Operational bounds and diagnostics for coherence in energy transfer

Abstract

Excitation energy transfer in light-harvesting aggregates is highly efficient, yet whether quantum coherence plays an operational role in transport remains debated. A central challenge is that coherence is usually inferred from spectroscopic signatures, whereas transport performance is assessed through specific observables and depends on both the open system dynamics and the initial state preparation. Here we develop a resource theoretic approach that quantifies the maximum change that initial site-basis coherence can induce in a chosen readout under fixed reduced dynamics. The central quantity is the resource impact functional, which yields state independent, readout specific bounds on coherence-induced changes in signals and transport figures of merit. We apply the framework to two models. For a donor-acceptor dimer, we analyse coherence sensitivity across coupling and bath-timescale regimes and bound trapping efficiency and average transfer time in terms of the impact functional. For a multi-site chain with terminal trapping, we derive rigorous criteria that distinguish population placement from sensitivity to initial state site-basis coherence. These include upper bounds on the largest advantage over incoherent preparations, necessary delocalization requirements for achieving a prescribed improvement, and a simple pairwise sufficient condition that can be checked from local information. For quasi-local reduced dynamics, we further obtain a Lieb-Robinson-type bound that constrains when coherence prepared in a distant region can influence a localized readout at finite times. Together, these results provide operational diagnostics and rigorous bounds for benchmarking coherence effects and for identifying regimes in which they are necessarily negligible or potentially relevant in excitonic transport models.

Figures (8)

• Figure 1: Donor-acceptor dimer with recombination to the joint ground state and an absorbing sink attached to the acceptor. The donor and acceptor are additionally coupled to site-local bosonic environments (not shown).
• Figure 2: Comparison between the donor population $\rho_{DD}(t)$ and $\mathcal{C}_{|A\rangle\!\langle A|}(\Lambda_t)$ for $J = 100\,\mathrm{cm}^{-1}$, $\Delta = 100\,\mathrm{cm}^{-1}$ and $T=300\,\mathrm{K}$, comparing a fast-bath setting $\tau_c \ll J^{-1}$ (left, $\tau_c = 2.65\,\mathrm{fs}$) with an intermediate-timescale setting $\tau_c \sim J^{-1}$ (right, $\tau_c = 53.1\,\mathrm{fs}$) for different ratios $J/E_R\in\{10,1,0.2\}$ at fixed $J$.
• Figure 3: Bounds on the coherence-induced change in trapping efficiency for the donor-acceptor dimer. For each initial state $\hbox{$| \Psi_0^{(\pm)} \rangle$}=\tfrac{1}{\sqrt{2}}(\hbox{$| D \rangle$}\pm\hbox{$| A \rangle$})$ and time scale, the upper panels show the efficiency $\eta$, its dephased baseline $\eta^{(\mathrm{free})}=\eta(\mathcal{G}(\rho_0))$, and the bound $\eta^{(\mathrm{free})}+\mathcal{C}_{M_\eta}(\mathrm{id})$. The lower panels illustrates Eq. \ref{['eq:DAM-bound-eta-heom']}. The system parameters are $J=\Delta=100\,\mathrm{cm}^{-1}$, $T=300\,\mathrm{K}$, asymmetric trapping $\kappa_A=1\,\mathrm{ps}^{-1}$, and recombination $\Gamma_A=\Gamma_D=0.1\,\mathrm{ps}^{-1}$. Results are shown for a fast bath ($\tau_c=2.65\,\mathrm{fs}$, $\tau_c\ll J^{-1}$; top row) and an intermediate bath ($\tau_c=53.1\,\mathrm{fs}$, $\tau_c\sim J^{-1}$; bottom row). The horizontal axis is the effective noise scale $\gamma_{\mathrm{eff}}$ obtained from the fast-bath/high-$T$ mapping. In the intermediate-bath regime it is used only as a monotonic parametrization of $E_R$ at fixed $\tau_c$ and $T$ (see text).
• Figure 4: Illustration of the state dependence of the upper bound on the coherence induced change $|\Delta\tau|$ in the average energy transfer time in Eq. \ref{['eq:Dtau-bound-improved-heom']} as a function of $\gamma_\mathrm{eff}$ for the donor-acceptor model with $J = \Delta = 100\,\text{cm}^{-1}$, $T= 300\,\mathrm{K}$, $\kappa_A= 1\,\text{ps}^{-1}$, and $\Gamma_A=\Gamma_D = 0.1\,\text{ps}^{-1}$, and the two initial states $\hbox{$| \Psi_0^{(\pm)} \rangle$} = \tfrac{1}{\sqrt{2}}(\hbox{$| D \rangle$}\pm\hbox{$| A \rangle$})$.
• Figure 5: Schematic of an $N$-site linear chain in the zero- and single-excitation manifold. An excitation can be trapped from site $N$ into an absorbing sink $\hbox{$| s \rangle$}$ at rate $\kappa$, recombine to the global ground state $\hbox{$| g \rangle$}$ at rate $\Gamma$, and undergo site-local pure dephasing at rate $\gamma_{\varphi}$.

Theorems & Definitions (13)

• Theorem 1: Coherence advantage gap bound for trapping
• Corollary 2: Pairwise lower bound and sufficient condition
• Theorem 3: Minimal required initial delocalization
• Corollary 4: Necessary IPR for a $\delta$-improvement
• Theorem 5: Localization of the optimal trapping state
• Theorem 6: Coherence light cone for local readouts
• Corollary 7
• proof
• proof
• proof