99 research outputs found
On Small Beams with Large Topological Charge II: Photons, Electrons and Gravitational Waves
Beams of light with a large topological charge significantly change their
spatial structure when they are focused strongly. Physically, it can be
explained by an emerging electromagnetic field component in the direction of
propagation, which is neglected in the simplified scalar wave picture in
optics. Here we ask: Is this a specific photonic behavior, or can similar
phenomena also be predicted for other species of particles? We show that the
same modification of the spatial structure exists for relativistic electrons as
well as for focused gravitational waves. However, this is for different
physical reasons: For electrons, which are described by the Dirac equation, the
spatial structure changes due to a Spin-Orbit coupling in the relativistic
regime. In gravitational waves described with linearized general relativity,
the curvature of space-time between the transverse and propagation direction
leads to the modification of the spatial structure. Thus, this universal
phenomenon exists for both massive and massless elementary particles with Spin
1/2, 1 and 2. It would be very interesting whether other types of particles
such as composite systems (neutrons or C) or neutrinos show a similar
behaviour and how this phenomenon can be explained in a unified physical way.Comment: 8 pages, 3 figure
Physical meaning of the radial index of Laguerre-Gauss beams
The Laguerre-Gauss modes are a class of fundamental and well-studied optical
fields. These stable, shape-invariant photons - exhibiting circular-cylindrical
symmetry - are familiar from laser optics, micro-mechanical manipulation,
quantum optics, communication, and foundational studies in both classical
optics and quantum physics. They are characterized, chiefly, by two modes
numbers: the azimuthal index indicating the orbital angular momentum of the
beam - which itself has spawned a burgeoning and vibrant sub-field - and the
radial index, which up until recently, has largely been ignored. In this
manuscript we develop a differential operator formalism for dealing with the
radial modes in both the position and momentum representations, and - more
importantly - give for the first time the meaning of this quantum number in
terms of a well-defined physical parameter: the "intrinsic hyperbolic momentum
charge".Comment: 12 pages, 4 figures, comments encourage
Quantum gate description for induced coherence without induced emission and related phenomena
We introduce unitary quantum gates for photon pair creation in spontaneous
parametric down-conversion nonlinear crystals (NLs) and for photon path
alignment. These are the two key ingredients for the method of "induced
coherence without induced emission" and many ensuing variations thereof. The
difficulty in doing so stems from an apparent mixing of the mode picture (such
as the polarization of photons) and the Fock picture (such as the existence of
the photons). We illustrate utility of these gates by obtaining quantum
circuits for the experimental setups of the frustrated generation of photon
pairs, identification of a point-like object with undetected photons, and
creation of a Bell state. We also introduce an effective nonunitary description
for the action of NLs in experiments where all the NLs are pumped coherently.
As an example, by using this simplifying picture, we show how NLs can be used
to create superposition of given quantum states in a modular fashion.Comment: 4+3 page
Quantifying high dimensional entanglement with two mutually unbiased bases
We derive a framework for quantifying entanglement in multipartite and high
dimensional systems using only correlations in two unbiased bases. We
furthermore develop such bounds in cases where the second basis is not
characterized beyond being unbiased, thus enabling entanglement quantification
with minimal assumptions. Furthermore, we show that it is feasible to
experimentally implement our method with readily available equipment and even
conservative estimates of physical parameters.Comment: 17 pages, 1 figur
Quantum Experiments and Graphs: Multiparty States as coherent superpositions of Perfect Matchings
We show a surprising link between experimental setups to realize
high-dimensional multipartite quantum states and Graph Theory. In these setups,
the paths of photons are identified such that the photon-source information is
never created. We find that each of these setups corresponds to an undirected
graph, and every undirected graph corresponds to an experimental setup. Every
term in the emerging quantum superposition corresponds to a perfect matching in
the graph. Calculating the final quantum state is in the complexity class
#P-complete, thus cannot be done efficiently. To strengthen the link further,
theorems from Graph Theory -- such as Hall's marriage problem -- are rephrased
in the language of pair creation in quantum experiments. We show explicitly how
this link allows to answer questions about quantum experiments (such as which
classes of entangled states can be created) with graph theoretical methods, and
potentially simulate properties of Graphs and Networks with quantum experiments
(such as critical exponents and phase transitions).Comment: 6+5 pages, 4+7 figure
Questions on the Structure of Perfect Matchings inspired by Quantum Physics
We state a number of related questions on the structure of perfect matchings.
