## There are four main branches of my interest:

*spectroscopy of spatially inhomogeneous solid structures,*
*investigation of the statistical properties of scattered light fields,*
*quantum optics - different types of the light interference,*
*quantum information and quantum communications.*

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.

**QUANTUM TELEPORTER**

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.

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