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

Inverse optimal transport

Discrete optimal transportation problems arise in various contexts in engineering, the sciences and the social sciences. Often the underlying cost criterion is unknown, or only partly known, and the observed optimal solutions are corrupted by noise. In this paper we propose a systematic approach to infer unknown costs from noisy observations of optimal transportation plans. The algorithm requires only the ability to solve the forward optimal transport problem, which is a linear program, and to generate random numbers. It has a Bayesian interpretation, and may also be viewed as a form of stochastic optimization. We illustrate the developed methodologies using the example of international migration flows. Reported migration flow data captures (noisily) the number of individuals moving from one country to another in a given period of time. It can be interpreted as a noisy observation of an optimal transportation map, with costs related to the geographical position of countries. We use a graph-based formulation of the problem, with countries at the nodes of graphs and non-zero weighted adjacencies only on edges between countries which share a border. We use the proposed algorithm to estimate the weights, which represent cost of transition, and to quantify uncertainty in these weights

Fast shuttling of a trapped ion in the presence of noise

We theoretically investigate the motional excitation of a single ion caused by spring-constant and position uctuations of a harmonic trap during trap shuttling processes. A detailed study of the sensitivity on noise for several transport protocols and noise spectra is provided. The effect of slow spring-constant drifts is also analyzed. Trap trajectories that minimize the excitation are designed combining invariant-based inverse engineering, perturbation theory, and optimal control

Trapped-ion quantum simulation of excitation transport: disordered, noisy, and long-range connected quantum networks

The transport of excitations governs fundamental properties of matter. Particularly rich physics emerges in the interplay between disorder and environmental noise, even in small systems such as photosynthetic biomolecules. Counterintuitively, noise can enhance coherent quantum transport, which has been proposed as a mechanism behind the high transport efficiencies observed in photosynthetic complexes. This effect has been called "environmental-assisted quantum transport" (ENAQT). Here, we propose a quantum simulation of the excitation transport in an open quantum network, taking advantage of the high controllability of current trapped-ion experiments. Our scheme allows for the controlled study of various different aspects of the excitation transfer, ranging from the influence of static disorder and interaction range, over the effect of Markovian and non-Markovian dephasing, to the impact of a continuous insertion of excitations. Our proposal discusses experimental error sources and realistic parameters, showing that it can be implemented in state-of-the-art ion-chain experiments.Comment: 14 pages, 11 figure

Coherent quantum transport in disordered systems I: The influence of dephasing on the transport properties and absorption spectra on one-dimensional systems

Excitonic transport in static disordered one dimensional systems is studied in the presence of thermal fluctuations that are described by the Haken-Strobl-Reineker model. For short times, non-diffusive behavior is observed that can be characterized as the free-particle dynamics in the Anderson localized system. Over longer time scales, the environment-induced dephasing is sufficient to overcome the Anderson localization caused by the disorder and allow for transport to occur which is always seen to be diffusive. In the limiting regimes of weak and strong dephasing quantum master equations are developed, and their respective scaling relations imply the existence of a maximum in the diffusion constant as a function of the dephasing rate that is confirmed numerically. In the weak dephasing regime, it is demonstrated that the diffusion constant is proportional to the square of the localization length which leads to a significant enhancement of the transport rate over the classical prediction. Finally, the influence of noise and disorder on the absorption spectrum is presented and its relationship to the transport properties is discussed.Comment: 23 pages, 7 figure