Table Of ContentQuantum Coherence, Correlation and
Decoherence in Semiconductor
Nanostructures
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Quantum Coherence, Correlation and
Decoherence in Semiconductor
Nanostructures
Edited by
T. Takagahara
Dept. of Electronics and Information Science,
Kyoto Institute of Technology,
Kyoto, Japan
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Preface
Semiconductor nanostructures occupy an intermediate position between bulk materials
and molecules and provide ample opportunities to discover unexpected phenomena and
to reveal new physical aspects. The discrete energy spectra of electrons, holes and
excitons due to the quantum confinement lead to the suppression of relaxation processes
that dominate in bulk materials, resulting in reduced homogeneous linewidth of relevant
transitions. The quantum confinement leads also to the relatively large oscillator strength
of the excitonic transitions. The wavefunction is extended coherently over a nanostructure
and all the atomic transition dipole moments within the wavefunction are added up
coherently. It is well-known that the Sommerfeld factor which represents the relative
importance of the continuum (unbound) exciton states is monotonically decreasing with
reducing the dimensionality of the system. Thus the discrete exciton states play the
essential role in the optical properties of semiconductor nanostructures. Thus we have
sharp optical transitions with large oscillator strength. This is the physical basis of the
recent remarkable progress in the linear and nonlinear optical spectroscopies of
semiconductor quantum dots.
Semiconductor nanostructures are attracting much interest as the most promising
device to implement the quantum information processing and the quantum computation.
The quantum coherence in nanostructures can be most elegantly manipulated by optical
means. Thus the excitons and multi-excitons in semiconductor nanostructures are the
most elementary objects in the quantum state control. Great progress has been made in
the last decade in the research of optical properties, relaxation and decoherence processes
in nanostructures. At the same time, the electron spin or the nuclear spin in semiconductors
is very promising to manipulate the quantum coherence due to their long coherence
times. The electron spin is reflected in the exciton polarization properties. The hyperfine
interaction between the electron spin and the nuclear spin would be enhanced due to the
quantum confinement of the electron wavefunction. Many interesting phenomena related
to this interaction have been discovered recently.
In addition to the enhanced exciton effect, the Coulomb interaction in semiconductor
nanostructures leads to strong correlation among electrons and holes. Recently, it has
been revealed that many-body interactions among carriers have specific spectral and
temporal signatures in nonlinear optical responses. As a consequence, new ultrafast
vi Preface
spectroscopic techniques combined with microscopic many-body theory have brought
dramatic progress in the study of many-body Coulomb interactions both in bulk and in
quantum confined structures. In particular, the role of Coulomb correlation among more
than two particles has been beautifully revealed in the last several years.
Another recent highlight in the nanostructure optics is the physics of microcavity
polariton. The striking aspect is the tunability of the exciton-photon coupling strength
from the weak perturbative regime to the strong normal mode coupling regime. Recent
experiments have revealed many interesting aspects of the nonlinear optical processes
associated with microcavity polaritons. Especially, the composite nanocrystal-microcavity
system is promising to realize the entangled states among several nanocrystals through
the whispering gallery modes in the strong coupling regime. Such an entangled state is
an indispensable step toward the quantum information processing. On the other hand, in
the weak or intermediate coupling regime of the light-matter interaction, there appears
an interesting feature in the resonant secondary emission, e.g. the coexistence of the
coherent part (Rayleigh scattering) and the incoherent part (photoluminescence) and the
interplay of disorder and polaritonic effects.
Last but not least, there is a fundamental interest in the ultrafast coherent phenomena
both in bulk semiconductors and in semiconductor nanostructures. The coherent nonlinear
pulse propagation and the carrier-wave Rabi flopping have been observed successfully
in the case of extremely strong pulse intensities. These studies have revealed a new
paradigm of the coherent light-matter interaction. Fundamentally new high-field effects
in semiconductor nanostructures have been predicted and are now being tested
experimentally.
The understanding of fundamental physics aspects of the optical coherence and
the spin coherence is now being revolutionized. This revolutional progress would bring
about breakthroughs in the field of the quantum information processing. In view of
these rapidly growing fields of research, we believe that it is timely to publish a book
which surveys the present status of our understanding of the quantum coherence, correlation
and decoherence in semiconductor nanostructures, putting emphasis on the basic physics
aspects.
Kyoto, Japan T. Takagahara
October 2002
List of Contributors
Numbers in parentheses indicate the pages on which the authors’ contributions begin.
