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That the speed of light in free space is constant is a cornerstone of modern physics. However, light beams have finite transverse size, which leads to a modification of their wavevectors resulting in a change to their phase and group velocities. We study the group velocity of single photons by measuring a change in their arrival time that results from changing the beams transverse spatial structure. Using time-correlated photon pairs we show a reduction of the group velocity of photons in both a Bessel beam and photons in a focused Gaussian beam. In both cases, the delay is several microns over a propagation distance of the order of 1 m. Our work highlights that, even in free space, the invariance of the speed of light only applies to plane waves. Introducing spatial structure to an optical beam, even for a single photon, reduces the group velocity of the light by a readily measurable amount.
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These lecture notes were prepared for a 25-hour course for advanced undergraduate students participating in Perimeter Institutes Undergraduate Summer Program. The lectures cover some of what is currently known about the possibility of superluminal travel and time travel within the context of established science, that is, general relativity and quantum field theory. Previous knowledge of general relativity at the level of a standard undergraduate-level introductory course is recommended, but all the relevant material is included for completion and reference. No previous knowledge of quantum field theory, or anything else beyond the standard undergraduate curriculum, is required. Advanced topics in relativity, such as causal structures, the Raychaudhuri equation, and the energy conditions are presented in detail. Once the required background is covered, concepts related to faster-than-light travel and time travel are discussed. After introducing tachyons in special relativity as a warm-up, exotic spacetime geometries in general relativity such as warp drives and wormholes are discussed and analyzed, including their limitations. Time travel paradoxes are also discussed in detail, including some of their proposed resolutions.
Based on the firm laws of physics rather than unproven foundations of mathematical complexity, quantum cryptography provides a radically different solution for encryption and promises unconditional security. Quantum cryptography systems are typically built between two nodes connected to each other through fiber optic. This chapter focuses on quantum cryptography systems operating over free-space optical channels as a cost-effective and license-free alternative to fiber optic counterparts. It provides an overview of the different parts of an experimental free-space quantum communication link developed in the Spanish National Research Council (Madrid, Spain).
Topological structures of electromagnetic fields could give access to nontrivial light-matter interactions and additional degrees of freedom for information and energy transfer. A characteristic example of such electromagnetic excitations are space-time non-separable single-cycle pulses, the exact solutions of Maxwell equation of toroidal topology predicted by Hellwarth and Nouchi in 1996 and recently observed experimentally. Here we introduce a new family of electromagnetic excitation of toroidal topology with increasing complexity in which the Hellwarth-Nouchi pulse is just the simplest member. The electromagnetic excitations of the new family can be parametrised by a single real number and exhibit skyrmionic structures of various orders. They feature multiple singularities in the electromagnetic and Poynting vector fields are accompanied by the fractal-like distributions of energy backflow. The generalized family of toroidal electromagnetic excitation with salient topologies are of interest for transient light-matter interactions, ultrafast optics, spectroscopy, and toroidal electrodynamics.
Owing to its capacity for unique (bio)-chemical specificity, microscopy withmid-IR illumination holds tremendous promise for a wide range of biomedical and industrial applications. The primary limitation, however, remains detection; with current mid-IR detection technology often marrying inferior technical capabilities with prohibitive costs. This has lead to approaches that shift detection towavelengths into the visible regime, where vastly superior silicon-based cameratechnology is available. Here, we experimentally show how nonlinear interferometry with entangled light can provide a powerful tool for mid-IR microscopy, while only requiring near-infrared detection with a standard CMOS camera. In this proof-of-principle implementation, we demonstrate intensity imaging overa broad wavelength range covering 3.4-4.3um and demonstrate a spatial resolution of 35um for images containing 650 resolved elements. Moreover, we demonstrate our technique is fit for purpose, acquiring microscopic images of biological tissue samples in the mid-IR. These results open a new perspective for potential relevance of quantum imaging techniques in the life sciences.
We give an exact self-consistent operator description of the spin and orbital angular momenta, position, and spin-orbit interactions of nonparaxial light in free space. Both quantum-operator formalism and classical energy-flow approach are presented. We apply the general theory to symmetric and asymmetric Bessel beams exhibiting spin- and orbital-dependent intensity profiles. The exact wave solutions are clearly interpreted in terms of the Berry phases, quantization of caustics, and Hall effects of light, which can be readily observed experimentally.
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