Polarization Operators

Hari Prakash, Ravi Shankar Singh

For monochromatic light propagating along z -direction, we define a polarization operator which is product of inverse annihilation operator for the x -linearly polarized mode and the annihilation operator for the y -linearly polarized mode. This polarization operator is helpful in testing whether light in a given state is perfectly polarized, and in knowing this perfect polarized state.

Ivana Marić, Shlomo Shitz Shamai, Osvaldo Simeone

Chandravati Prajapati, D. Ranganathan

We define a Susskind–Glogower operator that is unitary and acts as a true ladder operator for photons of a given frequency and any polarization. The operator acts on a Hilbert space consisting of all number states in both polarizations. The phase operator derived from this ladder operator satisfies the canonical commutation relations with the number operator. The eigenstates of this ladder operator are also found. Our method based on all the observable states enables us to write the operators for objects such as beam splitters, phase shifters or polarizers, as constant matrices; those used to study classical polarized beams. The Pegg–Barnett operator and the two-mode operator of Ban are special cases of our operator. We compared the phase state defined here with that obtained from the original Susskind–Glogower case, as well as that obtained by the method of Pegg and Barnett in the limit of a very small number of photons being present, and found that there are differences which may enable a direct experimental comparison of these operators.

Siegfried Hess

Tugrul Hakioglu

The operational approach to the measurement of phase studied by Noh, Fouger\`es, and Mandel [Phys. Rev. A 45, 424 (1992); 46, 2840 (1992); Phys. Rev. Lett. 71, 2579 (1993); Phys. Rev. A 47, 4535 (1993)] is applied to the measurement of the state of polarization of fully polarized light. Operational counterparts of the quantum Stokes parameters are introduced and their fluctuations are examined. It is shown that if the polarized field is weak, the measured fluctuations are influenced not only by the quantum properties of the source field but also that of the measurement. This character is reflected on the measured probability distributions of the parameters of polarization, which are also investigated independently for the fully polarized coherent states and the Fock states as the initial field strength is varied. Finally, connection between the operational approach to the measurement of polarization and the su(2) interferometry is examined.

J. Schirmer