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In the field of disordered photonics, a common objective is to characterize optically opaque materials for controlling light delivery or performing imaging. Among various complex devices, multi-mode optical fibers stand out as cost-effective and easy-to-handle tools, making them attractive for several tasks. In this context, we leverage the reservoir computing paradigm to recast these fibers into random hardware projectors, transforming an input dataset into a higher dimensional speckled image set. The goal of our study is to demonstrate that using such randomized data for classification by training a single logistic regression layer improves accuracy compared to training on direct raw images. Interestingly, we found that the classification accuracy achieved using the reservoir is also higher than that obtained with the standard transmission matrix model, a widely accepted tool for describing light transmission through disordered devices. We find that the reason for such improved performance could be due to the fact that the hardware classifier operates in a flatter region of the loss landscape when trained on fiber data, which aligns with the current theory of deep neural networks. These findings strongly suggest that multi-mode fibers possess robust generalization properties, positioning them as promising tools for optically-assisted neural networks. With this study, in fact, we want to contribute to advancing the knowledge and practical utilization of these versatile instruments, which may play a significant role in shaping the future of machine learning.

Quantum vortices are the quantized version of classical vortices. Their center is a phase singularity or vortex core around which the flow of particles as a whole circulates and is typical in superfluids, condensates and optical fields. However, the exploration of the motion of the phase singularities in coherently-coupled systems is still underway. We theoretically analyze the propagation of an interference dislocation in the regime of strong coupling between light and matter, with strong mass imbalance, corresponding to the case of microcavity exciton-polaritons. To this end, we utilize combinations of vortex and tightly focused Gaussian beams, which are introduced through resonant pulsed pumping. We show that a dislocation originates from self-interference fringes, due to the non-parabolic dispersion of polaritons combined with moving Rabi-oscillating vortices. The morphology of singularities is analyzed in the Poincar\'{e} space for the pseudospin associated to the polariton states. The resulting beam carries orbital angular momentum with decaying oscillations due to the loss of overlap between the normal modes of the polariton system., Comment: 9 pages, 6 figures

The Berry curvature provides a powerful tool to unify several branches of science through their geometrical aspect: topology, energy bands, spin and vector fields. While quantum defects -- phase vortices and skyrmions -- have been in the spotlight, as rotational entities in condensates, superfluids and optics, their dynamics in multi-component fields remain little explored. Here we use two-component microcavity polaritons to imprint a dynamical pseudospin texture in the form of a double full Bloch beam, a conformal continuous vortex beyond unitary skyrmions. The Berry curvature plays a key role to link various quantum spaces available to describe such textures. It explains for instance the ultrafast spiraling in real space of two singular vortex cores, providing in particular a simple expression -- also involving the complex Rabi frequency -- for their intricate velocity. Such Berry connections open new perspectives for understanding and controlling highly-structured quantum objects, including strongly asymmetric cases or even higher multi-component fields., Comment: 17 pages, 4 figures, 3 videos

Deep levels control the space charge in electrically compensated semi-insulating materials. They limit the performance of radiation detectors but their interaction with free carriers can be favorably exploited in these devices to manipulate the spatial distribution of the electric field by optical beams. By using semi-insulating CdTe diodes as a case study, our results show that optical doping functionalities are achieved. As such, a highly stable, flux-dependent, reversible and spatially localized space charge is induced by a line-shaped optical beam focused on the cathode contact area. Real-time non-invasive imaging of the electric field is obtained through the Pockels effect. A simple and convenient method to retrieve the two-dimensional electric field components is presented. Numerical simulations involving just one deep level responsible for the electrical compensation confirm the experimental findings and help to identify the underlying mechanism and critical parameters enabling the optical writing functionalities., Comment: main 17 pages, 7 figures, SM 5 pages, 6 figures, 1 video

