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Bulletin of the American Physical Society

An exactly solvable model for decoherence-assisted transport

Adriana Marais, Ilya Sinayskiy, Francesco Petruccione, ARTUR K. EKERT

Published Mar 23, 2011• 0 citations
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The dynamics of a dimer coupled to two different environments, each in a spin star configuration under the influence of decoherence, is studied. The exact analytical expression for the transition probability in the dimer system is obtained for different situations, i.e., independent and correlated environments. In all cases considered, it is shown that there exist well-defined ranges of parameters for which decoherent interaction with the environment assists energy transfer in the dimer system. In particular, we find that correlated environments can assist energy transfer more efficiently than separate baths.
We derive an exact mean nonsink residence time for a resonant three-state donor–bridge–acceptor open quantum system initialized in its Hamiltonian dark state, with local terminal pure dephasing and irreversible loss through the coherent bridge. The residence time has the exact form T(γφ) = A/γφ + B + Cγφ, with analytically determined coefficients, yielding the closed-form optimum γφ,opt = √2 gH/√(c⁴+s⁴). The optimum is exactly independent of the bridge-loss rate, is controlled by the inverse-participation factor of the bright state, and obeys an exact coupling-asymmetry bound. Independent transient-Liouvillian calculations verify the closed form to machine precision over 756 parameter combinations spanning both sides of the bright–bridge exceptional point. The result provides an exactly solvable realization of established environment-assisted quantum transport and mean-first-passage-time turnover frameworks.
In this paper, we report on a detailed study of how decoherence assists quantum transport in a dimer system. By carrying out analytical and numerical computations, we find that the decoherence induced by a Markovian (memoryless) environment only assists the maximum probability of quantum transport in the dimer system to 50% not close to the unity, and the decoherence induced by a non-Markovian environment with perfect memory (infinite memory time) can improve the maximum probability of quantum transport to unity. The combination of non-Markovian decoherence and Markovian decoherence assist the quantum transport more effectively. Comparing the classical environment with the quantum environment, we obtain that the classical non-Markovian environment cannot assist the maximum probability of quantum transport close to unity. In addition, enlarging the quantum environment can improve the maximum probability of quantum transport.