Large quantum photonic systems hold promise for surpassing classical computational limits, yet their state preparation remains a challenge. We propose an alternative approach to study multiparticle dynamics by mapping the excitation mode of these systems to physical properties of the Laguerre-Gauss modes. We construct coherent states establishing a direct link between excitation number dynamics and the evolution of the Laguerre-Gauss modes. This highlights the photon transverse spatial degree of freedom as a versatile platform for testing the fundamental aspects of quantum multiparticle systems.
Large quantum photonic systems hold promise for surpassing classical computational limits, yet their state preparation remains a challenge. We propose an alternative approach to study multiparticle dynamics by mapping the excitation mode of these systems to physical properties of the Laguerre-Gauss modes. We construct coherent states establishing a direct link between excitation number dynamics and the evolution of the Laguerre-Gauss modes. This highlights the photon transverse spatial degree of freedom as a versatile platform for testing the fundamental aspects of quantum multiparticle systems.
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.
The field of high-dimensional quantum photonics involves the use of multimode photonic degrees-of-freedom such as the spatial, temporal, or spectral structure of light to encode multi-level quantum states. Recent years have seen rapid progress in the development of methods to generate, manipulate, and distribute such quantum states of light and their use in a range of quantum technology applications that offer practical advantages over conventional qubit-based approaches. High-dimensional quantum states of light encoded in photonic time-bins, frequency-bins, transverse-spatial modes, waveguide paths, and temporal modes have enabled noise-robust fundamental tests of quantum mechanics, error-resilient and high-capacity quantum communication protocols, andas well as efficient approaches for quantum information processing, to name just a few examples. However, research in this field has progressed fairly independently, with little exchange across different photonic degrees-of-freedom or between experiment and theory and no comprehensive comparison between degrees-of-freedom. This roadmap aims to bridge this gap by surveying progress in each area and identifying shared challenges and opportunities that cut across two or more photonic degrees-of-freedoms. We review early work and state-of-the-art experimental techniques under development for high-dimensional quantum states encoded in single and entangled photons, as well as theoretical tools for their measurement and certification. We outline the main outstanding challenges for theory and each experimental degree-of-freedom, identifying promising future directions of research that may enable these to be overcome. We end by discussing interconnections and shared challenges centered around their distribution, measurement, and manipulation, with a view towards their integration into next-generation quantum technology platforms and applications.
We use the spatial degree of freedom of light modes to construct optical analogs of generalized quantum coherent states for Hermite- and Laguerre--Gauss modes. Our optical analogs preserve the statistical properties of their quantum counterparts, encoded in their amplitude and phase distributions. We explore three basic symmetries that provide generalized displaced, rotated, and squeezed coherent states. Given the substantial interest in squeezed states for probing matter, we believe that the optical analogs introduced here have significant implications for optical sensing. Specifically, the single-particle nature of our spatial modes makes them robust candidates for sensing photosensitive materials. Overall, our approach opens the door to optical metrology and sensing protocols that mimic those already existing in the quantum realm, and facilitates further exploration of the quantum state zoo through classical optical analogs.
Spatially entangled twin photons allow the study of high-dimensional entanglement, and the Laguerre-Gauss modes are the most commonly used basis to discretize the single-photon mode spaces. In this basis, to date only the azimuthal degree of freedom has been investigated experimentally due to its fundamental and experimental simplicity. We show that the full spatial entanglement is indeed accessible experimentally; i.e., we have found practicable radial detection modes with negligible cross correlations. This allows us to demonstrate hybrid azimuthal-radial quantum correlations in a Hilbert space with more than 100 dimensions per photon.
Spatially structured photons have attracted a lot of attention in quantum photonics, where they often serve as powerful tools for investigating fundamental properties of light, and for realizing high-dimensional quantum states with beneficial properties in quantum information tasks such as cryptography or quantum simulations [1] . One way of describing any spatial structure, in the paraxial limit, is through orthogonal transverse-spatial modes e.g. Laguerre-Gaussian (LG) modes. A unique feature of higher order LG modes is their twisted phase front, to which a theoretically unbounded orbital angular momentum can be attributed.
A new era of technology is fast approaching in which quantum computation may be practically realized. In the near future, researchers may require a method of correlating two isolated quantum systems. This would require a signal carrier to be a quantum entity itself. We investigate the quantum states of photons as a medium for encoding information. A communication scheme using the modulation of spatial modes and polarization states in free space or fiber optics is proposed. The Laguerre-Gaussian spatial mode is studied with these applications in mind. We also study photographic slide as a means of creating diffraction gratings. Holographic diffraction gratings were created in order to generate Laguerre-Gauss beam modes of varying quantum number n. The spatial mode phase characteristics were studied with a Mach-Zehnder interferometer.