A dissertation submitted in fulfillment of the requirements for the degree of Masters in Science in the, The Structured Light Group Department of Physics, University of the Witwatersrand, Johannesburg, 2018 / At the quantum level, entities and systems often behave counter-intuitively which we have
come to describe with wave-particle duality. Accordingly, a particle that moves definitively from
one position to another in our classical experience does something completely different on the
quantum scale. The particle is not localized at any one position, but spreads out over all the
possibilities as it moves. Here the particle can interfere with itself with wave-like propagation
and generate, what is known as a Quantum Walk. This is the quantum mechanical analogue of
the already well-known and used Random Walk where the particle takes random steps across the
available positions, building up a series of random paths.
The mechanics behind the random walk has already proved largely useful in many fields, from
finance to simulation and computation. Analogously, the quantum walk promises even greater
potential for development. Here, with many of the algorithms already developed, it would allow
computations to outperform current classical methods on an unprecedented level. Additionally,
by implementing these mechanics on various levels, it is possible to simulate and understand various quantum mechanical systems and phenomenon. This phenomenon consequently represents a
significant advancement in several fields of study.
Although there has been considerable theoretical development of this phenomenon, its potential now lies in implementing these quantum walks physically. Here, a physical system is required
such that the quantum walk may be sustainably achieved, easily detected and dynamically altered
as needed. Many systems have been subsequently proposed and demonstrated, but the criteria for
a useful quantum walk leaves many such avenues lacking with the largest number of steps yet to
reach 100 to the best of our knowledge. As a result, we explored a classical take on the quantum
walk, utilizing the wave properties of light to achieve analogous mechanics with the advantage of
the increased degree of control and robustness. While such an approach is not new, we considered
a particular method where the quantum walk could be implemented in the spatial modes of light.
By exploiting the non-separability (classical entanglement) of polarization and orbital angular momentum, such a classical quantum walk could be realized with greater intuitive implications and
the potential for further study into the quantum mechanical nature of this phenomenon, over and
above that of the other schemes, by walking the quantum-classical divide.
The work presented here subsequently centres on experimentally achieving a quantum walk
with classically entangled light for further development and useful implementation. Moreover,
this work focused on demonstrating the sustainability, control and robustness necessary for this
scheme to be beneficial for future development.
In Chapter 1, an intuitive introduction is presented, highlighting the mechanics of this phenomenon that make it different from the Random walk counterpart. We also explore why this
phenomenon is of such great importance with an overview of applications that physical implementation can result in. A more in-depth look into the dynamics and mathematical aspects of this
walk is found in Chapter 2. Here a detailed look into the mechanisms behind the walk is taken
with mathematical analysis. Furthermore, the subsequent differences and implications associated
viii
with utilizing classical light is explored, answering the question of what is quantum about the
quantum walk. As the focus of this chapter is largely cemented in establishing a solid theoretical
background, we also look into the physics behind classical light and develop the theoretical basis
in the direction of structured light, with an emphasis on establishing classically entangled beams.
Chapters 3 and 4 present the experimental work done throughout the course of this dissertation. With Chapter 3 we establish and characterize the elements necessary for obtaining a quantum
walk in the spatial modes of light by utilizing waveplates as coins, q-plates as step operators and
entanglement generators as well as mode sorters in a detection system. We also look into the
characteristics of the modes that will be produced with these elements, allowing the propagation
properties of the beam to be experimentally accounted for. In Chapter 4, we examine the experimental considerations of how to achieve a realistic and sustainable quantum walk. Here, we
consider and implement the scheme proposed by Goyal et. al. [] where a light pulse follows a
looped path, allowing the physical resources to be constant throughout the walk. We also show the
experimental limitations of the equipment being utilized and the various steps needed to compensate. Finally, we not only implement a quantum walk with classically entangled light for the first
time, but also demonstrate the flexibility of the system. Here, we achieve a maximum of 8 steps
and show 5 different types of walks with varying dynamics and symmetry.
The last chapter (Chapter 5) gives a summary of the dissertation in context of the goals and
achievements of this work. The outlook and implications of these results are discussed and future
steps outlined for extending this scheme into a highly competitive alternative for viable implementation of quantum walks for computing and simulation. / XL2019
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:wits/oai:wiredspace.wits.ac.za:10539/26899 |
| Date | January 2018 |
| Creators | Sephton, Bereneice B. |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | Online resource (xvii, 159 leaves), application/pdf |
Page generated in 0.0262 seconds