vs time is shown for a fully connected graph of nodes with for , . At one excitation is in the site 1 and the energy transfer evolves according to the quantum dynamics investigated in the text. The cases of an energy mismatch, i.e., (red line), a dephasing mismatch, i.e., , (green line), and the basic case (black line) are shown. For the latter, the population in the sink asymptotically reaches . Note that both the red and the green lines reach unit transfer asymptotically, but at considerably different rates.
A fully connected three-site network. In (a) the excitation wave function is delocalized over two sites (red and green) with equal probability of being found at either site. However, as the wave function is antisymmetric with respect to the interchange of red and green, this state has no overlap with the dissipative site (blue) due to the destructive interference of the tunneling amplitudes from each site in the superposition. The network can therefore store an excitation in this state indefinitely. In (b) pure dephasing causes the loss of this phase coherence and the two amplitudes no longer cancel, leading to total transfer of the excitation to the sink. An equivalent visualization based on the Mach–Zehnder interferometer is presented in Appendix B.
Dependence of at a fixed time as a function of , in the case of , , and . The initially sharp rise is due to the increasing rapidity at which the invariant subspace is destroyed, while the decreasing part is due to quantum Zeno effects.
Population of the sink as a function of time for increasing dephasing rates , in the case of . For short times, the system dynamics are identical to the case of zero dephasing, and for very weak dephasing a significant fraction of the excitation can be trapped in invariant subspace for a time of approximately .
Transport in a classical ladderlike system of sites, with steps of unit size , with a dissipation term (with rate ) into a sink, connected to the site 7. The energy levels fluctuate with a Lorentzian distribution (with width 1) to take into account line broadening effects and a symmetric hopping rate given by between the sites and and (red line), while also the noiseless case is shown (black line). An exactly similar effect is observed when the sink is placed at the bottom of the ladder, and the excitation starts from the top. This is because of the symmetry of the rates, i.e., . Inset: Pdf distribution for for over a sample of instances in both hopping scenarios. Notice that it is very narrow around the central value. In both cases, it is clearly shown that line broadening dramatically enhances the transport.
Left: Due to energy fluctuations, dephasing leads to a broadening of energy levels and hence increased overlap between sites. Right: Viewing these fluctuations dynamically, one finds that the energy gap between levels varies in time. A nonlinear dependence of the transfer rate on the energy gap may therefore lead to an enhancement of the average transfer rate in the presence of dephasing noise.
vs time (in picosecond) for the FMO complex. We show the noiseless case (black line) and the transfer for optimal dephasing (red line). The optimal dephasing values are given by . The inset shows the very narrow probability distribution of transfer probabilities at from samples, in the case of optimal dephasing but with a 20% static disorder in energy and coupling rates. This suggests that dephasing assisted enhanced transport is also robust against variations in the system parameters.
Entanglement, as quantified by the logarithmic negativity (Ref. 44) across different bipartitions, as specified in the inset, for optimized local dephasing rates at each site. The curves are for the 6 splits of the form vs , with , of the FMO complex sites. Under the action of local dephasing, entanglement in our model persists up to 1 ps and therefore quantum correlations are dissipated well before the excitation transfer (yellow line) is completed.
(a) A single photon entering a balanced Mach–Zehnder interferometer will always emerge in one output port as the path to the upper detector is blocked by destructive interference. (b) If the interferometer is unbalanced, as a result of a noisy process, the condition for destructive interference is inhibited and photodetections are observed in both ports. Thus, noise may open additional paths for propagation.
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