Markovian dynamics across monomer to tetramer aggregates. The framework provides a practical, geometry-aware tool for probing and controlling non-Markovian effects in quantum materials and devices, with potential extensions to finite temperature and other platforms such as trapped ions or superconducting qubits.

Abstract

We present a new approach for investigating the Markovian to non-Markovian transition in quantum aggregates strongly coupled to a vibrational bath through the analysis of linear absorption spectra. Utilizing hierarchical algebraic equations in the frequency domain, we elucidate how these spectra can effectively reveal transitions between Markovian and non-Markovian regimes, driven by the complex interplay of dissipation, aggregate-bath coupling, and intra-aggregate dipole-dipole interactions. Our results demonstrate that reduced dissipation induces spectral peak splitting, signaling the emergence of bath-induced non-Markovian effects. The spectral peak splitting can also be driven by enhanced dipole-dipole interactions, although the underlying mechanism differs from that of dissipation-induced splitting. Additionally, with an increase in aggregate-bath coupling strength, initially symmetric or asymmetric peaks with varying spectral amplitudes may merge under weak dipole-dipole interactions, whereas strong dipole-dipole interactions are more likely to cause peak splitting. Moreover, we find that spectral features serve as highly sensitive indicators for distinguishing the geometric structures of aggregates, while also unveiling the critical role geometry plays in shaping non-Markovian behavior. This study not only deepens our understanding of the Markovian to non-Markovian transition but also provides a robust framework for optimizing and controlling quantum systems.

Figures (9)

• Figure 1: Illustration of a quantum aggregate system with $N$ two-level monomers, each represented by a sphere with a dipole moment indicated by an arrow. The surrounding blue cloud represents the vibrational bath interacting with each monomer. The insert shows the electronic states for a single monomer, where $|\phi_n^g\rangle$ and $|\phi_n^e\rangle$ denote the ground and excited states, respectively, with an energy separation $\epsilon_n$. The dipoles are coupled through dipole-dipole interactions, influencing the excitation dynamics across the aggregate. A light source on the left excites the system, while the spectrum detector on the right captures the transition dynamics, illustrating the shift from Markovian to non-Markovian regimes.
• Figure 2: (color online) (a) Absorption spectrum $F(\gamma,\omega)$ of a monomer as a function of the dissipation rate $\gamma$. (b) One-dimensional spectra extracted from (a) for specific dissipation rates: $\gamma=0,\,1,\,5$. With the monomer's electronic transition frequency set to $\omega_0=0$, a spectral peak emerges at large $\gamma$ with $\omega \approx \omega_1^{\rm (L)} = 0$, consistent with Eq. (\ref{['eq:1D_eigenvalue']}). For $\gamma = 0$, these peaks are located at $\omega = \omega_1^{\rm (L)} = -1,\,0,1,\,2,\,3,\cdots$. Spectra are presented in units of $\mu^2$. The hierarchy depth is set to 12, with additional parameters $g = 1$ and $\Omega = 1$.
• Figure 3: (color online) (a) Contour plot of the absorption spectrum $F(g, \omega)$ for a monomer as a function of bath coupling strength $g$ and frequency $\omega$. The color scale represents the intensity of the absorption spectrum, with the electronic transition frequency set at $\omega_0 = 0$. (b) One-dimensional spectra extracted from the contour plot for specific values of bath coupling strength: $g = 0$ (green solid line, scaled by 100 for visibility), $g = 1$ (orange dashed line), and $g = 3$ (blue dash-dotted line). The spectra are plotted in units of $\mu^2$. The hierarchy depth is fixed at 12, and other parameters are $\gamma = 0.05$ and $\Omega = 1$, unless otherwise specified.
• Figure 4: (color online) Absorption spectrum $F(\gamma,\omega)$ of a dimer as a function of the dissipation rate $\gamma$, shown for dipole-dipole interaction strengths of (a) $V = 0.1$, (b) $V = 0.5$, and (c) $V = 1$ between two monomers. The spectral peaks at large $\gamma$, consistent with the values predicted by Eq. (\ref{['eq:1D_eigenvalue']}), are located at $\omega \approx \omega_1^{(L)} = 0,\, 0.1,\, 0.5$ for panels (a), (b), and (c), respectively. The hierarchy depth is set to 12, with the angle between the dipoles $\theta = 0$, and a bath coupling strength of $g = 1$. We set $\Omega=1$ as the energy unit. All other parameters are consistent with those used in Fig. \ref{['fig:fig_monomer']}.
• Figure 5: (color online) Absorption spectrum $F(g, \omega)$ of a dimer as a function of bath coupling strength $g$, shown for dipole-dipole interaction strengths of (a) $V = 0.1$, (b) $V = 0.5$, and (c) $V = 1$ between two monomers. The anti-crossing in (c) appears near $(\omega, g) \simeq (0.9, 0.7)$, with dashed curves offering clear visual guidance. The logarithmic color scale highlights the absorption intensity across the frequency range $\omega$, with the energy unit normalized to $\Omega = 1$. The transition frequency is fixed at $\omega_0 = 0$. Other parameters, including the damping rate $\gamma = 0.05$ and hierarchy depth of 12, are consistent with those used in Fig. \ref{['fig:fig_monomer_coupling']}.