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Russian Microelectronics

, Volume 35, Issue 1, pp 7–20 | Cite as

Schmidt modes and entanglement in continuous-variable quantum systems

  • A. Yu. Bogdanov
  • Yu. I. Bogdanov
  • K. A. Valiev
Article

Abstract

The extraction of Schmidt modes for continuous-variable systems is considered. An algorithm based on the singular-value decomposition of a matrix is proposed. It is applied to the entanglement in (i) an atom—photon system with spontaneous emission and (ii) a system of biphotons with spontaneous parametric downconversion (SPDC) of type II. For the atom—photon system, the evolution of entangled states is found to be governed by a parameter approximately equal to the fine-structure constant times the atom-to-electron mass ratio. An analysis is made of the dynamics of atom—photon entanglement on the assumption that the system’s evolution is determined by the superposition of an initial and a final state. It is shown that in the course of emission the entanglement entropy first rises on a timescale of order the excited-state lifetime and then falls, approaching asymptotically a residual level due to the initial energy spread of the atomic packet (momentum spread squared). SPDC of type II is analyzed by means of the polarization density matrix and a newly introduced coherence parameter for two spatially separated modes. The loss of intermodal coherence is addressed that results from the difference in behavior between ordinary-and extraordinary-ray photons in a nonlinear crystal. The degree of intermodal coherence is investigated as a function of the product of crystal length and pump bandwidth.

Keywords

Entangle State Entanglement Entropy Nonlinear Crystal Crystal Length Polarization Density 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Pleiades Publishing, Inc. 2006

Authors and Affiliations

  • A. Yu. Bogdanov
    • 2
  • Yu. I. Bogdanov
    • 1
  • K. A. Valiev
    • 1
  1. 1.Institute of Physics and TechnologyRussian Academy of SciencesMoscowRussia
  2. 2.Moscow State UniversityMoscowRussia

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