Recovering the transmission matrix of a disordered medium is a challenging problem in disordered photonics. Usually, its reconstruction relies on a complex inversion that aims at connecting a fully-controlled input to the deterministic interference of the light field scrambled by the device. At the moment, iterative phase-retrieval protocols provide the fastest reconstructing frameworks, converging in a few tens of iterations. Exploiting the knowledge of speckle correlations, we construct a new phase retrieval algorithm that reduces the computational cost to a single iteration. Besides being faster, our method is effective also using less measurements than state-of-the-art protocols. Thanks to reducing computation time by one order of magnitude, our result can be groundbreaking for real-time optical operations in medical imaging., Comment: 9 pages, 7 figures

Quantum vortices are the analogue of classical vortices in optics, Bose-Einstein condensates, superfluids and superconductors, where they provide the elementary mode of rotation and orbital angular momentum. While they mediate important pair interactions and phase transitions in nonlinear fluids, their linear dynamics is useful for the shaping of complex light, as well as for topological entities in multi-component systems, such as full Bloch beams. Here, setting a quantum vortex into directional motion in an open-dissipative fluid of microcavity polaritons, we observe the self-splitting of the packet, leading to the trembling movement of its center of mass, whereas the vortex core undergoes ultrafast spiraling along diverging and converging circles, in a sub-picosecond precessing fashion. This singular dynamics is accompanied by vortex-antivortex pairs creation and annihilation, and a periodically changing topological charge. The spiraling and branching mechanics represent a direct manifestation of the underlying Bloch pseudospin space, whose mapping is shown to be rotating and splitting itself. Its reshaping is due to three simultaneous drives along the distinct directions of momentum and complex frequency, by means of the differential group velocities, Rabi frequency and dissipation rates, which are natural assets in coupled fields such as polaritons. This state, displaying linear momentum dressed with oscillating angular momentum, confirms the richness of multi-component and open quantum fluids and their innate potentiality to implement sophisticated and dynamical topological textures of light., Comment: 12 pages, 8 figures, 3 videos

If a quantum fluid is driven with enough angular momentum, at equilibrium the ground state of the system is given by a lattice of quantised vortices whose density is prescribed by the quantization of circulation. We report on the first experimental study of the Feynman-Onsager relation in a non-equilibrium polariton fluid, free to expand and rotate. Upon initially imprinting a lattice of vortices in the quantum fluid, we track the vortex core positions on picosecond time scales. We observe an accelerated stretching of the lattice and an outward bending of the linear trajectories of the vortices, due to the repulsive polariton interactions. Access to the full density and phase fields allows us to detect a small deviation from the Feynman-Onsager rule in terms of a transverse velocity component, due to the density gradient of the fluid envelope acting on the vortex lattice., Comment: Main 6 pages, 4 figures, SM 4 pages, 5 figures

Topological physics and in particular its connection with artificial gauge fields is a forefront topic in different physical systems, ranging from cold atoms to photonics and more recently semiconductor dressed exciton-photon states, called polaritons. Engineering the energy dispersion of polaritons in microcavities through nanofabrication or exploiting the intrinsic material and cavity anisotropies has demonstrated many intriguing effects related to topology and emergent gauge fields. Here, we show that we can control the Berry curvature distribution of polariton bands in a strongly coupled organic-inorganic 2D perovskite single crystal. The spatial anisotropy of the perovskite crystal combined with photonic spin-orbit coupling make emerge two Hamilton's diabolical points in the dispersion. The application of an external magnetic field breaks time reversal symmetry thanks to the exciton Zeeman splitting. It splits the diabolical points degeneracy. The resulting bands show non-zero integral Berry curvature which we directly measure by state tomography. Crucially, we show that we can control the Berry curvature distribution in the band, the so-called band geometry, within the same microcavity., Comment: 30 pages, 10 figures

