My PH.D. thesis(1992) was entitled "Parametric Scattering of Light in Spatially Inhomogeneous Ferroelectrics". It was an experimental study of the spontaneous three-photon parametric scattering in media where linear and quadratic susceptibility were spatially inhomogeneous. The media considered were crystals with excited acoustic waves and (or) with quasi-periodic domain structures. Various characteristics of these media, such as dispersion law of polaritons, the profile of the susceptibilities spatial distribution, etc., have been determined.
From 1986 to 1994 my major work was experimental studying of the statistical properties of scattered light fields. This, in particular, includes the variation of the scattered light statistics which results from the increase of Raman frequency shift. The limit case is a quasi-elastic scattering by chaotic small particles with sizes of the same order as the light wavelength. At present, an analogous problem is being solved for the case of scattering by acoustic waves propagating in a crystal, so that their correlation properties are pre-determined by hand.
Another branch of my activity covers the problem of biphoton interference (1997-). We consider the field interference of the second- and the fourth order in different interferometric schemes for spontaneous parametric down-conversion. Also we developed the effective interferometric protocols to generate some specific quantum states of light (the Bell states) in the most common case: broad spectrum of the pump (in particular for the femtosecond laser), any type of phase-matching (either type-I or type-II), and arbitrary length of nonlinear crystals.
We implemented a quantum teleportation protocol in which nonlinear interactions were used for Bell state measurement (2000). The distinct feature of this experiment is that all four Bell states can be distinguished in the Bell state measurement.
The preparation, transformation and measurement of the given biphoton polarization states in single spatial mode is the main objective during last years (2000-).
At the present time we develop the concept of quantum trits or qutrits and quantum quarts or ququarts. We've demonstrated that these objects can be realized using polarization tates of frequency degenerate collinear biphoton field. Coherent superposition of three (four) orthogonal basic biphoton states emitted from three (four) nonlinear crystals implements photonic three-state (four-state) system. The protocosl of quantum tomography of qutrits (ququarts) was proposed and realized in our group in collaboration with Yuri Bogdanov. The operational criteria of qutrit orthogonality, proposed by M.Chekhova, A.Zhukov and G.Maslennikov in 2002, has been demonstrated in experiment. These experiments open the new possibilities for practical implementation of quantum key distribution protocol based on qutrits and ququarts.
The latest activity relates to practical realization of quantum key distribution protocol based on temporal coding of information suggested by Sergei Molotkov.
In 2000 together with Yoon-Ho Kim we teleported an unknown (actually we knew) state of light from one to another side of the optical table.
My Doctor of Science thesis (2001) was entitled "Interference of Biphoton Fields". Different conditions leading to biphoton field interference were studied. Such applications as generation of the Bell states, protocol of the quantum teleportation, based on complete Bell-state measurement, ternary quantum logic and interferometric spectroscopy of the biphoton fields were developed.