Time-Delay Polaritonics

Non-linearity and finite signal propagation speeds are omnipresent in nature, technologies, and real-world problems, where efficient ways of describing and predicting the effects of these elements are in high demand. Advances in engineering condensed matter systems, such as lattices of trapped condensates, have enabled studies on non-linear effects in many-body systems where exchange of particles between lattice nodes is effectively instantaneous. Here, we demonstrate a regime of macroscopic matter-wave systems, in which ballistically expanding condensates of microcavity exciton-polaritons act as picosecond, microscale non-linear oscillators subject to time-delayed interaction. The ease of optical control and readout of polariton condensates enables us to explore the phase space of two interacting condensates up to macroscopic distances highlighting its potential in extended configurations. We demonstrate deterministic tuning of the coupled-condensate system between fixed point and limit cycle regimes, which is fully reproduced by time-delayed coupled equations of motion similar to the Lang-Kobayashi equation

Directional planar antennae in polariton condensates

We report on the realization of all-optical planar microlensing for exciton-polariton condensates in semiconductor microcavities. We utilize spatial light modulators to structure a nonresonant pumping beam into a planoconcave lens-shape focused onto the microcavity plane. When pumped above condensation threshold, the system effectively becomes a directional polariton antenna, generating an intense focused beam of coherent polaritons away from the pump region. The effects of pump intensity, which regulates the interplay between gain and blueshift of polaritons, as well as the geometry of lens-shaped pump are studied and a strategy to optimize the focusing of the condensate is proposed. Our work underpins the feasibility to guide nonlinear light in microcavities using nonresonant excitation schemes, offering perspectives on optically reprogrammable on-chip polariton circuitry

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

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

Percolative phase separation induced by nonuniformly distributed excess oxygens

The zero-field $^{139}$La and $^{55}$Mn nuclear magnetic resonances were studied in $\rm La_{0.8}Ca_{0.2}MnO_{3+\delta}$ with different oxygen stoichiometry $\delta$. The signal intensity, peak frequency and line broadening of the $^{139}$La NMR spectrum show that excess oxygens have a tendency to concentrate and establish local ferromagnetic ordering around themselves. These connect the previously existed ferromagnetic clusters embedded in the antiferromagnetic host, resulting in percolative conduction paths. This phase separation is not a charge segregation type, but a electroneutral type. The magnetoresistance peak at the temperature where percolative paths start to form provides a direct evidence that phase separation is one source of colossal magnetoresistance effect.Comment: 4 pages, 5 figure

Inferring the Scale of OpenStreetMap Features

International audienceTraditionally, national mapping agencies produced datasets and map products for a low number of specified and internally consistent scales, i.e. at a common level of detail (LoD). With the advent of projects like OpenStreetMap, data users are increasingly confronted with the task of dealing with heterogeneously detailed and scaled geodata. Knowing the scale of geodata is very important for mapping processes such as for generalization of label placement or land-cover studies for instance. In the following chapter, we review and compare two concurrent approaches at automatically assigning scale to OSM objects. The first approach is based on a multi-criteria decision making model, with a rationalist approach for defining and parameterizing the respective criteria, yielding five broad LoD classes. The second approach attempts to identify a single metric from an analysis process, which is then used to interpolate a scale equivalence. Both approaches are combined and tested against well-known Corine data, resulting in an improvement of the scale inference process. The chapter closes with a presentation of the most pressing open problem

Shaping potential landscape for organic polariton condensates in double-dye cavities

We investigate active spatial control of polariton condensates independently of the polariton-, gain-inducing excitation profile. This is achieved by introducing an extra intracavity semiconductor layer, non-resonant to the cavity mode. Saturation of the optical absorption in the uncoupled layer enables the ultra-fast modulation of the effective refractive index and, through excited-state absorption, the polariton dissipation. Utilising these mechanisms, we demonstrate control over the spatial profile and density of a polariton condensate at room temperature

Zero Order Estimates for Analytic Functions

The primary goal of this paper is to provide a general multiplicity estimate. Our main theorem allows to reduce a proof of multiplicity lemma to the study of ideals stable under some appropriate transformation of a polynomial ring. In particular, this result leads to a new link between the theory of polarized algebraic dynamical systems and transcendental number theory. On the other hand, it allows to establish an improvement of Nesterenko's conditional result on solutions of systems of differential equations. We also deduce, under some condition on stable varieties, the optimal multiplicity estimate in the case of generalized Mahler's functional equations, previously studied by Mahler, Nishioka, Topfer and others. Further, analyzing stable ideals we prove the unconditional optimal result in the case of linear functional systems of generalized Mahler's type. The latter result generalizes a famous theorem of Nishioka (1986) previously conjectured by Mahler (1969), and simultaneously it gives a counterpart in the case of functional systems for an important unconditional result of Nesterenko (1977) concerning linear differential systems. In summary, we provide a new universal tool for transcendental number theory, applicable with fields of any characteristic. It opens the way to new results on algebraic independence, as shown in Zorin (2010).Comment: 42 page