Exciton-polaritons dans les systèmes de dimensionnalité basse, Exciton-polaritons in low dimensional structures
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Thèse soutenue le 17 novembre 2010: Clermont Ferrand 2
Quelques particularités des polaritons, (quasi) particules-modes normaux du système d'excitons en interaction avec des photons en régime de couplage dit fort, sont théoriquement et numériquement analysés dans les systèmes de dimensionnalité basse. Dans le chapitre 1 est donné un bref aperçu en structure 0D, 1D et 2D semi-conductrices avec une introduction générale au domaine des polaritons. Le chapitre 2 est consacré aux micro / nano fils. Les modes de galerie sifflants sont étudiés dans le cas général d'un système anisotrope ainsi que la formation des polaritons dans les fils de ZnO. Le modèle théorique est comparé à l’expérience. Dans le chapitre 3 la dynamique de type Josephson pour les condensats de Bose-Einstein des polaritons est analysé en prenant en compte le pseudospin. Le chapitre 4 commence par une introduction à l'effet Aharonov-Bohm, qui est la phase géométrique la plus connue. Une autre phase géométrique - phase de Berry, qui existe pour une large classe de systèmes en évolution adiabatique sur un contour fermé, est l'objet principal de cette section. Nous avons examiné une proposition d'un interféromètre en anneau avec exciton-polaritons basé sur l'effet phase de Berry. Le chapitre 5 concerne un système 0D: un exciton d’une boîte quantique fortement couplé avec des photons dans une cavité optique. Nous avons discuté de la possibilité d'obtenir des états intriqués à partir d'une boîte quantique embarquée dans un cristal photonique en régime polaritonique.
-Exciton-polaritons
-Condensat de Bose-Einstein
-Nano/micro fils
-ZnO
-Jonction Josephson Polaritonique
-Phase de Berry
-Boîte quantique
-Intrication quantique
Some special features of polaritons, quasi-particles being normal modes of system of excitons interacting with photons in so called strong coupling regime, are theoretically and numerically analyze in low dimensional systems. In Chapter 1 is given a brief overview of 0D, 1D and 2D semiconductor structures with a general introduction to the polariton field. Chapter 2 is devoted to micro / nano wires. The so called whispering gallery modes are studied in the general case of an anisotropic systems as well as polariton formation in ZnO wires. Theoretical model is compared with an experiment. In the Chapter 3 Josephson type dynamics with Bose-Einstein condensates of polaritons is analyzed taking into account pseudospin degree of freedom. Chapter 4 start with an introduction to Aharonov-Bohm effect, as the best known represent of geometrical phases. An another geometrical phase – Berry phase, occurring for a wide class of systems performing adiabatic motion on a closed ring, is main subject of this section. We considered one proposition for an exciton polariton ring interferometer based on Berry phase effect. Chapter 5 concerns one 0D system : strongly coupled quantum dot exciton to cavity photon. We have discussed possibility of obtaining entangled states from a quantum dot embedded in a photonic crystal in polariton regime.
