This article reviews recent theoretical and experimental advances in the fundamental understanding and active control of quantum fluids of light in nonlinear optical systems. In the presence of effective photon-photon interactions induced by the optical nonlinearity of the medium, a many-photon system can behave collectively as a quantum fluid with a number of novel features stemming from its intrinsically nonequilibrium nature. A rich variety of recently observed photon hydrodynamical effects is presented, from the superfluid flow around a defect at low speeds, to the appearance of a Mach-Cherenkov cone in a supersonic flow, to the hydrodynamic formation of topological excitations such as quantized vortices and dark solitons at the surface of large impenetrable obstacles. While the review is mostly focused on a specific class of semiconductor systems that have been extensively studied in recent years (planar semiconductor microcavities in the strong light-matter coupling regime having cavity polaritons as elementary excitations), the very concept of quantum fluids of light applies to a broad spectrum of systems, ranging from bulk nonlinear crystals, to atomic clouds embedded in optical fibers and cavities, to photonic crystal cavities, to superconducting quantum circuits based on Josephson junctions. The conclusive part of the article is devoted to a review of the future perspectives in the direction of strongly correlated photon gases and of artificial gauge fields for photons. In particular, several mechanisms to obtain efficient photon blockade are presented, together with their application to the generation of novel quantum phases.

Quantum fluids of light

It is shown that the ordinary semiclassical theory of the absorption of light by exciton states is not completely satisfactory (in contrast to the case of absorption due to interband transitions). A more complete theory is developed. It is shown that excitons are approximate bosons, and, in interaction with the electromagnetic field, the exciton field plays the role of the classical polarization field. The eigenstates of the system of crystal and radiation field are mixtures of photons and excitons. The ordinary one-quantum optical lifetime of an excitation is infinite. Absorption occurs only when "three-body" processes are introduced. The theory includes "local field" effects, leading to the Lorentz local field correction when it is applicable. A Smakula equation for the oscillator strength in terms of the integrated absorption constant is derived.

a Quantum-Mechanical Theory of the Contribution of Excitons to the Complex Dielectric Constant of Crystals.

This review is concerned with quantum confinement effects in low-dimensional semiconductor systems. The emphasis is on the optical properties, including luminescence, of nanometre-sized microcrysta...

Low-dimensional systems: quantum size effects and electronic properties of semiconductor microcrystallites (zero-dimensional systems) and some quasi-two-dimensional systems

We study the luminescence of surface modified CdSe nanocrystallites There has been much speculation as to the origin of the band edge emission in these quantum confined structures Because of their large surface to volume ratios it has been suggested that the emission originates from surface-related states However, recent theory suggests that the band edge luminescence arises from an optically inactive fine structure state or “dark” exciton To address this issue we modify the surface of CdSe nanocrystallites with a variety of organic and inorganic ligands We then monitor the effect changing the surface has on the energetics of the band edge luminescence through photoluminescence and fluorescence line narrowing experiments Our results are compared with theoretical predictions for the nonresonant and resonant luminescence We find good agreement between experiment and theory for CdSe nanocrystallites passivated with trioctylphosphine oxide, ZnS, 4-picoline, 4-(trifluoromethyl)thiophenol, and tris(2-eth

The band edge luminescence of surface modified CdSe nanocrystallites: Probing the luminescing state

Inverse opals or three-dimensionally ordered macroporous (3DOM) materials, prepared by colloidal crystal templating (CCT) methods, possess distinctive structural features that are important for the design of photonic crystals, sensors, power sources, catalysts, and various other applications. In the past decade, vast progress has been made in shaping these materials at various length scales. It is now possible to prepare 3DOM materials in a variety of simple and complex compositions, in which pore sizes, pore shapes, and skeletal geometries can be adjusted statically and sometimes even dynamically to alter the physical properties of the material. Hierarchical pore structures can be achieved by combining CCT with additional templating techniques. Furthermore, shaped porous nanoparticles may be synthesized using CCT methods. This review will highlight recent advances in controlling both the internal structure of inverse opals and their external morphology, enhancing compositional complexity, endowing these ...

Morphological Control in Colloidal Crystal Templating of Inverse Opals, Hierarchical Structures, and Shaped Particles†

A method is developed to obtain Wannier-Mott --- exciton wave functions in semiinfinite crystals in the framework of the effective-mass approximation. An analytical approximation is shown to agree well with numerical wave functions and is used to compute exciton nonlocal polarizability (in closed form) and $s$-wave reflectivity. The results are compared with normal-incidence reflectivity experiments in CdS, ZnSe, GaAs, and InP, and the experimental line shapes are well reproduced. The existence of an intrinsic dead layer is confirmed and a new additional boundary condition is derived. It is shown that the spike, frequently observed at the longitudinal-exciton frequency, is due to extrinsic dead layers.

Wannier-Mott excitons in semi-infinite crystals: Wave functions and normal-incidence reflectivity

We apply the fermion commutation technique for composite bosons to polariton-polariton scattering in semiconductor planar microcavities. Derivations are presented in a simple and physically transparent fashion. A procedure of orthogonolization of the initial and final two-exciton state wave functions is used to calculate the effective scattering-matrix elements and the scattering rates. We show how the bosonic stimulation of the scattering appears in this full fermionic approach whose equivalence to the bosonization method is thus demonstrated in the regime of low exciton density. We find an additional contribution to polariton-polariton scattering due to the exciton oscillator strength saturation, which we analyze as well. We present a theory of the polariton-polariton scattering with opposite spin orientations and show that this scattering process takes place mainly via dark excitonic states. Analytical estimations of the effective scattering amplitudes are given.

/pdf/polariton-polariton-scattering-in-microcavities-a-v8u1ngrfx6.pdf

Polariton-polariton scattering in microcavities: A microscopic theory

Des fonctions d'onde variationnelles sont proposees pour les deux plus bas etats d'excitons dans des blocs fins. Elles sont valables pour des blocs de CdS d'epaisseur superieure a 2,5 rayons d'exciton. Les maxima d'absorbance et minima de transmittance sont proches des niveaux des excitons de CdS pour L<500 A, ou les effets polaritoniques ne sont pas importants

Exciton quantization and polariton propagation in semiconductor slabs: From semi-infinite crystals to quantum wells.

Excitons in Confined Systems

In the recent literature, aspects of exciton-radiation interaction in multilayers have been discussed from the viewpoint of microscopic nonlocal optical response. This renewed interest has also revived a long lasting debate about the problem of additional boundary conditions in dispersive samples. In the present paper, the semiclassical framework for studying self-consistently the radiation-matter interaction in a dispersive multilayer medium is briefly reviewed, and applied to the case of a one-dimensional (1D) cluster of quantum wells under Bragg conditions. The optical response is computed as a function of quantum well number $N$ from the super-radiant regime (for rather small $N$ values) to the 1D Bragg reflector limit $(\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty}).$ The different contributions of the radiation-matter interaction to the optical response are discussed by Feenberg's decomposition of the polaritonic matrix. The polariton dispersion curves of a quantum well superlattice are computed and compared with the photonic dispersion curves due to the background dielectric function modulation. Finally, the modification of the photonic bands close to a resonance of the material system is discussed using selected numerical examples.

A. D'Andrea

Papers

Wannier-Mott excitons in semi-infinite crystals: Wave functions and normal-incidence reflectivity

Polariton-polariton scattering in microcavities: A microscopic theory

Exciton quantization and polariton propagation in semiconductor slabs: From semi-infinite crystals to quantum wells.

Excitons in Confined Systems

Spatial dispersion effects on the optical properties of a resonant Bragg reflector