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In this tutorial, we summarize four important matrix decompositions commonly used in quantum optics, namely the Takagi/Autonne, Bloch–Messiah/Euler, Iwasawa, and Williamson decompositions. The first two of these decompositions are specialized versions of the singular-value decomposition when applied to symmetric or symplectic matrices. The third factors any symplectic matrix in a unique way in terms of matrices that belong to different subgroups of the symplectic group. The last one instead gives the symplectic diagonalization of real, positive definite matrices of even size. While proofs of the existence of these decompositions exist in the literature, we review explicit constructions to implement these decompositions using standard linear algebra packages and functionalities such as singular-value, polar, Schur, and QR decompositions, and matrix square roots and inverses. [ABSTRACT FROM AUTHOR]

The generation of very narrow linewidth light sources is of great importance in modern science. One such source is the superradiant laser, which relies on collectively interacting ultra long lived dipoles driven by incoherent light. Here we discuss a different way of generating spectrally pure light by coherently driving such dipoles inside an optical QED cavity. The light exiting cavity carries information about the detuning between the driving light and the atomic transition, but is also affected by the noise originating from all the decoherence processes that act on the combined atom-cavity system. We calculate these effects to obtain fundamental limits for frequency estimation and stabilization across a range of values of input light intensities and atom-light interaction strengths, estimate these limits in state-of-the-art cavity experiments with alkaline-earth atoms and identify favorable operating conditions. We find that the achievable linewidths are comparable to those of the superradiant laser. [ABSTRACT FROM AUTHOR]

The elementary optical excitations of a two-dimensional electron or hole system have been identified as exciton-Fermi-polarons. Nevertheless, the connection between the bound state of an exciton and an electron, termed trion, and exciton-polarons is subject of ongoing debate. Here, we use an analogy to the Tavis-Cummings model of quantum optics to show that an exciton-polaron can be understood as a hybrid quasiparticle--a coherent superposition of a bare exciton in an unperturbed Fermi sea and a bright collective excitation of many trions. The analogy is valid to the extent that the Chevy Ansatz provides a good description of dynamical screening of excitons and provided the Fermi energy is much smaller than the trion binding energy. We anticipate our results to bring new insight that could help to explain the striking differences between absorption and emission spectra of two-dimensional semiconductors. [ABSTRACT FROM AUTHOR]

We review a few early studies on atom–photon interactions which took place in France after World War II and before the seventies. Several examples are discussed, including double resonance and optical pumping, radiofrequency multiphoton processes, quantum interference effects in radiative processes, master equation description of atom–photon interactions, optical resonators and laser media, etc. We try to point out the continuity which exists between these early studies and more recent investigations in new research fields, such as laser cooling and trapping. Some general conclusions about science policy will be finally drawn from such a historical review. [ABSTRACT FROM AUTHOR]

A new scheme focusing on modification and control of distortion in the reflection and transmission of Goos-Hänchen (GH) shifted beams, is discussed. The absorptivity, reflectivity, and transmissivity are measured for the new atomic scheme. The GH-shifted beam is modified by control fields and incident angle. The sum of absorption, transmission, and reflection coefficients is equal to one. For positive reflection GH-shift region, there is negative transmission GH shift. The distortion in the reflected and transmitted beam is controlled with incident angle and control fields. The results discussed in this article show significant applications in micro-optics and nano-optics, acoustics, and plasma physics. [ABSTRACT FROM AUTHOR]

The techniques of microwave quantum optics are applied to collective spin excitations in a macroscopic sphere of a ferromagnetic insulator. We demonstrate, in the single-magnon limit, strong coupling between a magnetostatic mode in the sphere and a microwave cavity mode. Moreover, we introduce a superconducting qubit in the cavity and couple the qubit with the magnon excitation via the virtual photon excitation. We observe the magnon–vacuum-induced Rabi splitting. The hybrid quantum system enables generation and characterization of non-classical quantum states of magnons. [ABSTRACT FROM AUTHOR]

Abstract: This article is devoted to the generation and the quantum correlations of triple photons, which correspond to the creation of three highly correlated photons from the splitting of a single photon by a phase-matched third-order parametric nonlinear process. These triples constitute a Greenberger–Horne–Zeilinger state of light and are interesting from a fundamental point of view but also for new schemes of quantum cryptography. We give here the classical and quantum descriptions of triple photon generation, we report on the first experimental demonstration of such a generation, and we calculate the Wigner function of three-photon quantum states of light. To cite this article: K. Bencheikh et al., C. R. Physique 8 (2007). [Copyright &y& Elsevier]

Abstract: We have experimentally studied parametric amplification in the c.w. regime using a type-II parametric medium inserted in a transverse-degenerate resonant optical cavity. We demonstrate that this device is able to amplify either in the phase insensitive or phase sensitive way single mode beams and multimode images. We have also observed various multimode correlation and squeezing effects on the amplified output of this device. To cite this article: L. Lopez et al., C. R. Physique 8 (2007). [Copyright &y& Elsevier]

We review the possible roles of quantum optics and quantum information methods for future developments of optical telecommunications. To cite this article: I. Abram, P. Grangier, C. R. Physique 4 (2003). [Copyright &y& Elsevier]

We review recent developments in three-dimensional photonic crystals. State of the art fabrication methods, such as layer-by-layer micromachining, self-assembly and various etching, lithographic and holographic techniques are discussed. We present an overview of optical studies of photonic band gap formation, such as reflectivity, transmission and time-resolved pulse propagation experiments. The fundamental issues associated with disorder and absorption are also considered. Progress towards the ultimate goal of full spontaneous emission control is reviewed. Finally, remaining open questions are summarized. To cite this article: A.F. Koenderink et al., C. R. Physique 3 (2002) 67–77 [Copyright &y& Elsevier]

We introduce to the physics of semiconductor microcavities in the strong coupling regime, also known as cavity-polariton. We discuss the optical response, cavity-polariton dispersion curve, inhomogeneous broadening due to disorder effect and homogeneous broadening due to acoustic phonon scattering. We present novel effects on high quality samples on elastic scattering and parametric oscillation effects in the non-linear response under resonant excitation. To cite this article: R. Houdre´ et al., C. R. Physique 3 (2002) 15–27 [Copyright &y& Elsevier]

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