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Journal of Experimental and Theoretical Physics

Optical polarization echo: Manifestation and study by methods of quantum tomography of states and processes

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

Published Jun 1, 2014• 9 citations
Publisher

Abstract

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.

DOI
10.1134/s1063776114050094

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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.
Optical quantum memory is one of the basic elements of quantum information systems. However, the possibilities of its application in such systems sometimes can hardly be estimated by existing methods for its characterization. In this work, the tomography of quantum memory has been implemented as a quantum process in a logical basis. It has been shown that the implemented quantum memory scheme for polarization photon qubits with a high accuracy corresponds to the identity transformation and is promising for application in quantum communication and quantum computing.
As it was emphasized several times above, the phenomenon of the photon echo is an optical analog of the spin echo that has been discovered [ 1 ] about a decade earlier. That is why many ideas from the theory of the spin echo has been transferred to the theory of the photon echo and appeared to be fruitful there. One of these ideas put forward by Fernbach and Proctor [ 2 ] is the idea of the possibility of the use of the phenomenon of the spin echo for writing, storage, and processing of the data. The authors [ 2 ] determined the conditions under which the signals of the spin and stimulated spin echo can reproduce (direct or time-reversed) shape of one of the exciting pulses. The theoretical analysis was proved by the corresponding experiments.
The essence and basic structural elements of the method of polarization tomography of quantum radiation (the reconstruction of the polarization states of a field solely from polarization measurements) are described. The essential features of the method are discussed in comparison with usual field and spin tomographies. A general scheme for experimentally implementing this method is suggested and its use in polarization tomography of biphotonic radiation with hidden polarization is briefly analyzed.
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.