Optimal efficiency of quantum transport in a disordered trimer

Disordered quantum networks, as those describing light-harvesting complexes, are often characterized by the presence of peripheral ring-like structures, where the excitation is initialized, and inner reaction centers (RC), where the excitation is trapped. The peripheral rings display coherent features: their eigenstates can be separated in the two classes of superradiant and subradiant states. Both are important to optimize transfer efficiency. In the absence of disorder, superradiant states have an enhanced coupling strength to the RC, while the subradiant ones are basically decoupled from it. Static on-site disorder induces a coupling between subradiant and superradiant states, creating an indirect coupling to the RC. The problem of finding the optimal transfer conditions, as a function of both the RC energy and the disorder strength, is very complex even in the simplest network, namely a three-level system. In this paper we analyze such trimeric structure choosing as initial condition a subradiant state, rather than the more common choice of an excitation localized on a site. We show that, while the optimal disorder is of the order of the superradiant coupling, the optimal detuning between the initial state and the RC energy strongly depends on system parameters: when the superradiant coupling is much larger than the energy gap between the superradiant and the subradiant levels, optimal transfer occurs if the RC energy is at resonance with the subradiant initial state, whereas we find an optimal RC energy at resonance with a virtual dressed state when the superradiant coupling is smaller than or comparable with the gap. The presence of dynamical noise, which induces dephasing and decoherence, affects the resonance structure of energy transfer producing an additional 'incoherent' resonance peak, which corresponds to the RC energy being equal to the energy of the superradiant state.Comment: This article shares part of the introduction and most of Section II with arXiv:1508.01613, the remaining parts of the two articles treat different problem

Optimal Dephasing for Ballistic Energy Transfer in Disordered Linear Chains

We study the interplay between dephasing, disorder, and openness on transport efficiency in a one-dimensional chain of finite length $N$, and in particular the beneficial or detrimental effect of dephasing on transport. The excitation moves along the chain by coherent nearest-neighbor hopping $\Omega$, under the action of static disorder $W$ and dephasing $\gamma$. The system is open due to the coupling of the last site with an external acceptor system (sink), where the excitation can be trapped with a rate $\Gamma_{\rm trap}$, which determines the opening strength. While it is known that dephasing can help transport in the localized regime, here we show that dephasing can enhance energy transfer even in the ballistic regime. Specifically, in the localized regime we recover previous results, where the optimal dephasing is independent of the chain length and proportional to $W$ or $W^2/\Omega$. In the ballistic regime, the optimal dephasing decreases as $1/N$ or $1/\sqrt{N}$ respectively for weak and moderate static disorder. When focusing on the excitation starting at the beginning of the chain, dephasing can help excitation transfer only above a critical value of disorder $W^{\rm cr}$, which strongly depends on the opening strength $\Gamma_{\rm trap}$. Analytic solutions are obtained for short chains.Comment: 16 pages, inlcuding 9 figure

Non-Hermitian Hamiltonian approach to quantum transport in disordered networks with sinks: validity and effectiveness

We investigate the validity of the non-Hermitian Hamiltonian approach in describing quantum transport in disordered tight-binding networks connected to external environments, acting as sinks. Usually, non-Hermitian terms are added, on a phenomenological basis, to such networks to summarize the effects of the coupling to the sinks. Here we consider a paradigmatic model of open quantum network for which we derive a non-Hermitian effective model, discussing its limit of validity by a comparison with the analysis of the full Hermitian model. Specifically, we consider a ring of sites connected to a central one-dimensional lead. The lead acts as a sink which absorbs the excitation initially present in the ring. The coupling strength to the lead controls the opening of the ring system. This model has been widely discussed in literature in the context of light-harvesting systems. We analyze the effectiveness of the non-Hermitian description both in absence and in presence of static disorder on the ring. In both cases, the non-Hermitian model is valid when the energy range determined by the eigenvalues of the ring Hamiltonian is smaller than the energy band in the lead. Under such condition, we show that results about the interplay of opening and disorder, previously obtained within the non-Hermitian Hamiltonian approach, remain valid when the full Hermitian model in presence of disorder is considered. The results of our analysis can be extended to generic networks with sinks, leading to the conclusion that the non-Hermitian approach is valid when the energy dependence of the coupling to the external environments is sufficiently smooth in the energy range spanned by the eigenstates of the network.Comment: Final version, 20 pages, 15 figure

Interplay of different environments in open quantum systems: Breakdown of the additive approximation

We analyze an open quantum system under the influence of more than one environment: a dephasing bath and a probability-absorbing bath that represents a decay channel, as encountered in many models of quantum networks. In our case, dephasing is modeled by random fluctuations of the site energies, while the absorbing bath is modeled with an external lead attached to the system. We analyze under which conditions the effects of the two baths can enter additively the quantum master equation. When such additivity is legitimate, the reduced master equation corresponds to the evolution generated by an effective non-Hermitian Hamiltonian and a Haken-Strobl dephasing super-operator. We find that the additive decomposition is a good approximation when the strength of dephasing is small compared to the bandwidth of the probability-absorbing bath

Enhanced robustness and dimensional crossover of superradiance in cuboidal nanocrystal superlattices

Cooperative emission of coherent radiation from multiple emitters (known as superradiance) has been predicted and observed in various physical systems, most recently in CsPbBr$_3$ nanocrystal superlattices. Superradiant emission is coherent and occurs on timescales faster than the emission from isolated nanocrystals. Theory predicts cooperative emission being faster by a factor of up to the number of nanocrystals ($N$). However, superradiance is strongly suppressed due to the presence of energetic disorder, stemming from nanocrystal size variations and thermal decoherence. Here, we analyze superradiance from superlattices of different dimensionalities (1D, 2D and 3D) with variable nanocrystal aspect ratios. We predict as much as a thirty-fold enhancement in robustness against realistic values of energetic disorder in three-dimensional (3D) superlattices composed of cuboid-shaped, as opposed to cube-shaped, nanocrystals. Superradiance from small $(N\lesssim 10^3)$ two-dimensional (2D) superlattices is up to 10 times more robust to static disorder and up to twice as robust to thermal decoherence than three-dimensional (3D) superlattices with the same $N$. As the number of $N$ increases, a crossover in the robustness of superradiance occurs from 2D to 3D superlattices. For large $N\ (> 10^3)$, the robustness in 3D superlattices increases with $N$, showing cooperative robustness to disorder. This opens the possibility of observing superradiance even at room temperature in large 3D superlattices, if nanocrystal size fluctuations can be kept small