We present the new experimental technique of measuring all polarization parameters of the single frequency-spatial mode of the optical fields in the fourth order approach. We experimentally studied several classical and nonclassical states of the single-mode field.

A method of optical realization of a protocol of restoration of the density matrix of an unknown state of a three-level system that represents an arbitrary polarization state of a single-mode biphoton field is proposed. The method is applied to a set of pure states of qutrits, with this set being determined by the properties of SU(2) transformations performed by polarization transformers (retardation plates).

We proposed the procedure of measuring the unknown state of the three-level system – the qutrit, which was realized as the arbitrary polarization state of the single-mode biphoton field. This procedure is accomplished for the set of the pure states of qutrits; this set is defined by the properties of SU(2) transformations, that are done by the polarization transformers.

The works devoted to studying the polarization properties of a two-photon light generated upon spontaneous parametric down-conversion in the collinear frequency-degenerate regime are briefly overviewed, with emphasis on the studies carried out by us over a period from 1999 to 2001 within the framework of the project “Polarization Optics of Biphotons” of the Russian Foundation for Basic Research. In particular, the polarization state of a two-photon light was analyzed and its pictorial mapping onto the Poincaré sphere was proposed. The experiments on polarization transformations of a two-photon light were performed; based on these transformations, a method was suggested for ternary quantum information coding. A two-photon state with the orthogonal photon polarizations was synthesized experimentally from the two beams of identically polarized correlated photons, and the spectral properties of this state were investigated. Finally, a method was suggested for measuring the polarization state of a two-photon light in the collinear frequency-degenerate case (“tomography”).

Four polarization-frequency Bell states are obtained experimentally for photon pairs (biphotons) emitted during spontaneous parametric scattering from continuous pumping in the collinear frequency-nondegenerate regime. The polarization properties of such states are investigated. It is shown that biphoton light in the singlet Bell state is not polarized in the second or fourth order in the field.

Second-order and fourth-order interference effects in spontaneous parametric down conversion (SPDC) are considered. Two basic schemes are discussed, analogous to linear Young and Mach-Zehnder interferometers. Interference effects are used for such applications as spectroscopy of nonlinear and linear media and preparation of novel two-photon polarization states.

We study the interference of biphotons generated via spontaneous parametric down-conversion from a pump with several longitudinal modes. It is shown that biphotons can interfere if the time difference between their birth moments is a multiple, to an accuracy of the pump coherence time, of T=2L/c, where L is the pump cavity length. This effect, although observed with a cw pump, is similar to a recently reported interference of biphotons generated from time-separated pump pulses.

Two beams of collinear type-I biphotons generated via spontaneous parametric down-conversion ~SPDC! from coherent pump beams are transformed without a loss into a state of correlated photons with orthogonal ~in the general case, elliptical! polarizations. This alternative state manifests remarkable properties: while having the spectrum of type-I SPDC, it has polarization properties similar to type-II SPDC. To test the state, we use the anticorrelation effect ~‘‘anticorrelation dip’’!.

Summary form only given. Consider a pair of collinear frequency-degenerate photons-a biphoton, which can be obtained by spontaneous parametric down-conversion (SPDC). Its state vector/sup 1/ is |/spl Psi/>=C/sub 1/|2,0>+C/sub 2/|0,2>+C/sub 3/|1,1>, (1) with |n,m>, n+m=2 denoting n H-polarized photons and m V-polarized photons. The first and the second terms describe type-I biphotons (correlated photons have similar H or V polarizations), and the third one describes type-II biphotons (correlated photons have orthogonal polarizations). In the present work we study an anticorrelation properties of the artificially synthesized type-II biphotons.

Second-order interference with respect to the field strength during spontaneous parametric light scattering was studied under the conditions of absorption at the frequencies of idler (polariton) modes. An expression is derived that describes the scattered light intensity as a function of the scattering angle for an arbitrary shape of the nonlinear interaction region. The interference was experimentally studied for the light scattering on polaritons in a nonlinear crystal (lithium iodate, iodic acid), with a double slit placed into a pumping beam in front of the crystal.

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Summary form only given. Consider a pair of collinear frequency-degenerate photons-a biphoton, which can be obtained by spontaneous parametric down-conversion (SPDC). Being a three-state quantum system, it is a ternary analog of a qubit. Its state vector is |/spl psi/>=c/sub 1/|2,0>+c/sub 2/|0,2>+c/sub 3/|1,1>, with |n,m>,n+m=2 denoting n X-polarized photons and m Y-polarized photons. The first two terms describe type-I biphotons (correlated photons have similar polarizations), and the third one type-II biphotons (correlated photons have orthogonal polarizations). An arbitrary biphoton state is given by four parameters.

Summary form only given. We study interference of biphotons generated via type-I degenerate collinear spontaneous parametric down-conversion from a multimode pump.

The transformation properties and the measurable parameters of a quasimonochromatic optical field consisting of two photons with the same directions of propagation and average frequency are analyzed. Like quarks, such a field possesses SU (3) symmetry.

Polarization state of biphoton light generated via collinear frequency-degenerate spontaneous parametric down-conversion is considered. A biphoton is described by a three-component polarization vector, its arbitrary transformations relating to the SU(3) group. A subset of such transformations, available with retardation plates, is realized experimentally. In particular, two independent orthogonally polarized beams of type-I biphotons are transformed into a beam of type-II biphotons. Polarized biphotons are suggested as ternary analogs of two-state quantum systems (qubits).

For the technique of near-forward Raman scattering, the possibility to measure relaxation times and group velocities of phonon polaritons at frequencies close to resonances is discussed. Polariton relaxation times are measured as a function of frequency for crystals of lithium iodate and niobate. For group velocity measurements, it is shown experimentally that the result depends on the way of processing the frequency-angular scattering spectra.

The interference of biphotons emitted during collinear parametric scattering from two spatially separated regions is investigated experimentally and theoretically. It is shown that in this case the phase of the interference is determined by the pump wavelength and there is no need to equalize the optical paths for radiation from different regions.