The fundamental mode of rotation in quantum fluids is given by a vortex, whose quantized value yields the orbital angular momentum (OAM) per particle. If the vortex is displaced (off-centered) from the reference point for rotation, the angular momentum is reduced and becomes fractional. Such displaced vortices can further exhibit a peculiar dynamics in presence of confining potentials or couplings to other fields. We study analytically a number of 2D systems where displaced vortices exhibit a noteworthy dynamics, including time-varying self-sustained oscillation of the OAM, complex reshaping of their morphology with possible creation of vortex-antivortex pairs and peculiar trajectories for the vortex core with sequences of strong accelerations and decelerations which can even send the core to infinity and bring it back. Interestingly, these do not have to occur conjointly, with complex time dynamics of the vortex core and/or their wavepacket morphology possibly taking place without affecting the total OAM. Our results generalize to simple and fundamental systems a phenomenology recently reported with Rabi-coupled bosonic fields, showing their wider relevance and opening prospects for new types of control and structuring of the angular momentum of light and/or quantum fluids., Comment: 13 pages, 6 figures

Two dimensional (2D) perovskites are promising materials for photonic applications, given their outstanding nonlinear optical properties, ease of fabrication and versatility. In particular, exploiting their high oscillator strength, the crystalline form of 2D perovskites can be used as excitonic medium in optical microcavities, allowing for the study of their optical properties in the strong light-matter coupling regime. While polariton condensation has been observed in different materials at room temperature, here we observe for the first time two distinct threshold processes in a 2D perovskite, a material that has never shown spontaneous phase transition up to now. In particular, we demonstrate lasing from the bi-exciton state which contributes to populate the lower polariton branch and, at higher excitation powers, eventually leads to the formation of a polariton condensate. The emission linewidth narrowing and a spatial coherence over 50 x 50 um2 area are the smoking gun, the formation of a quantum coherent state in 2D hybrid perovskite. Our results not only show the formation of a polariton condensate in 2D perovskites but they are also crucial for the understanding of the physical mechanisms that leads to coherent phase transition in perovskite-based polariton microcavities.

Exciton-polaritons are hybrid light-matter excitations arising from the non-perturbative coupling of a photonic mode and an excitonic resonance. Behaving as interacting photons, they show optical third-order nonlinearities providing effects such as optical parametric oscillation or amplification. It has been suggested that polariton-polariton interactions can be greatly enhanced by inducing aligned electric dipoles in their excitonic part. However direct evidence of a true particle-particle interaction, such as superfluidity or parametric scattering is still missing. In this work, we demonstrate that dipolar interactions can be used to enhance parametric effects such as self-phase modulation in waveguide polaritons. By quantifying these optical nonlinearities we provide a reliable experimental measurement of the direct dipolar enhancement of polariton-polariton interactions., Comment: Main text: 6 pages 4 figures. Supporting Information: 3 pages 4 figures

Quantum fluids of light are realized in semiconductor microcavities by exciton-polaritons, solid-state quasi-particles with a light mass and sizeable interactions. Here, we use the microscopic analogue of oceanographic techniques to measure the excitation spectrum of a thermalised polariton condensate. Increasing the fluid density, we demonstrate the transition from a free-particle parabolic dispersion to a linear, sound-like Goldstone mode characteristic of superfluids at equilibrium. Notably, we show that excitations are created with a definite direction with respect to the condensate, analogous to how a sea breeze develops surface waves aligned with the wind. These results reveal the effect of asymmetric pumping on the collective excitations of a condensate. Furthermore, we measure the critical sound speed for polariton superfluids close to equilibrium.

Quantum fluids of light are an emerging platform for energy efficient signal processing, ultra-sensitive interferometry and quantum simulators at elevated temperatures. Here we demonstrate the optical control of the topological excitations induced in a large polariton condensate, realising the bosonic analog of a long Josephson junction and reporting the first observation of bosonic Josephson vortices. When a phase difference is imposed at the boundaries of the condensate, two extended regions become separated by a sharp $\pi$-slippage of the phase and a solitonic depletion of the density, forming an insulating barrier with a suppressed order parameter. The superfluid behavior, that is a smooth phase gradient across the system instead of the sharp phase jump, is recovered at higher polariton densities and it is mediated by the nucleation of Josephson vortices within the barrier. Our results contribute to the understanding of dissipation and stability of elementary excitations in macroscopic quantum systems.

