Propagation of nonclassical light in structured media [Elektronische Ressource] / von Dmytro Vasylyev

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• Physik

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• Publié par: universitat_rostock
• Publié le: 01 janvier 2009
• Nombre de lectures: 47
• Langue: English
• Poids de l'ouvrage: 1 Mo

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Propagation of nonclassical light in
structured media
Dissertation
Zur Erlangung des akademischen Grades
Doctor rerum naturalium (Dr. rer. nat.)
Vorgelegt der
Mathematisch-Naturwissenschaftlichen Fakult¨at
der Universit¨at Rostock
Von Dmytro Vasylyev
geboren am 04.02.1982 in Winnitsa (Ukraine)URN: urn:nbn:de:gbv:28-diss2009-0213-8
Gutachter: Prof. Dr. Werner Vogel, Institut fu¨r Physik,
Universit¨at Rostock
Prof. Dr. Klaus Henneberger, Institut fu¨r
Physik, Universit¨at Rostock
Prof. Dr. Andreas Knorr, Institut fu¨r Theore-
tische Physik, Technische Universit¨at Berlin
Rostock, den 17. Juni 2009Thanks
I want to thank Prof. Dr. Werner Vogel very much for the opportu-
nity to work with him. The very nice and fruitful discussions with him
helpedmetogetadeeperinsightintomanycurrentprobleminthefield
of quantum optics. I am very thankful to Prof. Dr. Klaus Henneberger
and Dr. Andrey Semenov for the scientific collaboration and profitable
discussions. I am also very grateful to all my colleagues and collabora-
tors of the Quantum Optics groups in Rostock and in Jena and to my
colleagues from Bogolubov Institute of Theoretical Physics in Kiev, in
particular Prof. Dr. Dirk-Gunnar Welsch and Prof. Dr. Bohdan Lev for
effective collaboration and scientific consulting. I am also very grate-
ful to Dr. Gu¨nter Manzke, Felix Richter, Dr. Tim Schmielau, and Dr.
EvgenyShchukinfordiscussingphysicalandotherproblemsandforthe
agreeabletimespenttogetherinRostock. LastbutnotleastIalsowant
to thank my wife and daughter who have greatly supported me many
times.Contents
Introduction 1
1 Light-Matter Interaction and Nonclassical Light 7
1.1 Green’s functions and sources . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.1.1 Nonequilibrium Green’s functions . . . . . . . . . . . . . . . . . . . 10
1.1.2 Dyson equations and medium characteristics . . . . . . . . . . . . . 15
1.2 Quantum coherence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.2.1 Quasi-probability distributions . . . . . . . . . . . . . . . . . . . . . 21
1.2.2 Example of squeezed light generation in parametric optical process 23
1.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2 Nonclassicality of Quantum Systems 29
2.1 Characterization of nonclassicality . . . . . . . . . . . . . . . . . . . . . . . 30
2.2 Noisy quantum states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.2.1 Quantum state of a noisy system . . . . . . . . . . . . . . . . . . . 32
2.2.2 Testing the nonclassicality with unbalanced homodyning . . . . . . 38
2.2.3 An example: Fock state . . . . . . . . . . . . . . . . . . . . . . . . 39
2.3 Realistic optical cavities . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.3.1 Unwanted noise and replacement schemes . . . . . . . . . . . . . . 41
2.3.2 Noise-induced mode coupling . . . . . . . . . . . . . . . . . . . . . 43
2.3.3 Unbalanced and cascaded homodyne detection and quantum-state
reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3 Propagation of Nonclassical Light 51
3.1 Light interacting with semiconductors . . . . . . . . . . . . . . . . . . . . . 52
3.2 Light propagation in bounded media . . . . . . . . . . . . . . . . . . . . . 56
3.3 Restriction to the slab geometry . . . . . . . . . . . . . . . . . . . . . . . . 60
3.4 An exact property of photon GFs . . . . . . . . . . . . . . . . . . . . . . . 64
iCONTENTS CONTENTS
3.5 Dielectric properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.6 Propagation of squeezed light . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
Summary 75
Appendices: 77
A Functional integration 79
B Perturbative expansions and Feynman diagrams 83
C S-Matrix and the input-output relations 95
D Poynting’s theorem for bounded media 101
E Evaluation of some photon Green’s functions 105
iiIntroduction
Introduction
The fundamental objects of study of the contemporary theoretical physics are quantum
fields and their interactions. The gauge field theory within the standard model of particle
interactions establishes the relationship between the electromagnetic, weak and strong
interactions. The great challenge for the theoretical physics of our days is to extend the
standard model in order to include gravitation as well.
The electromagnetic interactions are a source of forces in a vast number of physical
