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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Mathematical modeling and experimental study of polarization echo in optically anisotropic media

Yu. I. Bogdanov, Alexander A. Kalinkin, S. P. Kulik, Ekaterina V. Moreva, Vladimir A. Shershulin, L. V. Belinsky

Published Jan 8, 2013• 1 citation
Publisher

Abstract

As optical systems are one of the candidates for implementation of a scalable quantum computer, it is important to develop an adequate method of description of both quantum states of light and operations performed by optical elements. Using the concept of chi-matrix representation of quantum operations and Choi-Jamiolkowski isomorphism we expand Jones calculus to allow description of evolution of mixed polarization states in linear optical systems. The developed method is then used to give a full description of polarization echo effect, which was described in 1 based on an analogy between the effects of polarization optics and spin dynamics. Theoretical predictions are confirmed by reconstructing operations performed by a series of quartz waveplates using quantum process tomography protocols.

DOI
10.1117/12.2017619

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As optical systems are one of the candidates for implementation of a scalable quantum computer, it is important to develop an adequate method of description of both quantum states of light and operations performed by optical elements. Using the concept of chi-matrix representation of quantum operations and Choi-Jamiolkowski isomorphism we expand Jones calculus to allow description of evolution of mixed polarization states in linear optical systems. The developed method is then used to give a full description of polarization echo effect, which was described in 1 based on an analogy between the effects of polarization optics and spin dynamics. Theoretical predictions are confirmed by reconstructing operations performed by a series of quartz waveplates using quantum process tomography protocols.
The polarization echo effect is demonstrated, which is manifested in the identity of a composite polarization transformation irrespective of the spectrum of the input polarization state. The pure input state transfers during its evolution to a completely mixed state and then returns to the initial state. The stages of this evolution are completely analogous to the corresponding stages of the “classical” spin echo effect. The adequacy of transformations performed for conditionally prepared one-photon polarization states is verified by the tomography of the quantum process.
The analogy between polarization optics effects and the dynamics of a spin in a magnetic field is analyzed based on the fact that the Bloch equation for a spin in a magnetic field is formally identical to the evolution equation for the quasi-spin vector of a light propagating in an optically anisotropic medium. Among the effects discussed within this framework are light polarization beats in a birefringent medium; optical activity suppression in the media with linear birefringence; suppression of linear birefringence in the media with spatially modulated gyration; 'adiabatic' transformation of light polarization in media of smoothly varying anisotropy, and two- and three-pulse polarization echoes.
We present a theoretical analysis of the connection between classical polarization optics and quantum mechanics of two-level systems. First, we review the matrix formalism of classical polarization optics from a quantum information perspective. In this manner the passage from the Stokes-Jones-Mueller description of classical optical processes to the representation of one- and two-qubit quantum operations, becomes straightforward. Second, as a practical application of our classical-vs-quantum formalism, we show how two-qubit maximally entangled mixed states can be generated by using polarization and spatial modes of photons generated via spontaneous parametric down conversion.
Conceptual and operational aspects of the description of the polarization of light in classical and quantum optics are discussed. Primary emphasis is placed on the concept of P -quasispin, which ensures an adequate analysis for arbitrary quantum light fields. In terms of this concept, the polarization density matrix, which is obtained by reduction of the total field density operator and which completely describes the polarization state of quantum radiation, as well as the operational (measured in polarization experiments) characteristics and the transformations of the polarization dynamics, are determined. Applications of the formalism developed to biphoton optics are discussed.
The statistical ensemble formalism of Kim et al [J. Opt. Soc. Am. A4, 433 (1987)] offers a realistic model for characterizing the effect of stochastic nonimage-forming optical media on the state of polarization of transmitted light. With suitable choice of the Jones ensemble, various Mueller transformations-some of which are hitherto unknown-are deduced. It is observed that the ensemble approach is formally identical to the positive-operator-valued measures (POVMs) on the quantum density matrix. This observation, in combination with the recent suggestion by Ahnert and Payne [Phys. Rev. A71, 012330-1 (2005)]-in the context of generalized quantum measurement on single photon polarization states-that linear optics elements can be employed in setting up all possible POVMs enables us to propose a way of realizing different types of Mueller devices.