# Quantum interference, complementarity and entanglement

Abstract (Summary)

A fundamental entity in quantum mechanics is the quantum mechanical state.
The only connection between the theory of quantum mechanics and our observable
world is provided by state measurements, and in this interference between
quantum states plays a key role.
Recent interference experiments probing the world of quantum mechanics
have started to resolve paradoxes and give new insights. While the classical
concepts of phase and polarization are well established, the understanding of
their quantum mechanical counterparts is not complete. While examining those
concepts the increased understanding of quantum interference give risetonew
applications: In quantum cryptography, secure (protected by the laws of physics)
secret quantum key distribution has been set-up between places tens of kilometers
apart. Quantum computers can be viewed as complex quantum interferometers.
This emerging technique anticipates the construction of a new class of computers
that can process data (superposition states) in parallel. Certain algorithms exist
that can solve problems that groves exponentially for classical computers on a
much faster polynomial growing time using quantum computers.
The thesis is focused on the generation and detection of some non-classical
few-photon states, and in particular on entangled states. A common aspect between
the experiments of the thesis is the use of quantum interference. In paper
A, the complementary wave-particle duality of light is examined. Paper B, C
and D implements relative phase and polarization rotation experiments based
on analogous theories. Using two photons, three orthogonal states of the relative
phase operator and the polarization rotation operator can be generated.
The techniques give a linear increase of the sensitivity of relative phase shifts
and polarization rotations with the number of available photons. The sensitivity
of classical measurement techniques are limited to the square of the number
of available photons. Paper E uses the complementary wave-particle duality of
light inaninterference experiment. The technique called interaction free measurements
enables (at least in principle) the perfect detection of an absorbing
object without the object absorbing any photon. Our method is based on the
principle that a Fabry Perot interferometer tuned to resonance transmits an impinging
photon. In contrast, when placing an object between the mirrors of the
Fabry Perot Interferometer, the impinging photon will be re ected from the rst
mirror. This technique using quantum objects could be used to produce entangled
multi-photon states that can be used to improve the schemes of papers A,
B, C, and D by going to an higher manifold (using a higher number of photons).
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Preface
This thesis is divided into three parts. Part I contains of ve chapters that
introduce the reader into the aspects of quantum optics considered in the original
work. There are no new results in these chapters. Instead, I have written these
chapters to give anintuitive and simpli ed background of the research areain
order to give anintroduction to the original work. Most of the contents could
be refereed to as \common knowledge
"
in the quantum optics community, and
other parts come from the cited sources.
In Part II I give a review of the new theory and the experimental setups that
are presented in the thesis. The relationship between the various experiments is
also shown in greater detail.
Part III contains two chapters. In chapter 9, a summary of the each paper
in the original work is provided, including a description of my own contribution.
The focus has been put on the scienti c relevance of the results and on the
relation to the work of other groups. Finally conclusions of the work are drawn
in chapter 10.
The scienti c news, that is, my contribution, through my thesiswork to the
scienti c progress, is found in the original work. The reprinted papers are found
at the end of the thesis.
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Bibliographical Information:

Advisor:

School:Kungliga Tekniska högskolan

School Location:Sweden

Source Type:Doctoral Dissertation

Keywords:

ISBN:91-7170-581-3

Date of Publication:01/01/2000