Orthogonal Operators and Phase Space Distributions in Quantum Optics

  • S. Billis
  • E. A. Mishkin
Conference paper


Electromagnetic fields at optical frequencies are excited by indeterministic sources. Their statistical description is usually given by means of the density operator ρ̂ or a phase-space distribution which is, in general, a quasi-probability distribution. Expansions of the density matrix ρ̂ in terms of a given complete set of orthogonal operators establishes a one-to-one correspondence between the expanded operator ρ̂ and the quasi-probability phase-space distribution that appears in said expansion. The time evolution of the field’s statistics are obtained then as a solution of the equation of motion of the density operator ρ̂ or the differential equation of the corresponding phase-space distribution. The latter method has the advantage of being unburdened by problems of commutativity associated with the ρ̂ operator. With the statistical information vested in the phase-space distribution, in lieu of the density matrix ρ̂ the expected value of an observable F̂ is given by an integral of the phase-space distribution multiplied by a weighting function which is representative of the observable F̂. This is essentially the method first introduced by Wigner[l] and Moyal[2].


Coherent State Density Operator Reduce Density Matrix Interaction Picture Phase Space Distribution 
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Copyright information

© Plenum Press, New York 1973

Authors and Affiliations

  • S. Billis
    • 1
  • E. A. Mishkin
    • 1
  1. 1.Polytechnic Institute of BrooklynBrooklynUSA

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