Delocalized Excitation Transfer in Open Quantum Systems with Long-Range Interactions

TL;DR

Delocalized excitation transfer in open quantum systems with long-range interactions investigates how coherence and dissipation shape vibronic excitation transfer in a Frenkel exciton model with long-range couplings $J_{ij}=J/d_{ij}^p$ ($p\approx 1$) to a damped collective bosonic mode. The authors analyze a two-monomer donor–acceptor system in perturbative and non-perturbative regimes, derive a Fermi golden rule expression with Franck-Condon factors, and show that delocalized triplet donor states maximize transfer while preserving entanglement; they also study static disorder, white noise, and finite temperature and extend to larger monomers. An experimental trapped-ion implementation is outlined, mapping electronic sites to qubits and vibronic modes to collective motional modes, with a detailed parameter map for realizing the model. The results provide design principles for light-harvesting materials and demonstrate a feasible analog quantum simulation platform for vibronic transport in non-perturbative regimes where classical simulation is resource-intensive.

Abstract

The interplay between coherence and system-environment interactions is at the basis of a wide range of phenomena, from quantum information processing to charge and energy transfer in molecular systems, biomolecules, and photochemical materials. In this work, we use a Frenkel exciton model with long-range interacting qubits coupled to a damped collective bosonic mode to investigate vibrationally assisted transfer processes in donor-acceptor systems featuring internal substructures analogous to light-harvesting complexes. We find that certain delocalized excitonic states maximize the transfer rate and that the entanglement is preserved during the dissipative transfer over a wide range of parameters. We investigate the reduction in transfer caused by static disorder, white noise, and finite temperature and study how transfer efficiency scales as a function of the number of dimerized monomers and the component number of each monomer, finding which excitonic states lead to optimal transfer. Finally, we provide a realistic experimental setting to realize this model in analog trapped-ion quantum simulators. Analog quantum simulation of systems comprising many and increasingly complex monomers could offer valuable insights into the design of light-harvesting materials, particularly in the non-perturbative intermediate parameter regime examined in this study, where classical simulation methods are resource-intensive.

Figures (10)

