We present a formal demonstration that light can simultaneously exhibit a superfluid behavior and spatial long-range order when propagating in a photonic crystal with self-focussing nonlinearity. In this way, light presents the distinguishing feature
s of matter in a supersolid phase. We show that this supersolid phase provides the stability conditions for nonlinear Bloch waves and, at the same time, permits the existence of topological solitons or defects for the envelope of these waves. We use a condensed matter analysis instead of a standard nonlinear optics approach and provide numerical evidence of these theoretical findings.
Discrete-Gauss states are a new class of gaussian solutions of the free Schrodinger equation owning discrete rotational symmetry. They are obtained by acting with a discrete deformation operator onto Laguerre-Gauss modes. We present a general analyti
cal construction of these states and show the necessary and sufficient condition for them to host embedded dark beams structures. We unveil the intimate connection between discrete rotational symmetry, orbital angular momentum, and the generation of focussing dark beams. The distinguishing features of focussing dark beams are discussed. The potential applications of Discrete-Gauss states in advanced optical trapping and quantum information processing are also briefly discussed.
We study how to search for photon-photon scattering in vacuum at present petawatt laser facilities such as HERCULES, and test Quantum Electrodynamics and non-standard models like Born-Infeld theory or scenarios involving minicharged particles or axio
n-like bosons. First, we compute the phase shift that is produced when an ultra-intense laser beam crosses a low power beam, in the case of arbitrary polarisations. This result is then used in order to design a complete test of all the parameters appearing in the low energy effective photonic Lagrangian. In fact, we propose a set of experiments that can be performed at HERCULES, eventually allowing either to detect photon-photon scattering as due to new physics, or to set new limits on the relevant parameters, improving by several orders of magnitude the current constraints obtained recently by PVLAS collaboration. We also describe a multi-cross optical mechanism that can further enhance the sensitivity, enabling HERCULES to detect photon-photon scattering even at a rate as small as that predicted by QED. Finally, we discuss how these results can be improved at future exawatt facilities such as ELI, thus providing a new class of precision tests of the Standard Model and beyond.
We determine the functional behavior near the discrete rotational symmetry axis of discrete vortices of the nonlinear Schrodinger equation. We show that these solutions present a central phase singularity whose charge is restricted by symmetry argume
nts. Consequently, we demonstrate that the existence of high-charged discrete vortices is related to the presence of other off-axis phase singularities, whose positions and charges are also restricted by symmetry arguments. To illustrate our theoretical results, we offer two numerical examples of high-charged discrete vortices in photonic crystal fibers showing hexagonal discrete rotational invariance.
We review the theory for photon-photon scattering in vacuum, and some of the proposals for its experimental search, including the results of our recent works on the subject. We then describe a very simple and sensitive proposal of an experiment and d
iscuss how it can be used at the present (HERCULES) and the future (ELI) ultrahigh power laser facilities either to find the first evidence of photon-photon scattering in vacuum, or to significantly improve the current experimental limits.
In a recent paper, we have shown that the QED nonlinear corrections imply a phase correction to the linear evolution of crossing electromagnetic waves in vacuum. Here, we provide a more complete analysis, including a full numerical solution of the QE
D nonlinear wave equations for short-distance propagation in a symmetric configuration. The excellent agreement of such a solution with the result that we obtain using our perturbatively-motivated Variational Approach is then used to justify an analytical approximation that can be applied in a more general case. This allows us to find the most promising configuration for the search of photon-photon scattering in optics experiments. In particular, we show that our previous requirement of phase coherence between the two crossing beams can be released. We then propose a very simple experiment that can be performed at future exawatt laser facilities, such as ELI, by bombarding a low power laser beam with the exawatt bump.
