Reconstruction of the probability density function by means of the degree of polarization for one-photon mixed states

In this paper the authors discuss an alternative way for reconstructing one-photon mixed states of a partially polarized optical field. The task is to represent the probability density distribution describing these kind of states with the Stokes parameters which also characterize the effective state of polarization. These parameters can be measured by means of the degree of polarization with an experimental setup containing a rotating linear polarizer and a circular polarizer. A thought experiment is presented which assumes that the measurement is undertaken on an analyzed beam coupled with a reference beam containing photons polarized in a well-known way. The method discussed in the paper is an alternative for the most commonly used quantum tomography approach.

[1]  M. Chekhova,et al.  Quantum reconstruction of an intense polarization squeezed optical state. , 2007, Physical review letters.

[2]  Petro O. Demianenko,et al.  About the nature of the coherence of light waves , 2011, Optical Systems Design.

[3]  D. Varshalovich,et al.  Quantum Theory of Angular Momentum , 1988 .

[4]  F. Arecchi,et al.  Atomic coherent states in quantum optics , 1972 .

[5]  Andrzej W. Domański,et al.  Problem of degree of polarization for photons , 2010, Symposium on Photonics Applications in Astronomy, Communications, Industry, and High-Energy Physics Experiments (WILGA).

[6]  D. Mattis.  Quantum Theory of Angular Momentum , 1981 .

[7]  M. Chekhova,et al.  Three-dimensional quantum polarization tomography of macroscopic Bell states , 2011, 1112.4282.

[8]  Marek Zukowski,et al.  Experimental interference of independent photons. , 2006, Physical review letters.

[9]  E. Wigner.  On the quantum correction for thermodynamic equilibrium , 1932 .

[10]  H. Weyl.  Quantenmechanik und Gruppentheorie , 1927 .

[11]  K. Banaszek,et al.  Direct measurement of the Wigner function by photon counting , 1999 .

[12]  T. Tudor,et al.  Pauli algebraic forms of normal and nonnormal operators. , 2007, Journal of the Optical Society of America. A, Optics, image science, and vision.

[13]  R. Dicke.  Coherence in Spontaneous Radiation Processes , 1954 .

[14]  R. Glauber.  Quantum Theory of Optical Coherence , 2006 .

[15]  Tiberiu Tudor,et al.  Interaction of light with the polarization devices: a vectorial Pauli algebraic approach , 2008 .

[16]  G. Li,et al.  High-spin yrast and yrare structures in 112In , 2010 .

[17]  Beck,et al.  Measurement of the Wigner distribution and the density matrix of a light mode using optical homodyne tomography: Application to squeezed states and the vacuum. , 1993, Physical review letters.

[18]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[19]  P. Knight,et al.  Introductory quantum optics , 2004 .

[20]  Ebrahim Karimi,et al.  Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications , 2011 .

[21]  46 , 2015, Slow Burn.

[22]  A. Domanski,et al.  Effective state of polarization of photon-beam , 2011 .

[23]  A. Domanski,et al.  Degree of polarization as a measurable quantity for a quantum optical field containing variously polarized photons , 2012 .

[24]  L. Mandel,et al.  Coherence Properties of Optical Fields , 1965 .

[25]  Vogel,et al.  Determination of quasiprobability distributions in terms of probability distributions for the rotated quadrature phase. , 1989, Physical review. A, General physics.