Vladimir ich Andreev

Generalized algorithm for the unified analysis and simultaneous evaluation of geometrical spin-redirection phase and Pancharatnam phase in a complex interferometric system

To permit unified analysis and simultaneous evaluation of geometrical spin-redirection phase and Pancharatnam phase, the conventional 2 x 2 Jones matrix calculation is generalized and a new scheme of 3 x 3 matrix calculation is proposed. With the proposed algorithm one can trace the polarization state changes and the geometric phase shifts caused by beam propagation along an arbitrary optical path that involves both reflection and refraction at surfaces with Fresnel shift and birefringence.

Star product, discrete Wigner functions, and spin-system tomograms

We develop the star-product formalism for spin states and consider different methods for constructing operator systems forming sets of dequantizers and quantizers, establishing a relation between them. We study the physical meaning of the operator symbols related to them. Quantum tomograms can also serve as operator symbols. We show that the possibility to express discrete Wigner functions in terms of measurable quantities follows because these functions can be related to quantum tomograms. We investigate the physical meaning of tomograms and spin-system tomogram symbols, which they acquire in the framework of the star-product formalism. We study the structure of the sum kernels, which can be used to express the operator symbols, calculated using different sets of dequantizers and also arising in calculating the star product of operator symbols, in terms of one another.

Minimal sets of dequantizers and quantizers for finite-dimensional quantum systems

Abstract The problem of finding and characterizing minimal sets of dequantizers and quantizers applied in the mapping of operators onto functions is considered, for finite-dimensional quantum systems. The general properties of such sets are determined. An explicit description of all the minimum self-dual sets of dequantizers and quantizers for a qubit system is derived.

Derivation of the Husimi symbols without antinormal ordering, scale transformation and uncertainty relations

We propose a new method for the derivation of Husimi symbols, for operators that are given in the form of products of an arbitrary number of coordinates, and momentum operators, in an arbitrary order. For such an operator, in the standard approach, one expresses coordinate and momentum operators as a linear combination of the creation and annihilation operators, and then uses the antinormal ordering to obtain the final form of the symbol. In our method, one obtains the Husimi symbol in a much more straightforward fashion, departing directly from operator explicit form without transforming it through creation and annihilation operators. With this method the mean values of some operators are found. It is shown how the Heisenberg and the Schrodinger–Robertson uncertainty relations, for position and momentum, are transformed under scale transformation . The physical sense of some states which can be constructed with this transformation is also discussed.

Relations between scaling-transformed Husimi functions, Wigner functions and symplectic tomograms describing corresponding physical states

Husimi Q-functions are the only functions from the class of Cohen quasi-distributions on phase space that after scaling transformation (q,p)→(λq, λp) remain in the same class when the modulus of the scaling parameter is smaller than unity and so, in this case, describe a physical state. We found the Wigner functions and symplectic tomograms of such states. We applied the obtained general results to the Fock states of the harmonic oscillator.

Tensor-product representation of qubits and tensor realization of one-qubit operators

We consider one-particle spin states. We show that all the information contained in the state can be written in an equivalent form using three completely decohered mixed states. The density matrix of such a system has the form of tensor product of three diagonal matrices. The unitary operators defined in the space of one-particle spin states are represented by some transformation of tensor products of diagonal matrices. We determine the explicit form of the unitary transformations acting on the representing three-qubit system and corresponding basic operators acting in the space of the initial qubit states.

The Bell inequality and correlation of spin projection functions

The Bell inequality two-particle spin states are considered. It is shown that violation of this inequality at experimental verifications is connected with the fact that it is proved for some arbitrary random variables, but in experimental verification random variables of special type are used. A new inequality is constructed. It contains a correlation coefficient of random variables, measured at the experiment, and does not have to be violated at experimental verification. For factorizable and separable states it coincides with the usual Bell inequality.

Possibility of existence of Raman faster-than-light pulses

The conditions when faster-than-light Raman pluses can appear are discussed. The formula connecting the shape of a pulse with its velocity is found.

Interferometric microimaging based on geometrical spin-redirection phase.

A novel scheme for an interferometric microscope with which to visualize a geometrical spin-redirection phase image that represents the local inclination of microsurface structures of an object is proposed. The observed phase depends on the state of polarization and the optical constants of the object material, which enable one to distinguish the spin-redirection phase from the conventional dynamical-phase. A preliminary experiment was performed, and the phase images obtained were found to be consistent with those predicted by computer simulation based on a theoretical model.

Visualization of Berry spin-redirection phase in polarization interferometer with geometric shear

A novel scheme of an interferometric microscope is proposed to visualize a geometrical spin-redirection phase image that represents the local inclination of micro surface structures of an object. The observed phase depends on the state of polarization and optical constants of the object material, which enables one to distinguish the spin-redirection phase from the conventional dynamical phase. A preliminary experiment was performed, and the phase images obtained were found to be consistent with those predicted by computer simulation based on a theoretical model.