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Polariton lasers. Hybrid lightmatter lasers without inversion
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2012 J. Phys. D: Appl. Phys. 45 313001
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IOP PUBLISHING JOURNAL OF PHYSICS D: APPLIED PHYSICS
J. Phys. D: Appl. Phys. 45 (2012) 409501 (1pp) doi:10.1088/0022-3727/45/40/409501
Corrigendum: Polariton lasers. Hybridlightmatter lasers without inversion2012 J. Phys. D: Appl. Phys. 45 313001
Dipartimento di Ingegneria Industriale e dellInformazione, via Ferrata 1, 27100 Pavia, Italy
Received 21 August 2012, in final form 23 August 2012Published 24 September 2012Online at stacks.iop.org/JPhysD/45/409501
Reference  in the paper refers to the wrong article. Thecorrect reference is Christmann G, Butte R, Feltin E, MoutiA, Stadelmann P A, Castiglia A, Carlin J F and Grandjean N2008 Phys. Rev. B 77 085310. Reference  is cited in thepaper in the second paragraph of page 13 and in the captionsof figures 11 and 12.
The year of publication of  is 2009 and not 2010 aswritten in the text.
The word polaritons is missing from the sixth sentenceof the first paragraph of page 12. The correct phrasing shouldread as In GaAs photonic crystals, surface passivation is verydifficult to obtain  and a solution has been found, for bothinterband  and intersubband  polaritons, by periodicallymodulating the exponential tail of the photonic part of thepolaritons confined in the planar waveguide. References are as in the original published text.
0022-3727/12/409501+01$33.00 1 2012 IOP Publishing Ltd Printed in the UK & the USA
IOP PUBLISHING JOURNAL OF PHYSICS D: APPLIED PHYSICS
J. Phys. D: Appl. Phys. 45 (2012) 313001 (17pp) doi:10.1088/0022-3727/45/31/313001
Polariton lasers. Hybrid lightmatterlasers without inversionDaniele Bajoni
Dipartimento di Ingegneria Industriale e dellInformazione, Universita di Pavia, via Ferrata 1, 27100Pavia, Italy
Received 15 February 2012, in final form 15 May 2012Published 17 July 2012Online at stacks.iop.org/JPhysD/45/313001
AbstractPolariton lasers are coherent emitters in which the fundamental constituents are not photonsamplified by a gaining medium but hybrid, part exciton and part photon, quasi-particles namedpolaritons. In this review we discuss some of the main topics in the field of polariton lasing:we start from an introduction to the concepts of strong coupling regime and polaritons, wethen discuss the mechanism of polariton lasing and the main difficulties in achieving it. Someof the main results on polariton lasing reported in the literature, from 2D samples to confinedstructures, are then reviewed. This latter case will allow us to discuss some of the peculiaritiesof polariton lasing with respect to traditional lasers. Polariton lasing mostly occurs atcryogenic temperatures, but we will see that it can also be observed at room temperature with aproper choice of materials. To conclude, we will discuss some perspectives for the field.
(Some figures may appear in colour only in the online journal)
The rapid development of advanced tools and techniquesfor manipulation, fabrication and characterization of matterat a nanometre length scale is opening new routes towardsthe efficient control of light propagation and confinement insolid-state materials. As a result, the interaction betweensemiconductor materials and the confined electromagneticmodes can be considerably enhanced. The ability to integratesemiconductor emitters and cavities to confine the emission hasled to a wealth of applications, such as commercially availablelight-emitting diodes and laser diodes, or to the observation ofeffects such as the acceleration of the emitter dynamics due tothe coupling with the cavity mode (Purcell effect ) or theemission of purely nonclassical states of light just to name afew examples.
In the case in which the interaction energy between theemitter and the photon mode becomes larger than their losses,the degeneracy between the emitter and the photon modeis lifted giving rise to two spectrally separated lightmattereigenstates: this regime is called the strong coupling regime. Aparticular case of strong coupling is that of excitons confined inquantum wells (QWs) and the modes of photonic cavities: the
result is hybrid excitonphoton quasi-particles named exciton-polariton (we will refer to them simply as polaritons for the restof the paper). Polariton lasing is the accumulation of a largepopulation of polaritons in a single quantum state. Polaritonlasers have many similarities with conventional lasers, but donot need population inversion to occur: this implies that thepolariton lasing threshold is much lower than the photon lasingthreshold in a given structure.
In this paper we give an introduction to polariton lasers,and we review some of the main experimental results inthe field. The paper is organized as follows: in section 2we mathematically introduce the concept of strong coupling,giving a definition of polariton and showing how they aremixed states with properties of both photons and matter quasi-particles; in section 3 we describe the mechanism of polaritonlasing and we compare it with traditional photon lasing; insection 3.2 we detail the main issues to achieve polariton lasingand in section 4 we show how they have been overcome andwe discuss some experimental evidence of polariton lasingin planar samples; in section 5 we discuss how a completethree-dimensional confinement of polaritons can be beneficialfor polariton lasing and we take a survey of experimentalresults of polariton lasing in micropillars and photonic crystal
0022-3727/12/313001+17$33.00 1 2012 IOP Publishing Ltd Printed in the UK & the USA
J. Phys. D: Appl. Phys. 45 (2012) 313001 Topical Review
cavities; we will also see how polariton and photon lasing canbe observed and compared in the same sample; in section 6we briefly review how polariton lasing has been achieved atroom temperature in large bandgap semiconductors. Finally,in section 7 we summarize the paper and we discuss someperspectives of the field.
2. The strong coupling regime and the concept ofpolariton
For most applications the physics of light matter interaction isdescribed to an excellent approximation by the Fermi goldenrule . This very general approach can be applied todescribe phenomena as diverse as photoluminescence, lasingor scattering of light by particles just to name a few. The regimepictured by the Fermi golden rule is termed weak couplingregime and is a regime of irreversible interaction betweenlight and matter; in such a regime the electromagnetic fieldis either emitted or absorbed by some material resonance (beit for example an atomic transition, a flip between differentspin levels of an ion, intersubband or interband transitions ina semiconductor) and then either the material oscillator or theelectromagnetic mode dephase before they can interact again.This dephasing may be due to interaction with the environment(for instance a phonon thermal bath in a solid-state systems),or the finite lifetime of the interacting resonances, or escapeof photons from the spatial region of overlap with the materialresonance.
In the ideal case in which decoherence is absent, theinteraction between a single material oscillator and a singlemode of the electromagnetic field is characterized by areversible exchange of energy. This regime of electrodynamicsis termed strong coupling regime and was firstly postulated byRabi for nuclear spins in gyrating magnetic fields . Thestrong coupling regime can be observed in actual systemsif the coupling time to the electromagnetic field is fasterthan all decoherence processes. Strong coupling has beenexperimentally reported for a wide variety of systems, forexample between the modes of high finesse optical cavitiesand ultra-cold atoms , superconducting qubits  or singlequantum dots .
In this paper we are interested in the strong couplingregime between excitons confined in a QW and the opticalmode of a semiconductor cavity containing the QW (asschematically showed in figure 1(a)), firstly observed byWeisbuch et al in 1992 . QW excitons are bound states ofan electron in the lower conduction band of the semiconductorand a hole in the valence band. In high quality QWs, excitonsare well described by a hydrogen atomic model. The stateof interest for the internal variable is the 1s orbital, while thecentre of mass moves freely in the plane of the QW. For lowin-plane wavevectors below the light cone, the dispersion ofthe ex