-Exciton-polaritons
-Bose-Einstein condensation
-Nano/micro wires
-ZnO
-Polaritonic Josephson Junctions
-Berry phase
-Quantum dots
-Quantum entanglement
Source: http://www.theses.fr/2010CLF22069/document
◦N d’Ordre: D.U. 2069
UNIVERSITE BLAISE PASCAL
U.F.R. Sciences et Technologies
ECOLE DOCTORALE DES SCIENCES FONDAMENTALES
◦N 657
THESE
present´ee pour obtenir le grade DOCTEUR D’UNIVERSITE,
specialit´e: Physique des Materiaux, par
Goran PAVLOVIC
Master
Exciton-Polaritons in Low-Dimensional
Structures
Soutenue publiquement le 17/11/2010, devant la comission d’examen:
WHITTAKER David rapporteur
KAVOKIN Alexey rapp
RICHARD Maxime examinateur
SHELYKH Ivan Pr`esident
MALPUECH Guillaume directeur de Th`ese
GIPPIUS Nikolay de Th`ese
SOLNYSHKOV Dmitry invit´e
tel-00632151, version 1 - 13 Oct 20112
tel-00632151, version 1 - 13 Oct 2011Contents
Acknowledgment 5
Introduction 7
1 Exciton-polaritons 11
1.1 Low dimensional semiconductor structures: excitons . . . . . . . . . . . . 12
1.2 Optical mode confinement . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.3 Strongly coupled excitons and photons: polaritons . . . . . . . . . . . . . . 19
1.3.1 Bulk polaritons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.3.2 Cavity p . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.3.3 Polariton-polariton interaction in microcavities. . . . . . . . . . . . 24
1.4 Bose-Einstein condensation. . . . . . . . . . . . . . . . . . . . . . . . . . . 26
1.4.1 Bose-Einstein condensation of ideal Bose gas . . . . . . . . . . . . . 26
1.4.2 Bose-Einstain in weakly-interacting gases . . . . . . . 29
1.4.3 condensation in non-uniform systems . . . . . . . . . 32
1.5 Pseudo-spin of exciton-polaritons . . . . . . . . . . . . . . . . . . . . . . . 34
1.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2 Exciton-polaritons in wires 39
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.2 Cylindrical and hexagonal wires . . . . . . . . . . . . . . . . . . . . . . . . 41
2.2.1 Mode symmetries . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.2.2 Formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.3 Numerical analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.4 Room-temperature 1D polaritons . . . . . . . . . . . . . . . . . . . . . . . 55
2.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
2.4.2 PL experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
2.4.3 One-dimensional exciton-polaritons . . . . . . . . . . . . . . . . . . 58
2.4.4 Interaction with phonons . . . . . . . . . . . . . . . . . . . . . . . 61
2.4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
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tel-00632151, version 1 - 13 Oct 20114 CONTENTS
3 Josephson effect of excitons and exciton-polaritons 65
3.1 Superconductor Josephson junction - SJJ . . . . . . . . . . . . . . . . . . . 66
3.2 Boson Josephson junctions - BJJ . . . . . . . . . . . . . . . . . . . . . . . 70
3.3 Josephson effect of exciton-polaritons . . . . . . . . . . . . . . . . . . . . . 73
3.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.3.2 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
3.3.3 Intrinsic Josephson effect and finite-life time effect . . . . . . . . . . 77
3.3.4 Spatial separation of polarization . . . . . . . . . . . . . . . . . . . 78
3.3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4 Berry phase of exciton-polaritons 83
4.1 Aharonov-Bohm phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.2 TE-TM splitting, Rashba spin-orbit interaction and devices . . . . . . . . . 87
4.3 Berry phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.3.1 Berry phase based interferometry with polaritons . . . . . . . . . . 92
4.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
5 Entanglement from a QD in a microcavity 101
5.1 Entanglement and quantum computing . . . . . . . . . . . . . . . . . . . . 102
5.2 Quantum dots as EPR-photon emitters . . . . . . . . . . . . . . . . . . . . 105
5.3 Strongly coupled dot-cavity system . . . . . . . . . . . . . . . . . . . . . . 108
5.4 Degree of Entanglement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
5.5 Experimental implementation . . . . . . . . . . . . . . . . . . . . . . . . . 115
5.6 Summary and conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
Bibliography 128
tel-00632151, version 1 - 13 Oct 2011Acknowledgment
This thesis has been done within the Chaire d’Excellence de l’Agence Nationale pour
la recherche, from December 2007 - November 2010 in LASMEA (Laboratoire des Sci-
ences et Mat´eriaux pour l’Electronique) in the Group ”Opto´electronique Quantique et
Nanophotonique”.
Before all I would like to thank to my parents - Nada and Zoran. Without their
support, of any kind, they have given me through the years, I would not be able to finish
this work.