The self-trapping of exciton-polariton condensates is demonstrated and explained by the formation of a new polaron-like state. Above the polariton lasing threshold, local variation of the lattice temperature provides the mechanism for an attractive interaction between polaritons. Due to this attraction, the condensate collapses into a small bright spot. Its position and momentum variances approach the Heisenberg quantum limit. The self-trapping does not require either a resonant driving force or a presence of defects. The trapped state is stabilized by the phonon-assisted stimulated scattering of excitons into the polariton condensate. While the formation mechanism of the observed self-trapped state is similar to the Landau-Pekar polaron model, this state is populated by several thousands of quasiparticles, in a strike contrast to the conventional single-particle polaron state.

Strongly-coupled quantum fields, such as multi-component atomic condensates, optical fields and polaritons, are remarkable systems where the simple dynamics of coupled oscillators can meet the intricate phenomenology of quantum fluids. When the coupling between the components is coherent, not only the particles number, but also their phase texture that maps the linear and angular momentum, can be exchanged. Here, on a system of exciton-polaritons, we have realized a so-called full-Bloch beam: a configuration in which all superpositions of the upper and the lower polariton -- all quantum states of the associated Hilbert space -- are simultaneously present at different points of the physical space, evolving in time according to Rabi-oscillatory dynamics. As a result, the light emitted by the cavity displays a peculiar dynamics of spiraling vortices endowed with oscillating linear and angular momentum and exhibiting ultrafast motion of their cores with striking accelerations to arbitrary speeds. This remarkable vortex motion is shown to result from distortions of the trajectories by a homeomorphic mapping between the Rabi rotation of the full wavefunction on the Bloch sphere and Apollonian circles in the real space where the observation is made. Such full-Bloch beams offer new prospects at a fundamental level regarding their topological properties or in the interpretation of quantum mechanics, and the Rabi-rotating vortices they yield should lead to interesting applications such as ultrafast optical tweezers., Comment: Published version, 18 pages, 8 figures, 4 ancillary movies

Quantum vortices, the quantized version of classical vortices, play a prominent role in superfluid and superconductor phase transitions. However, their exploration at a particle level in open quantum systems has gained considerable attention only recently. Here we study vortex pair interactions in a resonant polariton fluid created in a solid-state microcavity. By tracking the vortices on picosecond time scales, we reveal the role of nonlinearity, as well as of density and phase gradients, in driving their rotational dynamics. Such effects are also responsible for the split of composite spin-vortex molecules into elementary half-vortices, when seeding opposite vorticity between the two spinorial components. Remarkably, we also observe that vortices placed in close proximity experience a pull-push scenario leading to unusual scattering-like events that can be described by a tunable effective potential. Understanding vortex interactions can be useful in quantum hydrodynamics and in the development of vortex-based lattices, gyroscopes, and logic devices., Comment: 12 pages, 7 figures, Supplementary Material and 5 movies included in arXiv

We study the spin vortices and skyrmions coherently imprinted into an exciton-polariton condensate on a planar semiconductor microcavity. We demonstrate that the presence of a polarization anisotropy can induce a complex dynamics of these structured topologies, leading to the twist of their circuitation on the Poincar\'e sphere of polarizations. The theoretical description of the results carries the concept of generalized quantum vortices in two-component superfluids, which are conformal with polarization loops around an arbitrary axis in the pseudospin space., Comment: 8 pages, 4 figures, SI 3 pages, SI 6 movies at http://www.pnas.org/content/113/52/14926?tab=ds and https://drive.google.com/open?id=0B0QCllnLqdyBUkVaSFpqSHB0cHM

We report the observation of the Berezinskii-Kosterlitz-Thouless transition for a 2D gas of exciton-polaritons, and through the joint measurement of the first-order coherence both in space and time we bring compelling evidence of a thermodynamic equilibrium phase transition in an otherwise open driven/dissipative system. This is made possible thanks to long polariton lifetimes in high-quality samples with small disorder and in a reservoir-free region far away from the excitation spot, that allow topological ordering to prevail. The observed quasi-ordered phase, characteristic for an equilibrium 2D bosonic gas, with a decay of coherence in both spatial and temporal domains with the same algebraic exponent, is reproduced with numerical solutions of stochastic dynamics, proving that the mechanism of pairing of the topological defects (vortices) is responsible for the transition to the algebraic order. Finally, measurements in the weak-coupling regime confirm that polariton condensates are fundamentally different from photon lasers and constitute genuine quantum degenerate macroscopic states.

