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

(b) Write out the equations for the time dependence of ρ11, ρ22, ρ12 and ρ21 assuming that a light field interaction V = -μ12Ee iωt + c.c. couples only levels |1> and |2>, and that the excited levels exhibit spontaneous decay. (8 marks) (c) Under steady-state conditions, find the ratio of populations in states |2> and |3>. (3 marks) (d) Find the slowly varying amplitude ̃ ρ 12 of the polarization ρ12 = ̃ ρ 12e iωt . (6 marks) (e) In the limiting case that no decay is possible from intermediate level |3>, what is the ground state population ρ11(∞)? (2 marks) 2. (15 marks total) In a 2-level atom system subjected to a strong field, dressed states are created in the form |D1(n)> = sin θ |1,n> + cos θ |2,n-1> |D2(n)> = cos θ |1,n> sin θ |2,n-1>

The Quantum Theory of Light

In recent years, notions drawn from non-Hermitian physics and parity–time (PT) symmetry have attracted considerable attention. In particular, the realization that the interplay between gain and loss can lead to entirely new and unexpected features has initiated an intense research effort to explore non-Hermitian systems both theoretically and experimentally. Here we review recent progress in this emerging field, and provide an outlook to future directions and developments. This Review Article outlines the exploration of the interplay between parity–time symmetry and non-Hermitian physics in optics, plasmonics and optomechanics.

Non-Hermitian physics and PT symmetry

Tables of integrals

Hybrid quantum circuits combine two or more physical systems, with the goal of harnessing the advantages and strengths of the different systems in order to better explore new phenomena and potentially bring about novel quantum technologies. This article presents a brief overview of the progress achieved so far in the field of hybrid circuits involving atoms, spins, and solid-state devices (including superconducting and nanomechanical systems). How these circuits combine elements from atomic physics, quantum optics, condensed matter physics, and nanoscience is discussed, and different possible approaches for integrating various systems into a single circuit are presented. In particular, hybrid quantum circuits can be fabricated on a chip, facilitating their future scalability, which is crucial for building future quantum technologies, including quantum detectors, simulators, and computers.

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Hybrid quantum circuits: Superconducting circuits interacting with other quantum systems

We demonstrate Limacon-shaped microcavity λ=10 µm lasers with directional emission. Their performance is robust with respect to variations of the deformation factor near its optimum value e=0.40. Excellent agreement between experiments and theory is achieved.

Directional micro-cavity lasers with Limaçon-shaped chaotic resonator

We introduce three different mechanisms for the formation of exceptional points in whispering-gallery micro-cavities based on weak deformation or perturbation of the cavity's boundary. Sensors using exceptional points for enhanced sensitivity are discussed.

Exceptional Points in Whispering-Gallery Microcavities

Utilizing avoided resonance crossings we achieve unidirectional light emission from high-quality modes and give an explanation of the scarring phenomenon in deformed microdisks.

Avoided resonance crossings in optical microcavities: unidirectional light emission and scar formation

Using semiconductor quantum dots in a cavity-quantum electrodynamics laser we show a direct connection between superradiant pulse emission and the photon correlations. This demonstrates the importance of quantum correlations in novel optoelectronic devices.

Giant photon bunching and quantum correlations in superradiant quantum-dot microcavity lasers

Detailed experimental and theoretical investigations on coherence properties of high-β (In,Ga)As/GaAs quantum dot-based microcavity lasers are presented. Power dependent micro-photoluminescence measurements on the fundamental mode of the studied micropillar cavities exhibited a smooth transition from spontaneous into stimulated emission with a strong linewidth narrowing around the onset of lasing. This is accompanied by a steep increase in the coherence time of the fundamental mode emission, as derived from first-order field correlation measurements which revealed a gradual change in the g(1)(τ) lineshapes from Gaussian-like to more exponential. In addition, systematic coherence time measurements on various micropillars demonstrated that devices with smaller spontaneous emission coupling factor β reveal longer coherence time of the lasing emission. All experimental results are fully verified by an enhanced microscopic theory which describes the lasing properties of quantum dot (QD) micropillars. (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Jan Wiersig

Papers

Directional micro-cavity lasers with Limaçon-shaped chaotic resonator

Exceptional Points in Whispering-Gallery Microcavities

Avoided resonance crossings in optical microcavities: unidirectional light emission and scar formation

Giant photon bunching and quantum correlations in superradiant quantum-dot microcavity lasers

Coherence length of high‐β semiconductor microcavity lasers