CertainlymysupervisorsGuillaumeMalpuechandNikolayGippiusmeritmyprofound
gratitude. First, for the competent leading in my scientific maturation. Sometimes it
was needed to get over childhood diseases as I was a newcomer in the world of exciton-
polaritons. The cure I got in form of very pedagogical instructions helped me a lot to
get on my feet and enjoy playing in the exciton-polaritons playground. Second, apart the
time we spent solving scientific problems I appreciate very much the moments we were
just drinking some good wine or retelling anecdotes.
I profited also from collaboration with Ivan Shelykh. A lot of work we have done
together and I learned many new things inspired by his ideas and previous research in
domains like mesoscopic physics or polariton pseudospin.
I am glad to have met Dmitry Solnyshkov, Robert Johne, and Hugo Flayac. We
have been sharing not just the same office but also some of the best hours of my stay in
Clermont-Ferrand. Their contribution to my scientific formation is not negligible.
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tel-00632151, version 1 - 13 Oct 2011Introduction
Excitons-polaritons are the eigenmodes of system consisting of semiconductor excitons
coupled to photons in the case, when strength of this coupling overcomes the losses in-
duced by excitonic or photonic modes (strong coupling regime). They have been theoreti-
cally predicted independently by Hopfield [ 1](1958) and Agranovich(1959) [2], after Pekar
(1957) [3] explained in terms of additional waves (or Pekar’s waves) a series of experi-
ments on optically pumped excitons. Thirty years later Ulbrich and Weisbuch measured
polariton dispersion in GaAs [4].
Theinterestforpolaritonsisbothfundamental, for thestudying ofinteractionof light
with the matter, and applied, because the modern-era technologies are based on semi-
conductor materials. The term polaritons will be used throughout this thesis, referring
alwaystoexciton-polaritons,butitshouldbenotedthatpolaritonscanalsoarisefromthe
coupling of other type of quasiparticles with light, like phonon-polaritons, for example.
Polaritons, emerging from mixing of matter and light, as composite particles possess
very interesting properties inherited from their components.
First, they obey the Bose-Einstein statistics, undergoing at low temperatures a phase
transition to Bose-Einstein condensation (BEC). It is a new collective state of matter
in which we cannot anymore distinguish individual entities. This collective behavior is
characterized by coherence and occurs at the lengths smaller than the coherence length.
After a long search for the experimental evidence of BEC (seven decades), Cornell and
Wieman reported in ref. [5] on the atomic Bose-Einstein condensate at nanoKelvin tem-
perature (and received the Nobel Prize for this discovery, together with Ketterle a few
years later). Such a small temperature, coming from the high mass of the atomic species
(this dependence will be the subject of section on Bose-Einstein condesation), prohibits
any room-temperature applications. Contrary to atoms, polaritons are quasiparticles of
ultrasmall effective mass: compared to atoms, their mass is typically eight orders of mag-
nitudesmaller. Suchalightmassleadstohightemperaturesatwhichpolaritonscondense
in the Bose-Einstein sense. BEC of polaritons was the first time proposed by Imamoglu
inaformoflow-pumpinginversionlesspolaritonlaser[6]. Atroom-temperaturepolariton
lasing has been predicted in GaN-based microcavity by G. Malpuech in 2002 [7].
Second,toorganizepolaritonregimeoneneedstoconfinethelight,andtheefficiencyof
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tel-00632151, version 1 - 13 Oct 20118 CONTENTS
thisconfinementdeterminesthe polaritonlife-time beingseveraltens ofpicoseconds. The
finite life-time of polaritons in another striking difference of a polariton BEC comparing
to an atomic BEC.
Third, interaction of polaritons governed by their excitonic part is responsible for
variety of nonlinear behaviors, the most important being the blue shift effect of polariton
dispersion. Parametric oscillations [8], bistability and multistability [9] are also effects
arising from nonlinearity of polariton system under study.
The last but the most fundamental property of polaritons is their pseudospin. Total
angular momentum of a polariton state has two projections on the structure growth
ax