Those questions are inspired by and directly connected to Quantum Physics. In
particular, they concern the constructability of general quantum states using
modern photonic technology. For that we introduce a new concept, denoted as
inherited vertex coloring. It is a vertex coloring for every perfect matching.
The colors are inherited from the color of the incident edge for each perfect
matching. First, we formulate the concepts and questions in pure
graph-theoretical language, and finally we explain the physical context of
every mathematical object that we use. Importantly, every progress towards
answering these questions can directly be translated into new understanding in
quantum physics.Comment: 10 pages, 4 figures, 6 questions (added suggestions from peer-review
On Small Beams with Large Topological Charge
Light beams can carry a discrete, in principle unbounded amount of angular
momentum. Examples of such beams, the Laguerre-Gauss modes, are frequently
expressed as solutions of the paraxial wave equation. There, they are
eigenstates of the orbital angular momentum (OAM) operator. The paraxial
solutions predict that beams with large OAM could be used to resolve
arbitrarily small distances - a dubious situation. Here we show how to solve
that situation by calculating the properties of beams free from the paraxial
approximation. We find the surprising result that indeed one can resolve
smaller distances with larger OAM, although with decreased visibility. If the
visibility is kept constant (for instance at the Rayleigh criterion, the limit
where two points are reasonably distinguishable), larger OAM does not provide
an advantage. The drop in visibility is due to a field in the direction of
propagation, which is neglected within the paraxial limit.Comment: 6 pages, 2 figures; + supplementary informatio
Explaining strategic firm responsiveness to institutional processes in the evolution of corporate governance systems : the reform of director remuneration reporting in Germany
Due to economic and social globalization processes, the boundaries of national systems of corporate governance have become more permeable for the transfer of ideas and practices from other institutional contexts. I derive hypotheses from a multitheoretical framework to explain strategic firm responsiveness to national level pressures for corporate governance reform. This framework integrates institutional, resource dependence, social network, upper echelon, and organizational learning perspectives and portrays corporate governance reform as institutional change. I test hypotheses derived from this framework in the context of the issuance of the German corporate governance code. The code provision of interest recommends that German firms listed on the Frankfurt stock exchange publish a comprehensive director remuneration report for their management and supervisory boards, a practice that is arguably at odds with the traditional regulative, normative, and cognitive-cultural institutional pillars of the German corporate governance system. A unique longitudinal dataset of 189 stock exchange listed firms is used to explain strategic firm responsiveness to the issuance of this institutionally contested provision. In this context, this dissertation is the first study that (partly) operationalizes Oliver\u27s (1991) continuum of strategic responses to institutional processes. The findings reveal that in contrast to arguments advanced by financial economists and legal scholars, economic market forces do not significantly drive firms\u27 responsiveness to corporate governance reform pressures. Instead, firm ownership type and power, labor representatives, management characteristics, and different intra- and interorganizational learning processes are significant predictors of strategic firm responsiveness to national level corporate governance reform pressures. The findings generally provide support for the developed theoretical framework and help corporate governance research to expand beyond the traditional legal and financial economics perspective
Quantum Experiments and Graphs III: High-Dimensional and Multi-Particle Entanglement
Quantum entanglement plays an important role in quantum information
processes, such as quantum computation and quantum communication. Experiments
in laboratories are unquestionably crucial to increase our understanding of
quantum systems and inspire new insights into future applications. However,
there are no general recipes for the creation of arbitrary quantum states with
many particles entangled in high dimensions. Here, we exploit a recent
connection between quantum experiments and graph theory and answer this
question for a plethora of classes of entangled states. We find experimental
setups for Greenberger-Horne-Zeilinger states, W states, general Dicke states,
and asymmetrically high-dimensional multipartite entangled states. This result
sheds light on the producibility of arbitrary quantum states using photonic
technology with probabilistic pair sources and allows us to understand the
underlying technological and fundamental properties of entanglement.Comment: 7 pages, 7 figures; Appendix 3 pages, 5 figure
Gouy Phase Radial Mode Sorter for Light: Concepts and Experiments
We present an in principle lossless sorter for radial modes of light, using
accumulated Gouy phases. The experimental setups have been found by a computer
algorithm, and can be intuitively understood in a geometric way. Together with
the ability to sort angular-momentum modes, we now have access to the complete
2-dimensional transverse plane of light. The device can readily be used in
multiplexing classical information. On a quantum level, it is an analog of the
Stern-Gerlach experiment -- significant for the discussion of fundamental
concepts in quantum physics. As such, it can be applied in high-dimensional and
multi-photonic quantum experiments.Comment: main text: 7 pages, 5 figures. Supplementary Information: 5 pages, 4
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