S.R. Bolton (166), Physics Department, Williams College, 33 Lab Campus Drive,
Williamstown, MA 01267, USA
A.S. Bracker (207), Naval Research Laboratory, Washington, DC 20375, USA
Gang Chen (281), Harrison M. Randall Laboratory of Physics, University of Michigan,
Ann Arbor, MI 48109-1120, USA
Pochung Chen (281), Department of Physics, University of California San Diego, La
Jolla, CA 92093, USA
Al.L. Efros (207), Naval Research Laboratory, Washington, DC 20375, USA
J. Förstner (1), Institut für Theoretische Physik, Technische Universität Berlin,
D-10623 Berlin, Germany
D. Gammon (207, 281), Naval Research Laboratory, Washington, DC 20375, USA
H. Giessen (1), Department of Physics and Material Sciences Center, Philipps-Universität,
D-35032 Marburg, Germany
J.R. Guest (281), Harrison M. Randall Laboratory of Physics, University of Michigan,
Ann Arbor, MI 48109-1120, USA
S. Hughes (40), Department of Physics, University of Surrey, Guildford, Surrey GU2
7XH, UK
A. Knorr (1), Institut für Theoretische Physik, Technische Universität Berlin, D-10623
Berlin, Germany
S.W. Koch (1), Department of Physics and Material Sciences Center, Philipps-Universität,
D-35032 Marburg, Germany
V.L. Korenev (207), A.F. Ioffe Institute, St Petersburg, Russia
J. Kuhl (1), Max-Planck-Institut für Festkörperforschung, D-70569 Stuttgart, Germany
S. Linden (1), Max-Planck-Institut für Festkörperforschung, D-70569 Stuttgart, Germany
I.A. Merkulov (207), A.F. Ioffe Institute, St Petersburg, Russia
O.D. Mücke (23), Institut für Angewandte Physik, Universität Karlsruhe (TH), Wolfgang-
Gaede-Straße 1, 76131 Karlsruhe, Germany
N.C. Nielsen (1), Max-Planck-Institut für Festkörperforschung, D-70569 Stuttgart,
Germany
viii List of Contributors
C. Piermarocchi (281), Department of Physics, University of California San Diego, La
Jolla, CA 92093, USA
E. Runge (89), Humboldt University Berlin, Hausvogteiplatz 5-7, D-10117 Berlin,
Germany; Max Planck Institute for the Physics of Complex Systems, Nöthnitzer
Str. 38, D-01187 Dresden, Germany
V. Savona (89), Humboldt University Berlin, Hausvogteiplatz 5-7, D-10117 Berlin,
Germany
L.J. Sham (281), Department of Physics, University of California San Diego, La Jolla,
CA 92093, USA
D.G. Steel (281), Harrison M. Randall Laboratory of Physics, University of Michigan,
Ann Arbor, MI 48109-1120, USA
T.H. Stievater (281), Harrison M. Randall Laboratory of Physics, University of Michigan,
Ann Arbor, MI 48109-1120, USA
T. Takagahara (395), Department of Electronics and Information Science, Kyoto Institute
of Technology, Matsugasaki, Sakyo-ku, Kyoto 606-8585, Japan
J.G. Tischler (207), Naval Research Laboratory, Washington, DC 20375, USA
T. Tritschler (23), Institut für Angewandte Physik, Universität Karlsruhe (TH), Wolfgang-
Gaede-Straße 1, 76131 Karlsruhe, Germany
M. Wegener (23), Institut für Angewandte Physik, Universität Karlsruhe (TH), Wolfgang-
Gaede-Straße 1, 76131 Karlsruhe, Germany
Hailin Wang (366), Department of Physics and Oregon Center for Optics, University
of Oregon, Eugene, OR 97403, USA
R. Zimmermann (89), Humboldt University Berlin, Hausvogteiplatz 5-7, D-10117
Berlin, Germany
Contents
Preface..............................................................................................................................v
List of Contributors ...................................................................................................... vii
Chapter 1
Coherent nonlinear pulse propagation on a free-exciton
resonance in a semiconductor
N.C. Nielsen, S. Linden, J. Kuhl, J. Förstner, A. Knorr,
S.W. Koch, and H. Giessen
1.1 Introduction ...........................................................................................................1
1.2 Theoretical background.........................................................................................2
1.3 Samples and experimental techniques..................................................................6
1.4 Results and discussion..........................................................................................8
Excitation-induced suppression of temporal polariton beating......................8
Self-induced transmission and multiple pulse breakup................................10
Phonon-induced dephasing of the excitonic polarization.............................17
1.5 Conclusions .........................................................................................................18
Acknowledgments...........................................................................................19
References.......................................................................................................19
Chapter 2
Carrier-wave Rabi flopping in semiconductors
O.D. Mücke, T. Tritschler, and M. Wegener
2.1 Introduction .........................................................................................................23
2.2 Carrier-wave Rabi flopping ................................................................................25
Experiments ....................................................................................................27
Theory.............................................................................................................32
2.3 Conclusions .........................................................................................................37
