Diffusive lossless energy and coherence transfer by noisy coupling

Abstract

Here we show that noisy coupling can lead to diffusive lossless energy transfer between individual quantum systems retaining a quantum character leading to entangled stationary states. Coherence might flow diffusively while being summarily preserved even when energy exchange is absent. Diffusive dynamics persists even in the case when additional noise suppresses all the unitary excitation exchange: arbitrarily strong local dephasing, while destroying quantum correlations, is not affecting energy transfer. IntroductionDiffusive transfer of energy (and, ultimately, derivation of Fourier heat-transfer law from microscopic dynamics) up to day remain subjects of theoretical interest and even controversy [1][2][3][4][5]. For microscopic dynamics dominated by quantum effects establishing of diffusive energy transfer is far from being obvious. Commonly considered microscopic models, such as chains of unitarily connected networks of bosonic and/or fermionic systems with attached thermal reservoirs and noise sources can demonstrate both ballistic and diffusive behavior in dependence on interaction strengths and other parameters of the whole system, generally requiring approximations (such as long time and large size limits) for emergence of classical-like heat dynamics. Here we suggest a noise-mediated microscopic mechanism for diffusive transfer. Energy can propagate without loss, but through losses. Recently it has become quite usual to see noises not only as something destroying quantum coherence and reducing quantum states to classicality, but also as a tool to create and enhance quantumness. Non-local loss can preserve entanglement and even generate entangled stated from initially uncorrelated ones [6][7][8][9][10]. Engineered loss can lead to dissipative protection and coherence preservation [11][12][13] and deterministic creation of non-classical states [14,[17][18][19][20] and serve as a tool for quantum computing [15,16]. Networks of dissipatively coupled systems can support topologically protected states [21]. Even a pure local dephasing is no longer considered completely harmful: it can enhance quantum state transfer and suppress localizing effects of static disorder [22][23][24]. However, too strong local dephasing generally suppresses unitary excitation exchange and energy transfer stemming from it.Here we show a microscopic mechanism of diffusive lossless energy transfer, which is impervious to local dephasing. It arises when coupling constants describing common single-excitation hopping are fluctuating randomly, like it is, for example, with spin-spin dipolar coupling in random environments. Dynamics produced by fluctuating coupling might preserve certain quantum correlations, and even entanglement during evolution toward the stationary state. Populations are not coupled by the dynamics with the off-diagonal terms. So, for example,

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