Single photon emitters often rely on a strong nonlinearity to make the behavior of a quantum mode susceptible to a change in the number of quanta between one and two. In most systems, the strength of nonlinearity is weak, such that changes at the single quantum level have little effect. Here, we consider coupled quantum modes and find that they can be strongly sensitive at the single quantum level, even if nonlinear interactions are modest. As examples, we consider solid-state implementations based on the tunneling of polaritons between quantum boxes or their parametric modes in a microcavity. We find that these systems can act as promising single photon emitters. Introduction.-The construction of single photon sources [1,2] is a current aim of quantum nonlinear optics. Aside from contributing to the security of quantum cryptography [3], single photon sources are useful elsewhere, for example, in schemes for quantum computation using only linear optics and photodetection [4]. For some applications, it is enough to reduce the intensity of a laser source to obtain single photons with a probability limited by the Poisson distribution. To do better than Poisson statistics, one requires some form of nonlinearity. However, when one works in the single photon regime, a strong nonlinearity is not so easy to find.In semiconductor microcavities, light is strongly coupled to quantum well excitons resulting in new quasiparticles known as polaritons. Taking the best from both parents, polaritons have attracted particular attention for over a decade due to their strong nonlinearity (inherited from excitons) as well as their fast dynamics, long coherence, and ability to couple to external light (features of photons). Polariton-polariton interactions have resulted in micron-sized optical parametric oscillators [5][6][7], optical gates [8], spontaneous coherence [9-11], low threshold lasing at room temperature [12][13][14], and superfluidity [15]. While these effects involve many polaritons at once, we wish to focus on the single quantum regime. In planar cavities, quantum effects such as squeezing have been reported and several studies on quantum correlations undertaken [16][17][18][19]. More pronounced effects at the single polariton level are expected in quantum boxes [20][21][22], where polaritons are fully confined in three dimensions and forced to interact even more strongly. Available recently, such confinement has encouraging prospects for single photon sources.It has been predicted that for a very strong nonlinearity, the presence of a single polariton can block the resonant injection of another [23], analogous to the photon blockade [24] of nonlinear cavities. However, to obtain a strong enough nonlinearity for a single photon source, an ex-

Topological insulators are a striking example of materials in which topological invariants are manifested in robustness against perturbations [1,2]. Their most prominent feature is the emergence of topological edge states with reduced dimension at the boundary between areas with distinct topological invariants. The observable physical effect is unidirectional robust transport, unaffected by defects or disorder. Topological insulators were originally observed in the integer quantum Hall effect [3], and subsequently suggested [4-6] and observed [7] even in the absence of magnetic field. These were fermionic systems of correlated electrons. However, during the past decade the concepts of topological physics have been introduced into numerous fields beyond condensed matter, ranging from microwaves [8,9] and photonic systems [10-12] to cold atoms [13,14], acoustics [15,16] and even mechanics [17,18]. Recently, topological insulators were proposed [19-21] in exciton-polariton systems organized as honeycomb (graphene-like) lattices, under the influence of a magnetic field. Topological phenomena in polaritons are fundamentally different from all topological effects demonstrated experimentally thus far: exciton-polaritons are part-light part-matter quasiparticles emerging from the strong coupling of quantum well excitons and cavity photons [22]. Here, we demonstrate experimentally the first exciton-polariton topological insulator. This constitutes the first symbiotic light-matter topological insulators. Our polariton lattice is excited non-resonantly, and the chiral topological polariton edge mode is populated by a polariton condensation mechanism. We use scanning imaging techniques in real-space and in Fourier-space to measure photoluminescence, and demonstrate that the topological edge mode avoids defects, and that the propagation direction of the mode can be reversed by inverting the applied magnetic field. Our exciton-polariton topological insulator paves the way for a variety of new topological phenomena, as they involve light-matter interaction, gain, and perhaps most importantly -exciton-polaritons interact with one another as a nonlinear many-body system.Microcavity exciton-polaritons (polaritons) are composite bosons originating from the strong coupling of quantum well excitons to microcavity photons. While the excitonic fraction provides a strong non-linearity, the photonic part results in a low effective mass, allowing the formation of a driven-dissipative Bose-Einstein condensate [23,24] and a superfluid phase [25], making polaritons being referred to as "quantum fluids of light" [26]. For the epitaxially well-controlled III-V semiconductor material system, a variety of techniques are available to micropattern such cavities in order to precisely engineer the potential landscapes of polaritons [27]. With the recent advances of bringing topological effects to the realms of photonics [8][9][10][11][12]28], several avenues to realize topological edge propagation with polaritons have been suggested [19][20][21], wi...

