Measuring the Quantum Polarization State of Light

  • M. G. Raymer
  • A. C. Funk
  • D. F. McAlister

Abstract

Quantum-state tomography is proposed as a means to achieve a complete measurement of the quantum polarization state of a light wave. A set of measurements using dual-polarization balanced homodyne detection is shown to be tomographi-cally complete with respect to the statistics of the SU(2) Stokes operators on the Poincaré sphere. Complete reconstruction of the polarization sector of the density matrix of a partially polarized optical field can be achieved while randomizing the overall phase of the dual-polarization local oscillator.

Keywords

Density Matrix Coherent State Polarization Sector Stokes Operator Homodyne Detection 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    For an elementary review see M. G. Raymer, Measuring the Quantum Mechanical Wave Function, Contemp. Physics 38:343 (1997).ADSCrossRefGoogle Scholar
  2. 2.
    J. Ashburn, R. Cline, P. van der Burgt, W. Westerveld, and J. Risley, Experimentally determined density matrices for H(n=3) formed in H+−He collisions from 20 to 100 keV, Phys. Rev. A 41:2407 (1990).CrossRefADSGoogle Scholar
  3. 3.
    U. Leonhardt and M. Munroe, Number of phases required to determine a quantum state in optical homodyne tomography, Phys. Rev. A 54:3682 (1996).CrossRefADSGoogle Scholar
  4. 4.
    D. F. McAlister and M. G. Raymer, Correlation and joint density matrix of two spatial-temporal modes from balanced-homodyne sampling, J. Mod. Opt. 44:2359 (1997).ADSGoogle Scholar
  5. 5.
    D. T. Smithey, M. Beck, M. G. Raymer, and A Faridani, Measurement of the Wigner distribution and the density matrix of a light mode using optical homodyne tomography: application to squeezed states and the vacuum, Phys. Rev. Lett. 70:1244 (1993).CrossRefADSGoogle Scholar
  6. 6.
    Special Issue of the J. Mod. Opt. on “Quantum State Preparation and Measurement,” eds. W. Schleich and M. G. Raymer (vol. 44, 1997).Google Scholar
  7. 7.
    U. Leonhardt, “Measuring the Quantum State of Light,” Cambridge Univ. Press, Cambridge (1997).Google Scholar
  8. 8.
    D.-G. Welsch, W. Vogel, and T. Opatrny, Homodyne detection and quantum state reconstruction, (to appear in Progress in Optics).Google Scholar
  9. 9.
    E. Joos, Decoherence through interaction with the environment, in: “Decoherence And The Appearance Of A Classical World In Quantum Theory,” D. Giulini et al., eds., Springer, Berlin (1996), pg. 35.Google Scholar
  10. 10.
    W. Wootters, Local accessibility of quantum states, in: “Complexity, Entropy, And The Physics Of Information,” Wojciech H. Zurek, ed., Addison-Wesley, Redwood City (1990).Google Scholar
  11. 11.
    M. G. Raymer, D. T. Smithey, M. Beck, M. Anderson, and D. F. McAlister, Measurement of the Wigner function in quantum optics, Proceedings of the Third Annual International Wigner Symposium Sep. (1993).Google Scholar
  12. 12.
    D. F. McAlister and M. G. Raymer, Ultrafast photon-number correlations from dual pulse, phase-averaged homodyne detection, Phys. Rev. A 55:R1609 (1997).CrossRefADSGoogle Scholar
  13. 13.
    T. Opatrny, D.-G. Welsch, and W. Vogel, Multi-mode density matrices of light, via amplitude and phase control, Opt. Commun. 134:112 (1997); Homodyne detection for measuring internal quantum correlations of optical pulses, Phys. Rev. A 55:1416 (1996).ADSCrossRefGoogle Scholar
  14. 14.
    V. P. Karasev and A. V. Masalov, Unpolarized light states in quantum optics, Opt. Speetrosc. 74:551 (1993).ADSGoogle Scholar
  15. 15.
    V. N. Beskrovnyi and A. S. Chirkin, Polarization-squeezed light generation in a second order nonlinear medium, in: “Quantum Communication, Computing, and Measurement,” O. Hirota, A. S. Holevo, and C. M. Caves, eds., Plenum, New York (1997), pg. 483; Light source with nonclassical polarization state based on an optical frequency doubler, Quantum Semiclass. Opt. 10:263 (1998).Google Scholar
  16. 16.
    P. Grangier, R. E. Slusher, B. Yurke, and A. LaPorta, Squeezedlight enhanced polarization interferometer, Phys. Rev. Lett. 59:2153 (1987).CrossRefADSGoogle Scholar
  17. 17.
    J. M. Jauch and F. Rohrlich, “The Theory of Photons and Electrons,” Addison-Wesley, Reading (1955).Google Scholar
  18. 18.
    B. Yurke, S. L. McCall, and J. R. Klauder, SU(2) and SU(1,1) interferometers, Phys. Rev. A 33:4033 (1986).CrossRefADSGoogle Scholar
  19. 19.
    J. A. Cina, Phase-controlled optical pulses and the adiabatic electronic sign change, Phys. Rev. Lett. 66:1146 (1991).CrossRefADSGoogle Scholar
  20. 20.
    K. Wodkiewicz and J. H. Eberly, Coherent states, squeezed fluctuations, and the SU(2) and SU(1,1) groups in quantum optics applications, J. Opt. Soc. Am. B 2:458 (1985).ADSGoogle Scholar
  21. 21.
    For a review see L. Mandel and E. Wolf, “Optical Coherence and Quantum Optics,” Cambridge University Press, Cambridge (1995), Chap. 6.Google Scholar
  22. 22.
    Not to be confused with a coherent state of angular momentumm, as discussed in F. T. Arrechi, E. Courtens, R. Gilmore, and H. Thomas, Atomic coherent states in quantum optics, Phys. Rev. A 6:2211 (1972).ADSCrossRefGoogle Scholar
  23. 23.
    For a review see G. B. Malykin, Use of the Poincare sphere in polarization optics and classical and quantum mechanics. Review, Radiophysics and Quantum Electronics 40:175 (1997).MathSciNetCrossRefADSGoogle Scholar
  24. 24.
    R. Azzam and N. Bashara, “Ellipsometry and Polarized Light,” Oxford, north-Holland, Amsterdam (1977).Google Scholar
  25. 26.
    J. Lehner, U. Leonhardt, and H. Paul, Unpolarized light: classical and quantum states, Phys. Rev. A 53:2727 (1996).CrossRefADSGoogle Scholar
  26. 27.
    M. G. Raymer, D. F. McAlister and U. Leonhardt, Two-mode quantum-optical state measurement: Sampling the joint density matrix, Phys. Rev. A 54:2397 (1996).CrossRefADSGoogle Scholar

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • M. G. Raymer
    • 1
  • A. C. Funk
    • 1
  • D. F. McAlister
    • 1
  1. 1.Oregon Center for Optics and Department of PhysicsUniversity of OregonEugeneUSA

Personalised recommendations