There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry

Squeezed states of the electromagnetic field have been generated by nondegenerate four-wave mixing due to Na atoms in an optical cavity. The optical noise in the cavity, comprised of primarily vacuum fluctuations and a small component of spontaneous emission from the pumped Na atoms, is amplified in one quadrature of the optical field and deamplified in the other quadrature. These quadrature components are measured with a balanced homodyne detector. The total noise level in the deamplified quadrature drops below the vacuum noise level.

Observation of squeezed states generated by four-wave mixing in an optical cavity

Thirty years ago, Coullet et al. proposed that a special optical field exists in laser cavities bearing some analogy with the superfluid vortex. Since then, optical vortices have been widely studied, inspired by the hydrodynamics sharing similar mathematics. Akin to a fluid vortex with a central flow singularity, an optical vortex beam has a phase singularity with a certain topological charge, giving rise to a hollow intensity distribution. Such a beam with helical phase fronts and orbital angular momentum reveals a subtle connection between macroscopic physical optics and microscopic quantum optics. These amazing properties provide a new understanding of a wide range of optical and physical phenomena, including twisting photons, spin-orbital interactions, Bose-Einstein condensates, etc., while the associated technologies for manipulating optical vortices have become increasingly tunable and flexible. Hitherto, owing to these salient properties and optical manipulation technologies, tunable vortex beams have engendered tremendous advanced applications such as optical tweezers, high-order quantum entanglement, and nonlinear optics. This article reviews the recent progress in tunable vortex technologies along with their advanced applications.

/pdf/optical-vortices-30-years-on-oam-manipulation-from-2yknluuuga.pdf

Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities

In the last two decades there has been an enormous progress in the experimental investigation of single quantum systems. This progress covers fields such as quantum optics, quantum computation, quantum cryptography, and quantum metrology, which are sometimes summarized as `quantum technologies'. A key issue there is entanglement, which can be considered as the characteristic feature of quantum theory. As disparate as these various fields maybe, they all have to deal with a quantum mechanical treatment of the measurement process and, in particular, the control process. Quantum control is, according to the authors, `control for which the design requires knowledge of quantum mechanics'. Quantum control situations in which measurements occur at important steps are called feedback (or feedforward) control of quantum systems and play a central role here. This book presents a comprehensive and accessible treatment of the theoretical tools that are needed to cope with these situations. It also provides the reader with the necessary background information about the experimental developments. The authors are both experts in this field to which they have made significant contributions. After an introduction to quantum measurement theory and a chapter on quantum parameter estimation, the central topic of open quantum systems is treated at some length. This chapter includes a derivation of master equations, the discussion of the Lindblad form, and decoherence – the irreversible emergence of classical properties through interaction with the environment. A separate chapter is devoted to the description of open systems by the method of quantum trajectories. Two chapters then deal with the central topic of quantum feedback control, while the last chapter gives a concise introduction to one of the central applications – quantum information. All sections contain a bunch of exercises which serve as a useful tool in learning the material. Especially helpful are also various separate boxes presenting important background material on topics such as the block representation or the feedback gain-bandwidth relation. The two appendices on quantum mechanics and phase-space and on stochastic differential equations serve the same purpose. As the authors emphasize, the book is aimed at physicists as well as control engineers who are already familiar with quantum mechanics. It takes an operational approach and presents all the material that is needed to follow research on quantum technologies. On the other hand, conceptual issues such as the relevance of the measurement process for the interpretation of quantum theory are neglected. Readers interested in them may wish to consult instead a textbook such as Decoherence and the Quantum-to-Classical Transition by Maximilian Schlosshauer. Although the present book does not contain applications to gravity, part of its content might become relevant for the physics of gravitational-wave detection and quantum gravity phenomenology. In this respect it should be of interest also for the readers of this journal.

https://iopscience.iop.org/article/10.1088/0264-9381/27/24/249002/pdf

Quantum Measurement and Control

Characterization and applications of spatial mode multiplexers based on Multi-Plane Light Conversion

We demonstrate a 14.5-Tb/s bi-directional transmission over 2.2 km of OM2 fiber using the selective excitation of four mode groups based on multiplane light conversion technology, wavelength division multiplexing, and direct detection. Forty wavelengths per mode group are used; each wavelength is modulated with a discrete multitone scheme with a fast Fourier transform length of 1024 subcarriers. An 88-Gs/s digital-to-analog converter is used to drive an external lithium niobate Mach–Zehnder modulator. The impact of each component in the line is studied experimentally. Moreover, Chow's rate-adaptive algorithm for bit and power allocation is optimized and adapted to the region where the bit error rate (BER) increases. In this paper, we are considering a hard-decision forward error correction (FEC) limit corresponding to a BER of 5 × 10−3 and assume a 7% overhead. To the best of our knowledge, the achieved bitrate in this paper is the highest throughput transmitted over multimode fibers using direct detection.

High-Speed Bi-Directional Transmission Over Multimode Fiber Link in IM/DD Systems

We report on a 6-mode spatial multiplexer based on multi-plane light conversion with 4.6dB insertion loss and −23dB mode-to-mode crosstalk, designed for few-mode fiber transmission systems that do not rely on complex electronic post-processing.

Efficient and mode-selective spatial multiplexer based on multi-plane light conversion

We demonstrate 5Tb/s bidirectional transmission (2.5Tb/s in each direction) over 2.2km of OM2 fiber using selective excitation of 4 mode groups and WDM multiplexing with DMT modulation and direct detection.

5Tb/s transmission over 2.2 km of multimode OM2 fiber with direct detection thanks to wavelength and mode group multiplexing

We implement a free-space unitary transform inside a wavelength selective switch to produce rectangular shaped beams on the LCoS steering element. Compared to standard Gaussian illumination, the WSS can support 2× as many ports per pixel.

Pu Jian

Papers

Characterization and applications of spatial mode multiplexers based on Multi-Plane Light Conversion

High-Speed Bi-Directional Transmission Over Multimode Fiber Link in IM/DD Systems

Efficient and mode-selective spatial multiplexer based on multi-plane light conversion

5Tb/s transmission over 2.2 km of multimode OM2 fiber with direct detection thanks to wavelength and mode group multiplexing

Wavelength selective switch with optimal steering element utilization