Polariton lasing is the coherent emission arising from a macroscopic polariton condensate first proposed in 1996. Over the past two decades, polariton lasing has been demonstrated in a few inorganic and organic semiconductors in both low and room temperatures. Polariton lasing in inorganic materials significantly relies on sophisticated epitaxial growth of crystalline gain medium layers sandwiched by two distributed Bragg reflectors in which combating the built-in strain and mismatched thermal properties is nontrivial. On the other hand, organic active media usually suffer from large threshold density and weak nonlinearity due to the Frenkel exciton nature. Further development of polariton lasing toward technologically significant applications demand more accessible materials, ease of device fabrication, and broadly tunable emission at room temperature. Herein, we report the experimental realization of room-temperature polariton lasing based on an epitaxy-free all-inorganic cesium lead chloride perovskite nanoplatelet microcavity. Polariton lasing is unambiguously evidenced by a superlinear power dependence, macroscopic ground-state occupation, blueshift of the ground-state emission, narrowing of the line width and the buildup of long-range spatial coherence. Our work suggests considerable promise of lead halide perovskites toward large-area, low-cost, high-performance room-temperature polariton devices and coherent light sources extending from the ultraviolet to near-infrared range.

Exciton-polaritons are hybrid light-matter quasiparticles formed by strongly interacting photons and excitons (electron-hole pairs) in semiconductor microcavities. They have emerged as a robust solid-state platform for next-generation optoelectronic applications as well as for fundamental studies of quantum many-body physics. Importantly, exciton-polaritons are a profoundly open (that is, non-Hermitian) quantum system, which requires constant pumping of energy and continuously decays, releasing coherent radiation. Thus, the exciton-polaritons always exist in a balanced potential landscape of gain and loss. However, the inherent non-Hermitian nature of this potential has so far been largely ignored in exciton-polariton physics. Here we demonstrate that non-Hermiticity dramatically modifies the structure of modes and spectral degeneracies in exciton-polariton systems, and, therefore, will affect their quantum transport, localization and dynamical properties. Using a spatially structured optical pump, we create a chaotic exciton-polariton billiard--a two-dimensional area enclosed by a curved potential barrier. Eigenmodes of this billiard exhibit multiple non-Hermitian spectral degeneracies, known as exceptional points. Such points can cause remarkable wave phenomena, such as unidirectional transport, anomalous lasing/absorption and chiral modes. By varying parameters of the billiard, we observe crossing and anti-crossing of energy levels and reveal the non-trivial topological modal structure exclusive to non-Hermitian systems. We also observe mode switching and a topological Berry phase for a parameter loop encircling the exceptional point. Our findings pave the way to studies of non-Hermitian quantum dynamics of exciton-polaritons, which may uncover novel operating principles for polariton-based devices.

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The spin Hall effect consists of the generation of a spin current perpendicular to the charge current flow. Thirty-five years after its prediction by Dyakonov and Perel' 1 , it is the focus of experimental and theoretical investigations and constitutes one of the most remarkable effects of spintronics. Owing to scattering and dephasing in electronic gases, it is difficult to observe and has only been demonstrated for the first time a few years ago 2-5 . Recently, three of us have predicted the optical spin Hall effect 6 , which consists of a separation in real space and momentum space of spin-polarized exciton-polaritons generated by a laser in a semiconductor microcavity 7 . The separation takes place owing to a combination of elastic scattering of exciton-polaritons by structural disorder and an effective magnetic field coming from polarization splitting of the polariton states. The excitonic spin current is controlled by the linear polarization of the laser pump. Here, we report the first experimental evidence for this effect and demonstrate propagation of polariton spin currents over 100 µm in a high-quality GaAs/AlGaAs quantum microcavity. By rotating the polarization plane of the exciting light, we were able to switch the directions of the spin currents.The spin carries a quantum bit of information, which makes spin-based devices, also called spintronic devices, extremely promising for quantum-information processing 8 . More specifically, the spin Hall effect (SHE) has recently raised an increasing interest owing to its potentialities in spintronics 2,3 . In a similar way to the Hall effect, in which a magnetic field causes a particle to deviate depending on its charge, the spin Hall effect results in a spin current owing to the spin-dependent scattering of electrons by charged impurities or other defects (extrinsic SHE 1,9 ) or to the spin-orbit effects on the carrier energy dispersion (intrinsic SHE 10,11 ). It leads to a separation in real space and momentum space between spin-up and spin-down electrons and thus enables control of electron spin in semiconductor spintronic devices 12 . Optical 2,3 and electronic 4 measurements of the extrinsic SHE have been reported. Although successfully generated, electronic spin currents are subject to rapid dephasing and decay, mostly due to electron scattering. Recent theoretical studies 5,13 show that the intrinsic SHE is fully suppressed in macroscopic-sized samples because of electron scattering, which directs the system towards equilibrium. The use of neutral particles as carriers for spin currents is an alternative approach that may overcome the problem of dephasing. Here, we demonstrate the spin currents carried by (neutral) exciton-polaritons in a semiconductor microcavity and propagating coherently over 100 µm. We demonstrate for the first time experimentally that the spin currents can be controlled by an optical spin Hall effect (OSHE), which exhibits remarkable analogy to the spin Hall effect.Exciton-polaritons (or polaritons for short) are the 'mixed' exc...

