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New Journal of Physics

Exploiting the Poincaré–Bloch symmetry to design high-fidelity broadband composite linear retarders

Arzhang Ardavan

Published Feb 8, 2007• 31 citations
Publisher

Abstract

States can be mapped between the Poincaré space (representing photon polarizations) and the Bloch space (representing states of a quantum spin- particle). Using this mapping and analogous mappings for unitary operators, techniques and formalisms developed in one space can be applied in the other. As an example, error-correction strategies originally developed in the context of pulsed nuclear magnetic resonance experiments are applied to linear optics to propose the design of a new class of composite high-fidelity broadband linear retarder.

DOI
10.1088/1367-2630/9/2/024

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States can be mapped between the Poincaré space (representing photon polarizations) and the Bloch space (representing states of a quantum spin- particle). Using this mapping and analogous mappings for unitary operators, techniques and formalisms developed in one space can be applied in the other. As an example, error-correction strategies originally developed in the context of pulsed nuclear magnetic resonance experiments are applied to linear optics to propose the design of a new class of composite high-fidelity broadband linear retarder.
Composite pulses, which produce ultra-broadband, ultra-narrowband and ultra-passband x-, y-rotations R x (θ)=exp⁡{−iθσ x /2}, R y (θ)=exp⁡{−iθσ y /2} by the rotational angle θ = π on the Bloch-Poincaré sphere, are presented. In polarization optics, the first class plays a role in the design of achromatic polarization retarders, while the second class corresponds to chromatic polarization filters. The third class is an assortment of the above two classes. Besides, composite pulses, which produce ultra-broadband z-rotations R z (ζ)=exp⁡−iζσ z /2 by the phasal angle ζ = π on the same sphere, are presented. These phasal pulses coincide with achromatic polarization π rotators. The evolution matrix and the Jones matrix have similar forms in quantum optics and polarization optics. In the context of quantum optics, quantum computing, and quantum information processing, following the quantum-classical analogy, we achieve ultra-robust, ultrasensitive, and ultrasquare quantum control of an X (NOT) gate, and ultra-robust control of a Z phase gate, with respect to pulse area error. Our proposed UBBN (BatN), UNBN (SnakeN), UPBN (OctopusN), and UBBPhN (BatPhN) sequences are novel due to the novel methods of derivation. They surpass and outperform the superior candidates of the similar subclass of altering variable rotations in literature — BB2, NB2, and PB2, in precision parameters such as broadness, narrowness, FWHM, or execution time. We suggest that, in general, the presented composite pulse sequences are interdisciplinary and can have other possible applications, such as nuclear magnetic resonance (NMR), magnetic resonance imaging (MRI) and spectroscopy, quantum sensing, local addressing, optical switching, cold-atom interferometry, quantum communication, quantum cryptography, quantum image processing, and quantum steganography.
The use of two-level atomic systems in quantum optics allows for the design of highly efficient and broadband achromatic retarders through the application of adiabatic passage and composite pulse techniques. In this work, we propose shortcuts to adiabaticity to improve broadband polarization retarders with shorter lengths. We achieve this by inversely engineering the relative refractive indices and further optimizing them with respect to the perturbation of input wavelength. Our results are compared with adiabatic and composite protocols, demonstrating that our method provides the advantage of integrating efficiency and robustness.
Systematic errors in spin rotation operations using simple rf pulses place severe limitations on the usefulness of the pulsed magnetic resonance methods in quantum computing applications. In particular, the fidelity of quantum logic operations performed on electron spin qubits falls well below the threshold for the application of quantum algorithms. Using three independent techniques, we demonstrate the use of composite pulses to improve this fidelity by several orders of magnitude. The observed high-fidelity operations are limited by pulse phase errors, but nevertheless fall within the limits required for the application of quantum error correction.
Hybrid integration of solid-state quantum emitters (QEs) into nanophotonic structures opens enticing perspectives for exploiting multiple degrees of freedom of single-photon sources for on-chip quantum photonic applications. However, the state-of-the-art single-photon sources are mostly limited to two-level states or scalar vortex beams. Direct generation of high-dimensional structured single photons remains challenging, being still in its infancy. Here, we propose a general strategy to design highly entangled high-dimensional spin-orbital single-photon sources by taking full advantage of the spatial freedom to design QE-coupled composite (i.e., Moiré/multipart) metasurfaces. We demonstrate the generation of arbitrary vectorial spin-orbital photon emission in high-dimensional Hilbert spaces, mapping the generated states on hybrid-order Bloch spheres. We further realize single-photon sources of high-dimensional spin-orbital quantum emission and experimentally verify the entanglement of high-dimensional superposition states with high fidelity. We believe that the results obtained facilitate further progress in integrated solutions for the deployment of next-generation high-capacity quantum information technologies.