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Optics Letters

Efficient broadband polarization retarder via shortcuts to adiabaticity

Wei Wang, Yue Ban, Xi Chen

Published Jul 24, 2023• 2 citations
Publisher

Abstract

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.

DOI
10.1364/ol.499058

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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.
Conventional narrowband spectrum polarization devices are short but not robust, based on quasi-phase matching (QPM) technique, in periodically poled lithium niobate (PPLN) crystal. In this paper, we propose short-length and robust polarization rotators by using shortcuts to adiabaticity. Beyond the QPM condition, the electric field and period of PPLN crystal are designed in terms of invariant dynamics, and further optimized with respect to input wavelength/refractive index variations. In addition, the stability of conversion efficiency on the electric field and period of PPLN crystal is also discussed. As a consequence, the optimal shortcuts are fast as well as robust, which provide broadband spectrum polarization devices with short length.
Abstract The method of adiabatic frequency conversion, in analogy with a two‐level atomic system, has been put forward recently and verified experimentally to achieve robust frequency mixing processes such as sum and difference frequency generation. Here a comparative study of efficient frequency mixing using various techniques of shortcuts to adiabaticity such as counter‐diabatic driving and invariant‐based inverse engineering is presented. It is shown here that it is possible to perform sum frequency generation by properly designing the poling structure of a periodically poled crystal and the coupling between the input lights and the crystal. The required crystal length for frequency conversion significantly decreases beyond the adiabatic limit. This approach significantly improves the robustness of the process against the variation in temperature as well as the signal frequency. By introducing a single parameter control technique with constant coupling and combining with the inverse engineering, perturbation theory, and optimal control, it is shown that the phase mismatch can be further optimized with respect to the fluctuations of input wavelength and crystal temperature that results into a novel experimentally realizable mixing scheme.
By definition, quantum adiabatic process means a slow process which allows the state to follow the instantaneous eigenstates of time-dependent Hamiltonian. For some reasons, for example, to avoid the decoherence effects, or to implement large-scale quantum information processing, we may want to speed up the adiabatic process, that is, to achieve the adiabatic-like control but in very short time. In this talk, we present new methods to speeded-up expansion and transport of cold atoms in a harmonic trap. Such shortcuts to adiabaticity provide the fast expansion or transport, in which the final atomic state is the same as in the adiabatic process, but in arbitrarily short time, keeping the same populations of vibrational levels in the initial and final trap. These methods can also be generalized to Bose-Einstein Condensates. Moreover, we present shortcuts to adiabatic passage from one internal atomic state to another in twoor three-level atoms. In detail, we can apply Berry’s transitionless quantum driving method and invariant-based inverse engineering method to accelerate the Rapid Adiabatic Passage (RAP) and Stimulated Raman Adiabatic Passage (STIRAP) in twoand three-level atomic systems, respectively. We also examine and compare the stability of different schemes concerning different types of noise and system errors. Finally, we show that the technique of shortcuts to adiabaticity in two-level system can be applied in fast and robust spin flip in a quantum dot, to avoid the decoherent effects.
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.
Shortcuts to adiabaticity, originally developed in the context of quantum control, are powerful tools for the design of high coupling efficiency, robust, and short coupled-waveguide devices. The counterdiabatic protocol cancels the unwanted coupling in system evolution by the addition of a counterdiabatic term. The invariant-based inverse-engineering approach designs system evolution using the decoupled eigenstates of the Lewis-Riesenfeld invariant. The single-shot shaped-pulse technique directly parameterizes the solution of the coupled-mode equation. Starting from the counterdiabatic protocol, we show that these seemingly very different shortcuts to adiabaticity techniques are equivalent in the framework of coupled-waveguide systems. When combined with perturbation treatment of the coupled-mode equation, robust coupled-waveguide devices against errors can be obtained.