Along with the growing interest in using the transverse-spatial modes of light in quantum and classical optics applications, developing an accurate and efficient measurement method has gained importance. Here, we present a technique relying on a unitary mode conversion for measuring any full-field transverse-spatial mode. Our method only requires three consecutive phase modulations followed by a single mode fiber and is, in principle, error-free and lossless. We experimentally test the technique using a single spatial light modulator and achieve an average error of 4.2 % for a set of 9 different full-field Laguerre-Gauss and Hermite-Gauss modes with an efficiency of up to 70%. Moreover, as the method can also be used to measure any complex superposition state, we demonstrate its potential for quantum cryptography applications and in high-dimensional quantum state tomography.
Along with the growing interest in using the transverse-spatial modes of light in quantum and classical optics applications, developing an accurate and efficient measurement method has gained importance. Here, we present a technique relying on a unitary mode conversion for measuring any full-field transverse-spatial mode. Our method only requires three consecutive phase modulations followed by a single mode fiber and is, in principle, error-free and lossless. We experimentally test the technique using a single spatial light modulator and achieve an average error of 4.2 % for a set of 9 different full-field Laguerre-Gauss and Hermite-Gauss modes with an efficiency of up to 70%. Moreover, as the method can also be used to measure any complex superposition state, we demonstrate its potential for quantum cryptography applications and in high-dimensional quantum state tomography.
With the emergence of the field of quantum communications, the appropriate choice of photonic degrees of freedom used for encoding information is of paramount importance. Highly precise techniques for measuring the polarisation, frequency, and arrival time of a photon have been developed. However, the transverse spatial degree of freedom still lacks a measurement scheme that allows the reconstruction of its full transverse structure with a simple implementation and a high level of accuracy. Here we show a method to measure the azimuthal and radial modes of Laguerre-Gaussian beams with a greater than 99 % accuracy, using a single phase screen. We compare our technique with previous commonly used methods and demonstrate the significant improvements it presents for quantum key distribution and state tomography of high-dimensional quantum states of light. Moreover, our technique can be readily extended to any arbitrary family of spatial modes, such as mutually unbiased bases, Hermite-Gauss, and Ince-Gauss. Our scheme will significantly enhance existing quantum and classical communication protocols that use the spatial structure of light, as well as enable fundamental experiments on spatial-mode entanglement to reach their full potential.
Structure photons invoke interesting fundamental properties and enable novel applications, e.g. their use as high-dimensional quantum states, which are known to be beneficial in various quantum information tasks. However, to use their full potential the ability to perform any unitary operations is indispensable. Here, we present a scheme to perform arbitrary unitary operation for all transverse spatial modes, i.e. a so-called multiport for high-dimensional quantum states. We realize it by using multiple consecutive phase modulations, which are designed by wave front matching techniques. At first, we perform near-perfect measurements of full-field modes, i.e. modes with an azimuthal and radial structure [1]. Our method only requires three consecutive phase modulations followed by a single mode fiber and is, in principle, error-free and lossless. We achieve an average error of 4.2% for a set of 9 different full-field Laguerre-Gauss and Hermite-Gauss modes with an efficiency of up to 70%. We further demon-strate its potential in a quantum cryptography protocol and in high-dimensional quantum state tomography. We then use the multiport to implement high-dimensional quantum gates [2], such as cyclic and quantum Fourier transformations, known as Pauli X-gates and Hadamard H-gates, respectively. We achieve an aver-age visibility of more than 90% for dimensions up to 5 and obtain a process purity of 99% by means of a full quantum process tomography. We also demonstrate the benefit of the two independent spatial degrees of freedom, i.e. azimuthal and radial, and implement a two-qubit controlled-NOT quantum operation on a single photon. Using more efficient phase modulations will pave the way to novel multi-particle high-dimensional quantum information experiments. [1] M. Hiekkamäki, S. Prabhakar, R. Fickler, Near-perfect measuring of full-field transverse-spatial modes of light, arXiv:1909.01685 [2] F. Brandt, M. Hiekkamäki, F. Bouchard, M. Huber, R. Fickler, High-dimensional quantum gates using full-field spatial modes of photons, arXiv:1907.13002
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. \n \nIn 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). \n \nThis 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. \n \nWith 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.
As the generation of squeezed states of light has become a standard technique in laboratories, attention is increasingly directed towards adapting the optical parameters of squeezed beams to the specific requirements of individual applications. It is known that imaging, metrology, and quantum information may benefit from using squeezed light with a tailored transverse spatial mode. However, experiments have so far been limited to generating only a few squeezed spatial modes within a given setup. Here, we present the generation of single-mode squeezing in Laguerre-Gauss and Bessel-Gauss modes, as well as an arbitrary intensity pattern, all from a single setup using a spatial light modulator (SLM). The degree of squeezing obtained is limited mainly by the initial squeezing and diffractive losses introduced by the SLM, while no excess noise from the SLM is detectable at the measured sideband. The experiment illustrates the single-mode concept in quantum optics and demonstrates the viability of current SLMs as flexible tools for the spatial reshaping of squeezed light.
As the generation of squeezed states of light has become a standard technique in laboratories, attention is increasingly directed towards adapting the optical parameters of squeezed beams to the specific requirements of individual applications. It is known that imaging, metrology, and quantum information may benefit from using squeezed light with a tailored transverse spatial mode. However, experiments have so far been limited to generating only a few squeezed spatial modes within a given setup. Here, we present the generation of single-mode squeezing in Laguerre-Gauss and Bessel-Gauss modes, as well as an arbitrary intensity pattern, all from a single setup using a spatial light modulator (SLM). The degree of squeezing obtained is limited mainly by the initial squeezing and diffractive losses introduced by the SLM, while no excess noise from the SLM is detectable at the measured sideband. The experiment illustrates the single-mode concept in quantum optics and demonstrates the viability of current SLMs as flexible tools for the spatial reshaping of squeezed light. (C) 2016 Optical Society of America
Unitary transformations are the fundamental building blocks of gates and operations in quantum information processing, allowing the complete manipulation of quantum systems in a coherent manner. In the case of photons, optical elements that can perform unitary transformations are readily available only for some degrees of freedom, e.g., wave plates for polarization. However, for high-dimensional states encoded in the transverse spatial modes of light, performing arbitrary unitary transformations remains a challenging task for both theoretical proposals and actual implementations. Following the idea of multi-plane light conversion, we show that it is possible to perform a broad variety of unitary operations at high quality by using only a few phase modulation planes. More importantly, we experimentally implement several high-dimensional quantum gates for up to five-dimensional states encoded in the full-field mode structure of photons. In particular, we realize cyclic and quantum Fourier transformations, known as Pauli X ^ -gates and Hadamard H ^ -gates, respectively, with an average visibility of more than 90%. In addition, we demonstrate near-perfect “unitarity” by means of quantum process tomography, unveiling a process purity of 99%. Last, we demonstrate the benefit of the two independent spatial degrees of freedom, i.e., azimuthal and radial, and implement a two-qubit controlled-NOT quantum operation on a single photon. Thus, our demonstrations open up new paths to implement high-dimensional quantum operations, which can be applied to various tasks in quantum communication, computation, and sensing schemes.