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The Schmidt modes of biphoton qutrits: Poincare-sphere representation

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Chekhova,  M. V.
Quantum Radiation, Leuchs Division, Max Planck Institute for the Science of Light, Max Planck Society;
Chekhova Research Group, Research Groups, Max Planck Institute for the Science of Light, Max Planck Society;
Optical Technologies, Technology Development and Service Units, Max Planck Institute for the Science of Light, Max Planck Society;

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Citation

Chekhova, M. V., & Fedorov, M. V. (2013). The Schmidt modes of biphoton qutrits: Poincare-sphere representation. JOURNAL OF PHYSICS B-ATOMIC MOLECULAR AND OPTICAL PHYSICS, 46(9): 095502. doi:10.1088/0953-4075/46/9/095502.


Cite as: https://hdl.handle.net/11858/00-001M-0000-002D-6775-3
Abstract
For a general-form polarization biphoton qutrit, physically corresponding to a pair of arbitrarily polarized photons in a single frequency and wavevector mode, we explicitly find polarization Schmidt modes. A simple method is suggested for factorizing the state vector and the explicit expressions for the factorizing photon creation operators are found. The degrees of entanglement and polarization of a qutrit are shown to depend directly on the commutation features of the factorizing operators. Clear graphic representations for the Stokes vectors of the qutrit state as a whole, its Schmidt modes and factorizing single-photon creation operators are given based on the Poincare sphere. An experimental scheme is proposed for measuring the parameters of the Schmidt decomposition as well as for demonstrating the operational meaning of qutrit entanglement.