Unitary transformations of spatial modes for quantum experiments
Hiekkamäki, Markus (2019)
2019
Teknis-luonnontieteellinen DI-ohjelma - Degree Programme in Science and Engineering
Tekniikan ja luonnontieteiden tiedekunta - Faculty of Engineering and Natural Sciences
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Hyväksymispäivämäärä
2019-11-21
Julkaisun pysyvä osoite on
https://urn.fi/URN:NBN:fi:tuni-201911045708
https://urn.fi/URN:NBN:fi:tuni-201911045708
Tiivistelmä
Spatial modes have attracted a lot of attention in the quantum optics community because of their possible application in high-dimensional quantum bits, i.e. qudits. One crucial task in quantum communication and computation applications, is the ability to perform unitary transformations on these qudits. However, arbitrary unitary transformations between full-field spatial modes have not been realized so far. Thus, in order to bring spatial modes closer to communication and computation applications, methods for performing these transformations need to be devised.
In this thesis, we introduce a method for generating these unitary transformations. The method is based on multi-plane light conversion (MPLC), where the spatial structure of light is transformed through multiple consecutive transverse-phase modulations. The method we use for generating these task specific phase-modulations is called wavefront matching (WFM).
This thesis consists of three main sections. First, we will introduce some necessary theory behind high-dimensional quantum-states and single photons. We will also explore some theory behind the generation of single photons and introduce light's spatial modes in more detail. Second, we will introduce WFM along with other methods we needed for testing the unitary transformations experimentally. Finally, we will experimentally test the mode transformations in a spatial mode filter and in multi-mode transformations. We apply the mode filter in quantum key distribution (QKD) and quantum state tomography (QST) measurements, and we implement different high-dimensional quantum gates using the multi-mode transformations. Additionally, we introduce a method of potentially observing two-photon interference with these unitary transformations.
With the mode filter, we achieved error rates below five percent and in the QKD application we measured a theoretical data transmission rate of 1.98 bits per measured photon. With the quantum gates, we achieved accuracies of up to 98\% in all mutually unbiased bases (MUBs). The results shown in this thesis demonstrate the efficiency and unitarity of WFM in a broad set of different tasks. All the shown tasks are important in high-dimensional quantum communication and computation, and hence we believe that WFM will become an important tool in high-dimensional quantum information processing. We also give an outlook on how WFM could potentially be improved, and list some additional tasks, in which WFM could be useful. We believe that the broad applicability of WFM will enable some unexplored quantum information or photonics applications.
In this thesis, we introduce a method for generating these unitary transformations. The method is based on multi-plane light conversion (MPLC), where the spatial structure of light is transformed through multiple consecutive transverse-phase modulations. The method we use for generating these task specific phase-modulations is called wavefront matching (WFM).
This thesis consists of three main sections. First, we will introduce some necessary theory behind high-dimensional quantum-states and single photons. We will also explore some theory behind the generation of single photons and introduce light's spatial modes in more detail. Second, we will introduce WFM along with other methods we needed for testing the unitary transformations experimentally. Finally, we will experimentally test the mode transformations in a spatial mode filter and in multi-mode transformations. We apply the mode filter in quantum key distribution (QKD) and quantum state tomography (QST) measurements, and we implement different high-dimensional quantum gates using the multi-mode transformations. Additionally, we introduce a method of potentially observing two-photon interference with these unitary transformations.
With the mode filter, we achieved error rates below five percent and in the QKD application we measured a theoretical data transmission rate of 1.98 bits per measured photon. With the quantum gates, we achieved accuracies of up to 98\% in all mutually unbiased bases (MUBs). The results shown in this thesis demonstrate the efficiency and unitarity of WFM in a broad set of different tasks. All the shown tasks are important in high-dimensional quantum communication and computation, and hence we believe that WFM will become an important tool in high-dimensional quantum information processing. We also give an outlook on how WFM could potentially be improved, and list some additional tasks, in which WFM could be useful. We believe that the broad applicability of WFM will enable some unexplored quantum information or photonics applications.