We report a record-size, two-dimensional polariton condensate of a fraction of a millimeter radius free from the presence of an exciton reservoir. This macroscopically occupied state is formed by the ballistically expanding polariton flow that relaxes and condenses over a large area outside of the excitation spot. The density of this trap-free condensate is < 1 polariton/{\mu}m^2, reducing the phase noise induced by the interaction energy. Moreover, the backflow effect, recently predicted for the nonparabolic polariton dispersion, is observed here for the first time in the fast-expanding wave packet.

Superfluidity---the suppression of scattering in a quantum fluid at velocities below a critical value---is one of the most striking manifestations of the collective behaviour typical of Bose-Einstein condensates. This phenomenon, akin to superconductivity in metals, has until now only been observed at prohibitively low cryogenic temperatures. For atoms, this limit is imposed by the small thermal de Broglie wavelength, which is inversely related to the particle mass. Even in the case of ultralight quasiparticles such as exciton-polaritons, superfluidity has only been demonstrated at liquid helium temperatures. In this case, the limit is not imposed by the mass, but instead by the small exciton binding energy of Wannier-Mott excitons, which places the upper temperature limit. Here we demonstrate a transition from normal to superfluid flow in an organic microcavity supporting stable Frenkel exciton-polaritons at room temperature. This result paves the way not only to table-top studies of quantum hydrodynamics, but also to room-temperature polariton devices that can be robustly protected from scattering., Comment: 14 pages, 5 figures, supporting information 7 pages, 9 figures

Polaritons are quasi-particles originating from the coupling of light with matter that demonstrated quantum phenomena at the many-particle mesoscopic level, such as BEC and superfluidity. A highly sought and long-time missing feature of polaritons is a genuine quantum manifestation of their dynamics at the single-particle level. Although they are conceptually perceived as entangled states and theoretical proposals abound for an explicit manifestation of their single-particle properties, so far their behaviour has remained fully accountable for by classical and mean-field theories. In this Article, we report the first experimental demonstration of a genuinely-quantum manifestation of microcavity polaritons, by swapping, in a two-photon entangled state generated by parametric down-conversion, a photon for a polariton. Furthermore, we show how single polaritons are affected by polariton-polariton interactions in a propaedeutic demonstration of their qualities for quantum information applications., Comment: 19 pages, 6 figures

The strong-coupling of an excitonic transition with an electromagnetic mode results in composite quasi-particles called exciton-polaritons, which have been shown to combine the best properties of their bare components in semiconductor microcavities. However, the physics and applications of polariton flows in organic materials and at room temperature are still unexplored because of the poor photon confinement in such structures. Here we demonstrate that polaritons formed by the hybridization of organic excitons with a Bloch Surface Wave are able to propagate for hundreds of microns showing remarkable third-order nonlinear interactions upon high injection density. These findings pave the way for the studies of organic nonlinear light-matter fluxes and for a technological promising route of dissipation-less on-chip polariton devices working at room temperature., Comment: Improved version with polariton-polariton interactions. 13 pages, 4 figures, supporting 6 pages, 6 figures

Polaritons are hybrid light-matter quasi-particles that have gathered a significant attention for their capability to show room temperature and out-of-equilibrium Bose-Einstein condensation. More recently, a novel class of ultrafast optical devices have been realized by using flows of polariton fluids, such as switches, interferometers and logical gates. However, polariton lifetimes and propagation distance are strongly limited by photon losses and accessible in-plane momenta in usual microcavity samples. In this work, we show experimental evidence of the formation of room temperature propagating polariton states arising from the strong coupling between organic excitons and a Bloch surface wave. This result, which was only recently predicted, paves the way for the realization of polariton devices that could allow lossless propagation up to macroscopic distances.