The quantum walk is the quantum analogue of the well-known random walk, which forms the basis for models and applications in many realms of science. Its properties are markedly different from the classical counterpart and might lead to extensive applications in quantum information science. In our experiment, we implemented a quantum walk on the line with single neutral atoms by deterministically delocalizing them over the sites of a one-dimensional spin-dependent optical lattice. With the use of site-resolved fluorescence imaging, the final wave function is characterized by local quantum state tomography, and its spatial coherence is demonstrated. Our system allows the observation of the quantum-to-classical transition and paves the way for applications, such as quantum cellular automata.Interference phenomena with microscopic particles are a direct consequence of their quantum-mechanical wave nature [1,2,3,4,5]. The prospect to fully control quantum properties of atomic systems has stimulated ideas to engineer quantum states that would be useful for applications in quantum information processing, for example, and also would elucidate fundamental questions, such as the quantum-to-classical-transition [6]. A prominent example of state engineering by controlled multipath interference is the quantum walk of a particle [7]. Its classical counterpart, the random walk, is relevant in many aspects of our life providing insight into diverse fields: It forms the basis for algorithms [8], describes diffusion processes in physics or biology [8,9], such as Brownian motion, or has been used as a model for stock market prices [10]. Similarly, the quantum walk is expected to have implications for various fields, for instance, as a primitive for universal quantum computing [11], systematic quantum algorithm engineering [12] or for deepening our understanding of the efficient energy transfer in biomolecules for photosynthesis [13].Quantum walks have been proposed to be observable in several physical systems [12,14,15]. Special realizations have been reported in either the populations of nuclear magnetic resonance samples [16,17]; or in optical systems, in either frequency space of a linear optical resonator [18], with beam splitters [19], or in the continuous tunneling of light fields through waveguide lattices [20]. Recently, a three-step quantum walk in the phase space of trapped ions has been observed [21]. However, the coherent walk of an individual quantum particle with controllable internal states as originally proposed by Feynman [22] has so far not been observed. We present the experimental realization of such a single quantum particle walking in a one-dimensional (1D) lattice in position space. This basic example of a walk provides all of the relevant features necessary to understand the fundamental properties and differences of the quantum and classical regimes. For example, the atomic wave func- * Electronic address: karski@uni-bonn.de † Electronic address: widera@uni-bonn.de tion resulting from a quantum walk exhibit...

Pyrene derivatives substituted at the 2- and 2,7-positions are shown to display a set of photophysical properties different from those of derivatives substituted at the 1-position. It was found that, in the 2- and 2,7-derivatives, there was little influence on the S(2) ← S(0) excitation, which is described as "pyrene-like", and a strong influence on the S(1) ← S(0) excitation, which is described as "substituent-influenced". In contrast, the 1-substituted derivatives display a strong influence on both the S(1) ← S(0) and the S(2) ← S(0) excitations. These observations are rationalized by considering the nature of the orbitals involved in the transitions. The existence of a nodal plane passing through the 2- and 7-positions, perpendicular to the molecular plane in the HOMO and LUMO of pyrene, largely accounts for the different behavior of derivatives substituted at the 2- and 2,7-positions. Herein, we report the photophysical properties of a series of 2-R-pyrenes {R = C(3)H(6)CO(2)H (1), Bpin (2; pin = OCMe(2)CMe(2)O), OC(3)H(6)CO(2)H (3), O(CH(2))(12)Br (4), C≡CPh (5), C(6)H(4)-4-CO(2)Me (6), C(6)H(4)-4-B(Mes)(2) (7), B(Mes)(2) (8)} and 2,7-R(2)-pyrenes {R = Bpin (9), OH (10), C≡C(TMS) (11), C≡CPh (12), C≡C-C(6)H(4)-4-B(Mes)(2) (13), C≡C-C(6)H(4)-4-NMe(2) (14), C(6)H(4)-4-CO(2)C(8)H(17) (15), N(Ph)-C(6)H(4)-4-OMe (16)} whose syntheses are reported elsewhere. Furthermore, we compare their properties to those of several related 1-R-pyrene derivatives {R = C(3)H(6)CO(2)H (17), Bpin (18), C≡CPh (19), C(6)H(4)-4-B(Mes)(2) (20), B(Mes)(2) (21)}. For all derivatives, modest (0.19) to high (0.93) fluorescence quantum yields were observed. For the 2- and 2,7-derivatives, fluorescence lifetimes exceeding 16 ns were measured, with most being ca. 50-80 ns. The 4-(pyren-2-yl)butyric acid derivative (1) has a long fluorescence lifetime of 622 ns, significantly longer than that of the commercially available 4-(pyren-1-yl)butyric acid (17). In addition to measurements of absorption and emission spectra and fluorescence quantum yields and lifetimes, time-dependent density functional theory calculations using the B3LYP and CAM-B3LYP functionals were also performed. A comparison of experimental and theoretically calculated wavelengths shows that both functionals were able to reproduce the trend in wavelengths observed experimentally.

We utilize Particle Swarm Optimization to optimize molecules in a machine-learned continuous chemical representation with respect to multiple objectives such as biological activity, structural constrains or ADMET properties.

We report on the experimental realization of electric quantum walks, which mimic the effect of an electric field on a charged particle in a lattice. Starting from a textbook implementation of discrete-time quantum walks, we introduce an extra operation in each step to implement the effect of the field. The recorded dynamics of such a quantum particle exhibits features closely related to Bloch oscillations and interband tunneling. In particular, we explore the regime of strong fields, demonstrating contrasting quantum behaviors: quantum resonances versus dynamical localization depending on whether the accumulated Bloch phase is a rational or irrational fraction of 2π.

A series of copper­(I) complexes bearing a cyclic (amino)­(aryl)­carbene (CAArC) ligand with various complex geometries have been investigated in great detail with regard to their structural, electronic, and photophysical properties. Comparison of [CuX­(CAArC)] (X = Br (1), Cbz (2), acac (3), Ph2acac (4), Cp (5), and Cp* (6)) with known CuI complexes bearing cyclic (amino)­(alkyl), monoamido, or diamido carbenes (CAAC, MAC, or DAC, respectively) as chromophore ligands reveals that the expanded π-system of the CAArC leads to relatively low energy absorption maxima between 350 and 550 nm in THF with high absorption coefficients of 5–15 × 103 M–1 cm–1 for 1–6. Furthermore, 1–5 show intense deep red to near-IR emission involving their triplet excited states in the solid state and in PMMA films with λem max = 621–784 nm. Linear [Cu­(Cbz)­(DippCAArC)] (2) has been found to be an exceptional deep red (λmax = 621 nm, ϕ = 0.32, τav = 366 ns) thermally activated delayed fluorescence (TADF) emitter with a radiative rate constant k r of ca. 9 × 105 s–1, exceeding those of commercially employed IrIII- or PtII-based emitters. Time-resolved transient absorption and fluorescence upconversion experiments complemented by quantum chemical calculations employing Kohn–Sham density functional theory and multireference configuration interaction methods as well as temperature-dependent steady-state and time-resolved luminescence studies provide a detailed picture of the excited-state dynamics of 2. To demonstrate the potential applicability of this new class of low-energy emitters in future photonic applications, such as nonclassical light sources for quantum communication or quantum cryptography, we have successfully conducted single-molecule photon-correlation experiments of 2, showing distinct antibunching as required for single-photon emitters.