Ebook: Electron and Photon Confinement in Semiconductor Nanostructures

This Volume originates from the lectures delivered at the CL Course of the “Enrico Fermi” School, which was held in Varenna from June 25 to July 5, 2002. The purpose of the course was to give an overview of the physics of artificial semiconductor structures confining electrons and photons. The study of the light-matter interaction in this kind of systems is relevant both to fundamental Solid State Physics and to related fields like Quantum Optics. Furthermore, it furnishes the background for several applications in particular in the domain of optical devices, lasers, light-emitting diodes or photonic crystals. In recent years the research in this field has focused on the electronic and optical properties of confined semiconductor structures like Quantum Wells, Quantum Wires, Quantum Dots and semiconductor microcavities. In this context, several exciting effects have been observed. In particular, we mention the effects related to the microcavity polaritons, which are mixed electromagnetic radiation-exciton states inside a semiconductor microcavity.

The study of the characteristics of such states, besides a wide interest by itself, shows strong relations with the domain of cavity quantum electrodynamics and thus with the investigation of some fundamental theoretical concepts. Also topics like the exciton localization due to disorder or the coherent control of optical pulses emitted by confined structures belong to the subjects which are considered in the domain of semiconductor confined structures. The emission characteristics of low-dimensional systems like Quantum Wells, Quantum Wires and Quantum Dots are of enormous importance for the development of new types of semiconductor lasers and light-emitting diodes. These topics were presented during the Course by a team of very distinguished lecturers, whose contributions to the physics of confined electrons and photons have been seminal.

The basic theoretical tools relevant to the field have been introduced by G. Bastard in his lecture on the quantum mechanics of semiconductor nanostructures. S. Koch and B. Jusserand lectured on the semiconductor Bloch equations and on the electron-phonon interaction in semiconductor nanostructures, respectively. Optical crystals were the argument by the lectures of P. S. J. Russell. The concept and the physics of polaritons in quantum wells and microcavities were introduced in the lectures by C. Andreani and J. Baumberg. The link between confined semiconductor physics and quantum optics has been established in the lectures by E. Giacobino on quantum optics in semiconductor nanostructures and in that by J. Ryan on squeezing in non-linear waveguides. Effects of disorder on the optical properties of confined systems was treated in the lecture by V. Savona, coherent control in that by D. Citrin, whereas ultrafast dynamical effects were presented by T. Elsässer. C. Piermarocchi and C. Ciuti presented elements of spintronics in their lectures on quantum computing with spin-polarized excitons and on dynamics and imprinting of electron spin in semiconductors, respectively. One- and zero-dimensional confinement have been the subjects of the lectures by E. Kapon (Semiconductor quantum wires) and D. Bimberg (Semiconductor quantum dots). Lasing in low-dimensional systems and quantum cascade lasers were presented by D. Oberli and by C. Gmachl, respectively. C. Weisbuch gave in his lecture an overview on devices based on confined semiconductor systems.

The Course was attended by a large number of students from all over the world, who followed the lectures with great interest and assiduity. They had the opportunity to present their research work in two poster sessions, which were very successful. Thanks to the enthusiasm of the lecturers and of the participants, we found again the friendly and exciting atmosphere we enjoyed years ago as students in Villa Monastero. We take the occasion to warmly thank everybody. However, the Course had never been successful without the precious help of the team of the Società Italiana di Fisica including Barbara Alzani, Marcella Missiroli, Ramona Brigatti, Franca Sabadini, Marta Pigazzini and Guglielmo Comini. We particularly appreciated the friendly support of the president of the Società Italiana di Fisica Franco Bassani. Finally we kindly acknowledge the financial support of the Società Italiana di Fisica, the European Community and the Ecole Polytechnique Fédérale de Lausanne.

