Geometric frustration in polygons of polariton condensates creating vortices of varying topological charge.

Vorticity is a key ingredient to a broad variety of fluid phenomena, and its quantised version is considered to be the hallmark of superfluidity. Circulating flows that correspond to vortices of a large topological charge, termed giant vortices, are notoriously difficult to realise and even when externally imprinted, they are unstable, breaking into many vortices of a single charge. In spite of many theoretical proposals on the formation and stabilisation of giant vortices in ultra-cold atomic Bose-Einstein condensates and other superfluid systems, their experimental realisation remains elusive. Polariton condensates stand out from other superfluid systems due to their particularly strong interparticle interactions combined with their non-equilibrium nature, and as such provide an alternative testbed for the study of vortices. Here, we non-resonantly excite an odd number of polariton condensates at the vertices of a regular polygon and we observe the formation of a stable discrete vortex state with a large topological charge as a consequence of antibonding frustration between nearest neighbouring condensates.

Kinetics of D,L-Lactide Polymerization Initiated with Zirconium Acetylacetonate.

The kinetic of D,L-lactide polymerization in presence of biocompatible zirconium acetylacetonate initiator was studied by differential scanning calorimetry in isothermal mode at various temperatures and initiator concentrations. The enthalpy of D,L-lactide polymerization measured directly in DSC cell was found to be ΔH=-17.8±1.4 kJ mol-1. Kinetic curves of D,L-lactide polymerization and propagation rate constants were determined for polymerization with zirconium acetylacetonate at concentrations of 250-1000 ppm and temperature of 160-220 °C. Using model or reversible polymerization the following kinetic and thermodynamic parameters were calculated: activation energy Ea =44.51±5.35 kJ mol-1, preexponential constant lnA=15.47±1.38, entropy of polymerization ΔS=-25.14 J mol-1 K-1. The effect of reaction conditions on the molecular weight of poly(D,L-lactide) was shown.

Noninvasive high-frequency acoustic microscopy for 3D visualization of microstructure and estimation of elastic properties during hydrolytic degradation of lactide and ε-caprolactone polymers.

The monitoring of degradation processes' kinetics in polymers is one of the attractive possibilities of ultrasound technique applications that provide non-destructive imaging of polymers' internal microstructure and measurements of elastic properties. In this work, biodegradable polymers and copolymers based on L,L-lactide, D,L-lactide and ε-caprolactone have been studied at different stages of hydrolysis at 37 °C by high-frequency (100 and 200 MHz) ultrasound. The acoustic microscopy technique has been developed to reveal changes in the internal microstructure and bulk sound speed in polymer samples over a hydrolysis period of 25 weeks. Ultrasound imaging provides visualization of amorphous and crystalline phases, internal imperfections, variation in packing density, and other microstructural features. Acoustic images demonstrate nucleation, growth, and the changes in internal inhomogeneities in polymers during degradation accompanied by a decrease in the polymers' molecular weight. We associate the changes in the elastic properties (the speed of a longitudinal wave) with crystallinity variations in polymers during hydrothermal aging. The results of the ultrasound investigations are supplemented by gel permeation chromatography, differential scanning calorimetry, and wide-angle X-ray spectroscopy. STATEMENT OF SIGNIFICANCE: Monitoring the kinetics of degradation processes in polymers is one of the attractive possibilities of applying ultrasound techniques that provide non-destructive imaging of the polymers' internal microstructure and measurements of elastic properties. In this work, visualization of nucleation, growth, and evolution of internal inhomogeneities in the volume of polymers and variation of values of speed of longitudinal and transverse sound waves during hydrolysis are compared with measurements of molecular weight, density, data of DSC curves, and X-ray scattering analysis. We discuss several common phenomena that occur in the volume of poly(L-lactide) and poly(D,L-lactide) over the degradation process as well as improvement of elastic properties of the poly(ε -caprolactone) and poly(L-lactide-co-caprolactone) during hydrothermal aging.

Simulating Ising and n-State Planar Potts Models and External Fields with Nonequilibrium Condensates.

Classical spin models with discrete or continuous degrees of freedom arise in many studies of complex physical systems. A wide class of hard real-life optimization problems can be formulated as a minimization of a spin Hamiltonian. Here we show how to simulate the discrete Ising and n-state planar Potts models with or without external fields using the physical gain-dissipative platforms with continuous phases, such as lasers and various nonequilibrium Bose-Einstein condensates. The underlying operational principle originates from a combination of resonant and nonresonant pumping. Our results lay grounds for the physical simulations of a broad range of Hamiltonians with complex interactions that can vary in time and space and with combined symmetries.

Global optimization of spin Hamiltonians with gain-dissipative systems.

Recently, several platforms were proposed and demonstrated a proof-of-principle for finding the global minimum of the spin Hamiltonians such as the Ising and XY models using gain-dissipative quantum and classical systems. The implementation of dynamical adjustment of the gain and coupling strengths has been established as a vital feedback mechanism for analog Hamiltonian physical systems that aim to simulate spin Hamiltonians. Based on the principle of operation of such simulators we develop a novel class of gain-dissipative algorithms for global optimisation of NP-hard problems and show its performance in comparison with the classical global optimisation algorithms. These systems can be used to study the ground state and statistical properties of spin systems and as a direct benchmark for the performance testing of the gain-dissipative physical simulators. Our theoretical and numerical estimations suggest that for large problem sizes the analog simulator when built might outperform the classical computer computations by several orders of magnitude under certain assumptions about the simulator operation.

Realizing the classical XY Hamiltonian in polariton simulators.

The vast majority of real-life optimization problems with a large number of degrees of freedom are intractable by classical computers, since their complexity grows exponentially fast with the number of variables. Many of these problems can be mapped into classical spin models, such as the Ising, the XY or the Heisenberg models, so that optimization problems are reduced to finding the global minimum of spin models. Here, we propose and investigate the potential of polariton graphs as an efficient analogue simulator for finding the global minimum of the XY model. By imprinting polariton condensate lattices of bespoke geometries we show that we can engineer various coupling strengths between the lattice sites and read out the result of the global minimization through the relative phases. Besides solving optimization problems, polariton graphs can simulate a large variety of systems undergoing the U(1) symmetry-breaking transition. We realize various magnetic phases, such as ferromagnetic, anti-ferromagnetic, and frustrated spin configurations on a linear chain, the unit cells of square and triangular lattices, a disordered graph, and demonstrate the potential for size scalability on an extended square lattice of 45 coherently coupled polariton condensates. Our results provide a route to study unconventional superfluids, spin liquids, Berezinskii-Kosterlitz-Thouless phase transition, and classical magnetism, among the many systems that are described by the XY Hamiltonian.