From a theoretical point of view, we discuss a variety of phenomena linked to the spin and polarization degree of freedom of exciton-polaritons in semiconductor microcavities. We start with linear optical effects including the optical spin Hall effect, formation of polarization vortices and ballistic propagation of polarized exciton-polaritons. Next, the interplay between spin-dependent dynamics and Bose condensation in the 2D system of microcavity polaritons is addressed. Theoretically, this many-body system of interacting particles is described by the spinor Gross-Pitaevskii equations. These equations provide a description of the time evolution of polarized polariton fields under different conditions of optical excitation as well as an understanding of the phenomena of superfluidity, multistability and hysteresis via renormalization of the dispersion of elementary excitations. The comprehension of polarization-sensitive dynamics can be made through the introduction of several effective fields of different nature acting on the polariton pseudospin. The theory of parametric scattering of exciton-polaritons is presented, using the second quantization formalism. It is found that the combination of nonlinearity and various mechanisms of spin reorientation leads to self-organization and the formation of polarized patterns such as polarization crosses, vortices and rings. The manipulation of polariton spins can lead to various applications in signal processing, including the construction of optical logic gates and spin memory elements; the creation of spin currents; and the control of polarized signal propagation in the microcavity plane. The concept of polariton neurons is discussed in this connection.

A polariton condensate transistor switch is realized through optical excitation of a microcavity ridge with two beams. The ballistically ejected polaritons from a condensate formed at the source are gated using the 20 times weaker second beam to switch on and off the flux of polaritons. In the absence of the gate beam the small builtin detuning creates potential landscape in which ejected polaritons are channelled toward the end of the ridge where they condense. The low loss photon-like propagation combined with strong nonlinearities associated with their excitonic component makes polariton based transistors particularly attractive for the implementation of all-optical integrated circuits. 71.36.+c Contemporary electronics face ever increasing obstacles in achieving higher speeds of operation. Down-scaling which has served Moore's law for decades is approaching the inherent limits of semiconductor materials [1][2][3][4]. Even though a number of novel approaches [5][6][7] have managed to improve operating frequency and power consumption, it is commonly acknowledged that in the future, charged carriers will have to be replaced by information carriers that do not suffer from scattering, capacitance and resistivity effects. Although photonic circuits have been proposed, a viable optical analogue to an electronic transistor has yet to be identified as switching and operating powers of these devices are typically high [8].Polaritons which are hybrid states of light and electronic excitations offer an attractive solution as they are a natural bridge between these two systems. Their excitonic component allows them to interact strongly giving rise to the nonlinear functionality enjoyed by electrons. On the other hand, their photonic component restricts their dephasing allowing them to carry information with minimal data loss. Notably from the view of solid state physics polaritons are bosonic particles with a particularly light effective mass. These properties allow for the condensation of polaritons into a massively occupied single low-energy state, which shows many similarities to atomic Bose Einstein condensates [9][10][11][12]. The macroscopic quantum properties of polariton condensates combined with their photonic nature make them ideal candidates for use in quantum information devices and all optical circuits [13][14][15][16][17]. Several recent works address the possibility of optical manipulation of polariton condensate flow however these stop short of demonstrating actual gating of polariton condensate flow a prerequisite for implementation of integrated optical circuits [17][18][19][20].In this paper, a high finesse microcavity sample fabricated into a ridge is utilized to develop an exciton-polariton condensate transistor switch. A polariton condensate formed by optical excitation serves as a source of polaritons which are ballis-tically ejected along the channel as shown in Figure 1(a). Polariton propagation can be controlled using a second weaker beam that gates the polariton flux by modifying the energy ...