Topological transformations of speckles

Deterministic control of coherent random light is highly important for information transmission through complex media. However, only a few simple speckle transformations can be achieved through diffusers without prior characterization. As recently shown, spiral wavefront modulation of the impinging beam allows permuting intensity maxima and intrinsic $\pm 1$-charged optical vortices. Here, we study this cyclic-group algebra when combining spiral phase transforms of charge $n$, with $D_3$- and $D_4$-point-group symmetry star-like amplitude modulations. This combination allows statistical strengthening of permutations and controlling the period to be 3 and 4, respectively. Phase saddle-points are shown to complete the cycle. These results offer new tools to manipulate critical points in speckles.Comment: 14 pages, 10 figures, 4 table

Relation between o-equivalence and EA-equivalence for Niho bent functions

Boolean functions, and bent functions in particular, are considered up to so-called EA-equivalence, which is the most general known equivalence relation preserving bentness of functions. However, for a special type of bent functions, so-called Niho bent functions there is a more general equivalence relation called o-equivalence which is induced from the equivalence of o-polynomials. In the present work we study, for a given o-polynomial, a general construction which provides all possible o-equivalent Niho bent functions, and we considerably simplify it to a form which excludes EA-equivalent cases. That is, we identify all cases which can potentially lead to pairwise EA-inequivalent Niho bent functions derived from o-equivalence of any given Niho bent function. Furthermore, we determine all pairwise EA-inequivalent Niho bent functions arising from all known o-polynomials via o-equivalence.publishedVersio

Spectrum of collective excitations of a quantum fluid of polaritons

We use a recently developed high-resolution coherent probe spectroscopy method to investigate the dispersion of collective excitations of a polaritonic quantum fluid. We measure the dispersion relation with high energy and wavenumber resolution, which allows us to determine the speed of sound in the fluid and to evidence the contribution of an excitonic reservoir. We report on the generation of collective excitations at negative energies, on the ghost branch of the dispersion curve. Precursors of dynamical instabilities are also identified. Our methods open the way to the precise study of quantum hydrodynamics of quantum fluids of light

Observation of the diffusive Nambu-Goldstone mode of a non-equilibrium phase transition

Second-order phase transitions are governed by spontaneous symmetry breaking, which yield collective excitations with a gapless spectrum called Nambu-Goldstone (NG) modes. While NG modes in conservative systems are propagating excitations, non-equilibrium phase transitions have been predicted to feature a diffusive NG mode. We present the first experimental evidence of a diffusive NG mode in a non-equilibrium Bose-Einstein condensate of microcavity polaritons. The NG mode is observed as a spectral narrowing in the spectroscopic response of the condensate. Additionally, explicitly breaking the symmetry causes the opening of a gap in the spectrum and the disappearance of the NG mode. Our observations confirm the diffusive dynamics of the NG mode of non-equilibrium phase transitions and establish a promising framework to investigate fundamental questions in statistical mechanics.Comment: 8 pages + refs + appendix, 6 figure

Spontaneous generation, enhanced propagation and optical imprinting of quantized vortices and dark solitons in a polariton superfluid: towards the control of quantum turbulence

In resonantly pumped polariton superfluids we recently explored a new regime based on the bistability of the polariton system to enhance the propagation of polariton fluids up to macroscopic distances. This technique together with an all-optical imprinting method allowed the generation and control of various topological excitations such as quantized vortices and dark solitons. The flexibility and scalability of the new experimental scheme opens the way to the systematic study of quantum turbulence in driven dissipative quantum fluids of light. In this article we review the basic working principles of the bistability enhanced propagation and of the imprinting technique and we discuss the main achieved results as well as the most promising future research directions.Comment: Review, 12 pages, 16 figure

Relation between o-equivalence and EA-equivalence for Niho bent functions

Boolean functions, and bent functions in particular, are considered up to so-called EA-equivalence, which is the most general known equivalence relation preserving bentness of functions. However, for a special type of bent functions, so-called Niho bent functions there is a more general equivalence relation called o-equivalence which is induced from the equivalence of o-polynomials. In the present work we study, for a given o-polynomial, a general construction which provides all possible o-equivalent Niho bent functions, and we considerably simplify it to a form which excludes EA-equivalent cases. That is, we identify all cases which can potentially lead to pairwise EA-inequivalent Niho bent functions derived from o-equivalence of any given Niho bent function. Furthermore, we determine all pairwise EA-inequivalent Niho bent functions arising from all known o-polynomials via o-equivalence

"La sensación de la soledad" en las Rimas de Bécquer (Aproximación a la poesía metafísica)

In our article we try to approximate to the topic of Spanish romanticism and the cosmovision of Gustavo Adolfo Bécquer in particular. We evaluate the role of universal romantic symptom – the feeling of loneliness in Bécquer’s Rimas and observe how his poetic world is linked to the existensial vision of Miguel de Unamuno.En nuestro artículo intentamos acercarnos al tema del romanticismo español, y a la visión romántica de Gustavo Adolfo Bécquer en particular. Dentro de ello investigamos el papel del síntoma universal del romanticismo – la sensación de la soledad en las Rimas de Bécquer y observamos cómo está vinculado su mundo romántico con la visión existencialista de Miguel de Unamuno