systems, and accordingly deserve to be singled out. The quantum theory of these inter-
actions, called quantum electrodynamics, underlies the foundations of most modern areas
of physics. Optics and electrodynamics, atomic and molecular physics, the solid-state
physics and physics of fluids, gases, and plasmas are all special applications of quantum
electrodynamics. In all these areas of physics the first and foremost important object of
study is the electromagnetic field and its interaction with particles or other fields.
Quantum opticsoriginatesfromthelowenergy sectorofquantumelectrodynamics and
deals merely with the phenomena in the energy range of optical waves and microwaves,
i.e., in an energy range where the relativistic effects can be neglected. Moreover, due
to the coherent properties of a large number of these phenomena, the classical theory
of the electromagnetic field can be successfully applied for their description in a good
approximation degree.
The main research area of quantum optics is the study of light-matter interaction,
at a microscopic level of understanding. The characterization of light-matter coupling
requires the use of quantum theory, which can be used to describe the electromagnetic
field, and also the matter itself. But there exist some less sophisticated approaches for the
descriptionoflightinteractionwithmatterthatcangiveabetterinsightintothephysicsof
processes that supplement this interaction. For some particular systems the semiclassical
approach (the field treated classically and the matter – quantum mechanically) to the
problem is more favorable than the fully quantum one. For example, R. Glauber [1] has
showninearly60’sthattheinteractionofmatterwiththecoherentlightfromtheperfectly
stabilized laser can be described semiclassically by representing the field amplitude by the
so-called coherent states. A coherent state is defined as a specific kind of quantum state
of the quantum harmonic oscillator that describes a maximal kind of coherence and a
classical kind of behavior. Another example of electromagnetic field whose dynamics can
be treated classically is the thermal radiation. This radiation was modeled in the early
daysofquantumtheorybyanensemble ofclassical, radiatingharmonicoscillatorsinorder
to describe the black body radiation [2].
Since quantum optics is a closest descendant of quantum electrodynamics it inherited
1Introduction
also the whole mathematical apparatus of the latter. Among the various mathematical
toolstheformalismofGreen’s functions(i.e., correlationfunctions ofradiationandmatter
fields)playanoutstandingrole. Indeed,inquantumoptics,theusuallyconsideredphysical
quantities are the electromagnetic fields; in addition to their macroscopic averages, their
correlations and their fluctuations due to the underlying quantum character of the states
are of great relevance. On the other hand, for the description of the dynamics of these
correlations and fluctuations of interacting electromagnetic fields the knowledge of the
medium correlation functions is usually required. Therefore, Green’s functions (GFs) are
perfectly suited for purposes of quantum optics. The formalism of Green’s functions has
been applied successfully in atomic quantum optics [3], in nonlinear quantum optics [4],
quantum optics of dielectrics and semiconductors [5], to name just a few.
Another area of quantum optics involves nonclassical light, such as squeezed states
of light, having unusual quantum noise properties. By nonclassical light is meant a light
whoseobservedpropertiescannotbedescribedwithcustomaryvisualizationbyconsidering
a light beam as a set of waves. In other terms, the nonclassical light produces effects
that have no classical analogies. Usually, the nonclassicality manifests itself in specific
properties of quantum statistics, which sometimes cannot be described in the framework
of the probability theory [6]. Usually the nonclassical light is generated in the nonlinear
optical processes and in contrast to the classical fields the interaction of such a field with
matter should be performed fully quantum mechanically.
Recent years have witnessed a flowering of theoretical and experimental interest in the
nonclassical properties of the radiation field. New technical possibilities led to the direct
experimental realization of large variety of nonclassical quantum states of the electromag-
netic field. Starting from the first realization of squeezed radiation in four-wave mixing
experiments by the group of R. E. Slusher [7], in the last 20 years dozens of new quantum
states have been produced. Among them are the famous Schr¨odinger cat states [8], single
photon states [9], multi-quantum Fock states [10], to name just