Quantum scrambling is the dispersal of local information into many-body quantum entanglements and correlations distributed throughout the entire system. This concept underlies the dynamics of thermalization in closed quantum systems, and more recently has emerged as a powerful tool for characterizing chaos in black holes [1][2][3][4][5]. However, the direct experimental measurement of quantum scrambling is difficult, owing to the exponential complexity of ergodic many-body entangled states. One way to characterize quantum scrambling is to measure an out-of-time-ordered correlation function (OTOC); however, since scrambling leads to their decay, OTOCs do not generally discriminate between quantum scrambling and ordinary decoherence. Here, we implement a quantum circuit that provides a positive test for the scrambling features of a given unitary process [6,7]. This approach conditionally teleports a quantum state through the circuit, providing an unambiguous litmus test for scrambling while projecting potential circuit errors into an ancillary observable. We engineer quantum scrambling processes through a tunable 3-qubit unitary operation as part of a 7-qubit circuit on an ion trap quantum computer. Measured teleportation fidelities are typically ∼ 80%, and enable us to experimentally bound the scrambling-induced decay of the corresponding OTOC measurement.

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The synthesis and properties of well‐defined core–shell type fluorescent metal‐chelating polymer nanoparticles NP, in the 15 nm diameter range, with a fluorophore (9,10‐diphenylanthracene: DPA) entrapped in the particle core and a selective ligand (1,4,8,11‐tetraazacyclotetradecane: Cyclam), grafted onto the surface are presented. NPs with different number of dye‐per‐particle are readily obtained by entrapment of the fluorophore within the polymer core. The ligand‐coated NPs exhibit a high affinity for Cu2+ ions in aqueous solution and quenching of the DPA fluorescence is observed upon binding of copper. The quenching of fluorescence arises through energy transfer (FRET) from the dye to the copper‐cyclam complexes that form at the NP surface with an operating distance (d) in the 2 nm range. A simple core–shell model accounts for the steady‐state and time‐resolved fluorescence titration experiments: dye molecules located in the outer sphere (thickness d) of the NPs are quenched while the fluorescence of dyes embedded more deeply is not affected by the binding of copper ions. The observed high quenching efficiency (60–65 %), which is tightly correlated to the volumic and microstructural features of the NPs, shed light on the enhanced accessibility inherent in nano‐sized templates. The response towards different metal ions was investigated and this confirmed the selectivity of the nanoparticle template‐assembled sensor for cupric ions.

The study of information scrambling in many-body systems has sharpened our understanding of quantum chaos, complexity and gravity. Here, we extend the framework for exploring information scrambling to infinite dimensional continuous variable (CV) systems. Unlike their discrete variable cousins, continuous variable systems exhibit two complementary domains of information scrambling: i) scrambling in the phase space of a single mode and ii) scrambling across multiple modes of a many-body system. Moreover, for each of these domains, we identify two distinct 'types' of scrambling; genuine scrambling, where an initial operator localized in phase space spreads out and quasi scrambling, where a local ensemble of operators distorts but the overall phase space volume remains fixed. To characterize these behaviors, we introduce a CV out-of-time-order correlation (OTOC) function based upon displacement operators and offer a number of results regarding the CV analog for unitary designs. Finally, we investigate operator spreading and entanglement growth in random local Gaussian circuits; to explain the observed behavior, we propose a simple hydrodynamical model that relates the butterfly velocity, the growth exponent and the diffusion constant. Experimental realizations of continuous variable scrambling as well as its characterization using CV OTOCs will be discussed.

The self-assembly of the amphiphilic block copolymer poly(n-butyl methacrylate)-block-poly[2-(dimethylamino)ethyl methacrylate] at the air-water interface has been investigated at different pH values. Similar to Rehfeldt et al. (J. Phys. Chem. B 2006, 110, 9171), the subphase pH strongly affects the monolayer properties. The formation of calcium phosphate beneath the monolayer can be tuned by the subphase pH and hence the monolayer charge. After 12 h of mineralization at pH 5, the polymer monolayers are still transparent, but transmission electron microscopy (TEM) shows that very thin calcium phosphate fibers form, which aggregate into cotton ball-like features with diameters of 20 to 50 nm. In contrast, after 12 h of mineralization at pH 8, the polymer film is very slightly turbid and TEM shows dense aggregates with sizes between 200 and 700 nm. The formation of calcium phosphate is further confirmed by Raman and energy dispersive X-ray spectroscopy. The calcium phosphate architectures can be assigned to the monolayer charge, which is high at low pH and low at high pH. The study demonstrates that the effects of polycations should not be ignored if attempting to understand the colloid chemistry of biomimetic mineralization. It also shows that basic block copolymers are useful complementary systems to the much more commonly studied acidic block copolymer templates.

Interest in nanostructures, artificial compartments and smart materials is steadily increasing as a result of beneficial applications in sensors, tissue engineering, nanoreactors and drug delivery systems. Block copolymers, peptide-based hybrid materials, expressed protein-like copolymers, and peptides that selfassemble in aqueous solution fulfill the demands of such applications while providing maximum biocompatibility. Herein, we focus on the formation of self-assembled particles using an amphiphilic amino acid (AA) sequence derived by solid-phase peptide synthesis (SPPS) and describe its purification and characterisation. The prepared undecamer features a repetitive L-tryptophan and D-leucine [LW-DL] motif representing the hydrophobic block, and an N-terminally attached hydrophilic (lysine or acetylated lysine) section. For peptides containing charged lysine, aggregation into micelles and a minor fraction of peptide particles was observed. Charge shielding with anionic counter ions shifted the equilibrium towards the larger peptide aggregates, with their size depending on the counter ion's position in the Hofmeister series. Similarly, the corresponding uncharged (acetylated) peptide was also demonstrated to assemble into micelles and subsequently into peptide particles, termed 'peptide beads', which we hypothesise to be multicompartment micelles. The formation of the peptide beads was studied as a function of temperature and solvent composition by means of electron paramagnetic resonance (EPR), dynamic and static light scattering, fluorimetry and electron microscopy. The results suggest an equilibrium between single peptide molecules, micelles, and peptide beads. Interestingly once formed the peptide beads show high mechanical stability and preserve their shape and dimensions even after isolation from solution.

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Many topological phenomena first proposed and observed in the context of electrons in solids have recently found counterparts in photonic and acoustic systems. In this work, we demonstrate that non-Abelian Berry phases can arise when coherent states of light are injected into "topological guided modes" in specially fabricated photonic waveguide arrays. These modes are photonic analogues of topological zero modes in electronic systems. Light traveling inside spatially well-separated topological guided modes can be braided, leading to the accumulation of non-Abelian phases, which depend on the order in which the guided beams are wound around one another. Notably, these effects survive the limit of large photon occupation, and can thus also be understood as wave phenomena arising directly from Maxwell's equations, without resorting to the quantization of light. We propose an optical interference experiment as a direct probe of this non-Abelian braiding of light.