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.

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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

We experimentally demonstrate and investigate the effect of limited aperture size on a 200-Gbit/s retro-reflected free-space optical link between a ground station and a UAV up to ∼100-m roundtrip distance by multiplexing 2 OAM beams.

Effect of Limited Aperture Size on a Retro-reflected Communication Link Between a Ground Station and a UAV using Multiplexing of Orbital-Angular-Momentum Beams

A methodology is introduced that enables an absolute, quantum-limited measurement of sub-wavelength interferometric displacements. The technique utilizes a high-frequency optical path modulation within an interferometer operated in a homodyne configuration. All of the information necessary to fully characterize the resultant path displacement is contained within the relative strengths of the various harmonics of the phase modulation. The method, which is straightforward and readily implementable, allows a direct measurement of the theoretical Cramer-Rao limit of detection without any assumptions on the nature of the light source.

Absolute Measurement of Quantum-Limited Interferometric Displacements

Laser microprocessing using Ultra-Short Pulse lasers has developed thanks to the achieved process quality. The main challenge of those processes is the yield improvement. This study will focus on yield improvement of applications such as such as probe card manufacturing for electronic applications with a green USP laser using beam splitting. We present here a fully reflective beam splitter compatible with 500fs green lasers. The compatibility with an industrial machine is demonstrated through a F-theta lens, as well as through a precession head. We show here the process results including the repeatability of the pattern, and the achievable ablation rate. 

Versatile fully reflective beam splitter for high throughput manufacturing with high power green femtosecond laser

The rotational Doppler shift is the counterpart of the usual linear Doppler effect for rotating bodies. We study by an experimental approach coupled with theoretical considerations the rotational shift of a fundamental laser light reflected on an ideal rotating propeller. We decompose the reflected light on a Laguerre–Gaussian basis and show that only modes having the same rotational symmetry as the propeller are involved in the decomposition. The latter experience a frequency shift proportional to the rotation frequency of the propeller and the topological charge of the beam. Extensions of this work in the microwave domain are then considered. 

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Rotational Doppler effect on reflection upon an ideal rotating propeller

Quantum protocols require multiple entangled modes. We demonstrate a set of tools that generate, manipulate and detect multimode entanglement within a single beam of light. This new method is flexible and computer controlled.

Pu Jian

Papers

Effect of Limited Aperture Size on a Retro-reflected Communication Link Between a Ground Station and a UAV using Multiplexing of Orbital-Angular-Momentum Beams

Absolute Measurement of Quantum-Limited Interferometric Displacements

Versatile fully reflective beam splitter for high throughput manufacturing with high power green femtosecond laser

Rotational Doppler effect on reflection upon an ideal rotating propeller

Experimental demonstration of computer reconfigurable multimode entanglement