A. V. Burlakov

Polarization state of a biphoton: Quantum ternary logic

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).

Measurement of qutrits

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).

Polarization optics of biphotons

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”).

Polarized biphotons as “optical quarks”

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.

Three-photon interference: Spectroscopy of linear and nonlinear media

The nonlinear interference accompanying three-photon spontaneous parametric light scattering is considered. The frequency-angle line shape of the scattering is calculated for nonlinear-crystal/ linear-dispersive-medium/nonlinear-crystal and nonlinear-crystal/nonlinear-crystal systems. The question of the possible use of nonlinear interference in spectroscopy is discussed.

Biphoton light generation in polarization-frequency bell states

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.

Interference between spontaneous two-photon radiation from two macroscopic regions

Interference is observed between the spontaneous parametric radiation from two nonlinear crystals separated by a macroscopic air gap and excited in series by a common pump beam. The phase of the interference depends on the phase shifts at three frequencies. A simple quantum model agrees well with the experimental results and makes it possible to interpret the effect in terms of general vacuum fluctuations which give rise to the spontaneous emission of mutually coherent radiation from the two crystals.

Three-wave interference with participation of polaritons

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.

Propagation and decay of equilibrium phonon polaritons studied via near-forward Raman scattering

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.

Fourth-order interference between independent biphotons

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.