• Figure 1: Model and trapped-ion implementation:(a) A chain of 4 qubit ions and 2 coolants can realize the Frenkel exciton model (see main text). The red (blue) ions on the sides represent donor and acceptor monomers, respectively, and the information in each ion is encoded in a qubit. The two cyan ions in the middle represent the cooling ions used for the sympathetic cooling of the ion chain motion. (b) Pictorial representation of the spectrum of the total Hamiltonian in the symmetric case, described by Eqs. \ref{['H0J']} and \ref{['HperTS']}. Donor (red) and acceptor (blue) surfaces are shown as a function of the normalized reaction coordinate $y/y_0=1/2(a^\dag+a)$ with their respective non-interacting harmonic wavefunctions. The effect of the bath is illustrated by the cyan wavy arrows that represent the relaxation with rate $\gamma$. The qubits in the donor/acceptor sites are strongly coupled and can be described in terms of local triplet and singlet states $|T_{D,A}\rangle,|S_{D,A}\rangle$ separated by an energy $2J$. These states are, in turn, coupled by inter-monomer couplings $J_{AB}$, where $AB=TT,ST,SS$ (see main text). The inter-monomer couplings $J_{AB}$ induce anti-crossings between the two surfaces allowing the donor to acceptor transfer.
• Figure 2: Excitation transfer: Transfer rate $k_T$ in the perturbative ((a) and (b)) and non-perturbative regimes ((c) and (d)). (a) Transfer rate $k_T$ as a function of $\epsilon$ in the perturbative regime ($J,\gamma \ll \omega$) for the different initial states $\vert T_D \rangle$ (T), $\vert S_A \rangle$ (S), and $\vert 2 \rangle$ (P). The black solid line represents the transfer predicted for initial state $\vert T_D \rangle$ using the Fermi Golden Rule $k_T^{\rm FGR}$. Note that we defined $\tilde{k}_{T}^{\rm FGR}=\frac{1}{5}k_{T}^{\rm FGR}$ where we rescale by a factor of $\frac{1}{5}$ to display it clearly in the same plot. (b) Dynamics at the highest resonances of (a). Solid lines represent the population in the donor sites $P_D$, while the x-markers illustrate the behavior of $1-P_{T_A}$ with $P_{T_A}$ being the population of $\vert T_A \rangle$. All curves correspond to the initial state $\vert T_D \rangle$. The parameters for (a) and (b) not specified in the plots are $g=\omega$, $J = 0.03 \omega$, $\gamma=0.015 \omega$, $p=1$, and $\bar{n}=0.01$. (c) Transfer rate $k_T$ as a function of $\epsilon$ in the non-perturbative regime $(J\sim \lambda)$ for different initial conditions and parameter values. The parameter sets of data points marked by stars are analyzed further in panel (d). (d) Dynamics of the donor population for the parameters signaled by stars in (c). Solid lines and x-markers are defined as in (b). The parameters for (c) and (d) not specified in the plots are $g=\omega$, $J = 0.3 \omega$, $p=1$, and $\bar{n}=0.01$.
• Figure 3: Optimal transfer and static disorder: (a) The transfer rate as a function of $J_{TT}/\gamma$ is presented for different parameter conditions. $J$ is kept fixed for each plot and $\gamma$ is varied. The reference parameter set (REF in the legend) corresponds to $J=0.3\omega$, $p=1$, $g=\omega$, $\epsilon=3\omega$, and $\bar{n}=0.01$. For all other curves, one of these parameters is modified, as indicated in the legend, while all others remain the same. Four $\gamma$ values are chosen for further analysis (see Table \ref{['table:parameter sets']} for the exact values of $\gamma$). These parameter sets are labeled as $p_1$, $p_2$, $p_3$, and $p_4$, corresponding to the square, circle, diamond, and triangle markers, respectively. The horizontal dashed line is used to illustrate that $p_2$, $p_3$, and $p_4$ yield almost identical transfer rates. (b) Transfer rate as a function of the standard deviation of the static disorder in the $g_j$ couplings. $k_T*$ represents the transfer value without disorder. Each data point is the average over one hundred disorder realizations, and error bars represent the 25th and 75th percentiles. (c) Same as in (b) but for disordered on-site energies $\epsilon_j$. (d) Transfer rate as a function of the dephasing rate $\gamma_d$. $k_T*$ represents the transfer rate value without noise. All markers and colors are defined as in (b) and (c).
• Figure 4: Effects of temperature: (a) Transfer rate $k_T$ as a function of $\epsilon$ in the for different values of $\bar{n}$. All other parameters are defined as in parameter set $p_1$ (see Table \ref{['table:parameter sets']}) for this and subsequent panels. (b) Schematics of the triplet-triplet transfer for a thermal state. An initial thermal state with electronic state $\vert T_D\rangle$ gets coupled to the acceptor states through the coherent coupling $J_{TT}$. Coherent evolution and dissipative dynamics ($\gamma$) produce a thermal distribution in the acceptor site in the steady state. A portion of the population remains trapped in the acceptor, while the rest remains coherently coupled to some donor states. The ratio of these two populations depends on the value of $\bar{n}$. (c) Population of the donor as a function of time for different temperatures. x-markers denote 1-$P_{T_A}$. Here $\epsilon=3\omega$. (d) Transfer rate $k_T$ and equilibration rate $\Gamma$ as a function of temperature. Open markers denote $k_T/k_T*$ while filled markers denote $\Gamma/\Gamma*$, with $k_T*$ and $\Gamma*$ being the rates at zero temperature. The error bars for filled markers denote the 95% confidence intervals of the exponential fit. Different colors signal different values of $\epsilon/\omega$.
• Figure 5: Higher complexity monomer structures: (a) Transfer rate as a function of the number of qubits per monomer ($L$). The inset shows a schematic representation of how more two-level systems are incorporated in each monomer. The solid line connects results for an initial $\vert W_D\rangle$ electronic state while a dashed line is used for an initial $\vert \mathcal{E}^1_D\rangle$ state. Lines are only a guide for the eye. (b) Population dynamics for the case of five qubits per monomer. Dashed lines represent results for $\vert \mathcal{E}^1_D\rangle$ as the initial electronic state, while solid lines are used when $\vert W_D\rangle$ is taken as the initial state. Orange, pink, and purple are used to signal the population of the donor sites, acceptor sites, and the W state in the acceptor $\vert W_A\rangle$, respectively. (c) Transfer rate $k_T$ as a function of the number of qubits ($N$), where the number of monomers, in this case, is given by $N/2$. The inset shows a schematic representation of how more monomers are incorporated into the system. Orange circles denote the simulation of the full Hamiltonian, while pink diamonds represent the simulation considering only the coupling between nearest-neighboring sites (see main text). Dashed and solid lines connecting markers are a guide for the eye. (d) Population dynamics for the case of five monomers. The population of the donor and the acceptor are identified by orange and purple solid lines, respectively, while the population of the three intermediate states $P_{I_1}$, $P_{I_2}$, and $P_{I_3}$ (second to fourth monomers) are indicated by different broken lines. $\vert T_D\rangle$ is the initial state for all results in panels (c) and (d). For all panels, we consider the parameter values of the parameter set $p_1$ (see Table \ref{['table:parameter sets']}).