Light with Tunable Non-Markovian Phase Imprint

Abstract

We introduce a simple and flexible method to generate spatially non-Markovian light with tunable coherence properties in one and two dimensions. The unusual behavior of this light is demonstrated experimentally by probing the far field and by recording its diffraction pattern after a double slit: In both cases we observe, instead of a central intensity maximum, a line-or cross-shaped dark region, whose width and profile depend on the non-Markovian coherence properties. Because these properties can be controlled and easily reproduced in experiment, the presented approach lends itself to serving as a test bed to study and gain a deeper understanding of non-Markovian processes. DOI: 10.1103/PhysRevLett.115.073901 PACS numbers: 42.25.Fx, 03.65.Yz, 42.30.Kq, 42.50.Ar In nature, non-Markovian processes are far more common than Markovian ones; however, scientists often prefer to describe the behavior of nature with Markovian models. This might be the case because Markovian models are easier to build, and it is significantly easier to combine them when constructing more complex models. Recently, however, there has been increasing interest in understanding the specific impact of non-Markovian behavior on chemical and biological processes such as electron transfer [1], the kinetics of protein folding [2], or the ion transport through membranes [3], to name but a few. In optics, the radiation dynamics in photonic crystals [4], optical gain in quantumwell lasers [5], and dephasing processes in coupled quantum-dot cavities [6] have been experimentally observed to be governed by non-Markovian behavior. Characterizing non-Markovian evolutions of quantum properties at the loss of entanglement has become the center of extensive theoretical and experimental efforts [7,8]; it is hoped that this will pave the way for better read-out mechanisms in quantum computing [9] or even controlled generation of entangled states [10]. Such quantum phenomena, or their application in logical circuits [11], are often studied using optical means [7,8]. Furthermore, the recent suggestion to initialize controlled quantum states by "optical pumping" [10] opens exciting possibilities for shaping desired quantum properties, including designed non-Markovian characteristics, in the optical regime and then transferring them to other physical systems [12,13].Non-Markovian light, which might serve as an effective tool towards these objectives, has been previously generated by overlaying a light beam with a delayed copy or echo of itself [14]. An alternative approach employs a micromechanical oscillator as a mirror in order to obtain non-Markovian properties from its Brownian movements [15]. The two methods result in light with non-Markovian properties in the time domain; they offer only a limited degree of control and practically no repeatability if the exact same conditions need to be reproduced. In this Letter we, therefore, introduce and experimentally demonstrate a technique to create spatially non-Markovian light to overcome these limitations. By u...

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“…1(d). To generate correlated random phases, we use a variation of a two-dimensional scheme of input phases proposed to investigate diffraction patterns of non-Markovian light [57] and recently used to investigate rogue waves generation in linear and nonlinear media [58]. We start a correlated phase sequence by taking a random permutation of the L distinct phases.…”

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“…Such a set would result, for example, from drawing distinct balls from a sac without replacing them, so that the outcome of each draw depends on all previous draws. In order to produce a two-dimensional phase pattern that would be non-Markovian on the one hand, and uniformly distributed within the range [−π, π] on the other hand, we followed the procedure described by Fischer et al 36 and illustrated in Fig. 1.…”

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