B. Deveaud, A. Quattropani and P. Schwendimann

Introduction

Confinement energies (V(r) = 0)

Subbands and densities of states

The realm of the Fermi Golden Rule

Effective 2D problems

1. Introduction

2. Semiclassical semiconductor optics

3. Semiconductor quantum optics

4. Summary and outlook

1. Introduction

2. Phonons and electron-phonon interactions in bulk polar semiconductors

3. Phonons in low-dimensional semiconductors

4. Electron-phonon interaction in low-dimensional structures

1. Introduction

2. Definitions

3. Dispersion, wave vectors and slowness surfaces

4. Example dispersion relations

5. Bloch wave optics

6. Thin photonic crystal films

7. Photonic crystal fibres

8. Concluding remarks

Polaritons are the mixed modes that result from the interaction between material excitations (phonons, excitons, $\ldots$) and the retarded electromagnetic field. The semiclassical theory of polaritons was developed in the fifties by Huang [1] and Born and Huang [2] in the context of long-wavelength lattice vibrations in ionic crystals. Exciton-polaritons and their quantum-mechanical theory were introduced by Fano [3], Hopfield [4] and Agranovich [5]. The concept of polaritons has proven to be a very fruitful one and has been subject to numerous experimental and theoretical investigations for more than 40 years. The developments of nanostructure physics led to several new phenomena and concepts related to radiation-matter interaction and stimulated novel studies of excitons and polaritons in confined electron and photon systems. In particular, the demonstration of the strong-coupling regime between excitons and photons in planar microcavities and the recent discovery of stimulated scattering and amplification of cavity polaritons have opened exciting and very active areas of research.

In the present lectures I shall review a few main concepts related to excitons and polaritons in bulk and quantum-confined semiconductor systems. I shall concentrate on the following topics: polaritons in bulk semiconductors, excitons and polaritons in thin films and quantum wells, and finally radiation-matter interaction in microcavities, especially with three-dimensional photonic confinement. A unifying theme in these lectures may be the evolution of basic quantities like the exciton oscillator strength or the polariton coupling in going from the bulk to different kinds of confined systems.

1. Polaritons in bulk semiconductors

2. Excitons in thin films and quantum wells

3. Polaritons in thin films and quantum wells

4. Radiation-matter interaction in microcavities

5. Conclusions

The strong-coupling regime of semiconductor microcavities is reviewed. Their nonlinear optical properties are shown to depend critically on the shape of the new polariton dispersions, particularly on the sides, neck and bottom of the polariton trap in momentum space. Both nonlinear scattering and photoluminescence is found to originate from Coulomb pair scattering between polaritons. The implications for a new type of polariton laser which operates without inversion are presented in detail. This system breaks the connection between stimulation and emission, normally ubiquitous in the Einstein coefficients of a lasing transition. The relation to Bose-Einstein condensates is discussed, and the operation of polariton condensates is shown to be practical.

1. Introduction

2. Atoms and excitons

3. Linear optical properties

4. Scattering

5. Polariton lasing and condensation

6. Future work

1. Introduction

2. Quantum fluctuations and squeezed states

3. Noise detection

4. Quantum fluctuation treatment

5. Quantum properties of the exciton-polariton system

6. Experimental study of the noise in the light reflected by semiconductor microcavities

1. Introduction

2. Generation of squeezed light

3. Detection of squeezed states

4. Midgap nonlinear optical properties of semiconductors

5. Squeezing by multi-photon absorption

6. Squeezing by combined self-phase modulation and spectral filtering

1. Introduction

2. Exciton states in quantum wells

3. Resonant Rayleigh scattering

4. Conclusions

1. Introduction

2. Model

3. Coherent control of the pump-induced spectral hole

4. All-optical switching?

5. Conclusion

1. Introduction

2. Intersubband excitations in quasi–two-dimensional semiconductors

3. Experimental techniques

4. Coherent intersubband excitations and their manipulation

5. Coherent electron transport in quantum cascade structures

1. Introduction

2. Spin reflection off a ferromagnet

3. 2DEG coupled to a ferromagnetic gate

4. Conclusions

1. Introduction

2. Single quantum dot as a prototype quantum computer

3. Optical control of electronic spin qubit

4. Conclusions

1. Introduction

2. Gain mechanisms in semiconductors

3. Coulomb correlations in QWRs

4. Lasing in semiconductor quantum wires

5. Gain from localized excitons

6. Summary and outlook

1. Introduction

2. Fundamentals of quantum cascade lasers

3. High-performance designs of active regions

4. Multi-wavelength quantum cascade lasers

5. Conclusion and outlook

1. Introduction

2. Growth

3. Edge-emitting lasers

4. Vertical cavity surface-emitting lasers

5. QD amplifiers

6. Conclusion

1. The case for device physics

2. Lasers

3. Microcavities

4. Photonic crystals