Ivan I. Popov

Signals of the femtosecond photon echo in inorganic films and their recording

We report the results of the first experiment on recording of photon echo and self-diffraction signals in a zinc oxide semiconductor film of nanoscale thickness, which are excited by two-photon absorption of femtosecond laser pulses with wavelengths of 800 to 840nm for the exciton transition at room temperature.

Photon echoes in molecular iodine vapors and nanofilms as a method of optical data processing

Properties and parameters of the photon echoes (PEs) used in optical data processing are analyzed. Physical methods for constructing functional processors and measuring devices on the basis of PE are proposed. Experiments on detecting femtosecond PEs in inorganic nanofilms at the room temperature are described.

Non-Faraday rotation of the photon echo polarization vector under variation in the interval between exciting pulses and its application to range finding

Formation modes are investigated and detection accuracy is evaluated for the non-Faraday rotation of the polarization vector of the photon echo in a gas. Possible applications of this effect for construction of optical measuring systems are discussed.

Application of quaternion algebra for calculation of photon echo signal

Mathematical formalism of photon echo exciting at interaction of two-level quantum system with an electromagnetic field within the framework of quaternion algebra is offered. The rotation quaternion is used instead of density operator for representation of interaction dynamics of an exterior field with two-level atom, where the components of rotation quaternion are the coordinates of Bloch vector. Liouville fon-Neumann equation for density matrix evolution is substituted by the differential quaternion equation in a quaternion model. The expression for rotation quaternion appropriating to an unitary operator of rotation in matrix representation is obtained. It is shown that the solution of the differential quaternion equation does not require the difficult mathematical operation connected to an evaluation of an exponent from a matrix. The expression for a quaternion superoperator is obtained.

Modeling of the multipulse photon echo and its application in specialized optical computers

A physical principle of the design of two parallel coprocessors for solving the knapsack problem was proposed. These coprocessors operate on the basis of polarization properties of multipulse excitation and recording of the photon echo signals. The exciting pulse area is optimized to improve the resolution in solving combinatory problems.

Photon echo as a method of optical processor construction for realization of computing operations above hypercomplex numbers

We inform on modelling a photon echo (PhE) shaping conditions as analog process which substitutes a part of labourconsuming computing operations at numerical calculation PhE in a formalism of quaternions algebra, and about its application for a computer construction (CC) for quaternion magnitudes.

Multipulse excitation of photon echo and principles of parallel functioning of optical echo-processors

The phenomenon of multipulse photon echo in two-level quantum systems is used to construct a conceptual sketch of a device which involves two optical coprocessors operating in parallel. The device is designed for accelerated solution of NP-hard problems of discrete analysis. As an example, the application of coprocessors to the trinomial knapsack problem is considered in detail. The coprocessors work with sequences of exciting laser pulses of different amplitude-time forms and polarizations.

Input and output principles of quaternion information in optical echo-processor

Principle possibility of construction of optical echo-processors with hypercomplex architecture on the basis of physics of photon echo for computational process is shown. Mathematical basis of presentation of quaternion type in optical echo processor is developed. Coding and decoding protocols of information processing with quaternion type are offered. Example of calculating quaternion Fourier transform is demonstrated.

Physical measurings and quantum control in technique of a photon echo

The effect of the rotating of the photon echo polarization vector is offered for a construction of the opto-electronic current transformer. As an active medium that allows get the photon echo the vapors of molecular iodine are used. The theoretical model of the opto-electronic current transformer is discussed. The results of investigation of photon echo (PE), excited by complexly coded laser pulses in molecular Iodine vapors under action of the homogeneous longitudinal magnetic field are given in this work. The recording possibility of special information by exciting pulses on a pair of quantum levels of resonant gas (molecular Iodine vapors) in technique PE is shown experimentally. In this shown experiment the information has two by two values of two relevant features and is represented by the amplitude-time shape and direction of linear polarization vector of radiation. The possibility of using the detected features of formation PE under the action of magnetic field for development the physical principles of the quantum control and for optical information processing introduced by hypercomplex number - quaternion - is shown.

Features of application of quaternions at the solution of the Bloch equation

Quaternion algebra is offered as the mathematical formalism of dynamics of interaction of a two-level quantum system with an electromagnetic field. Condition of two-level atom, densities operator, Bloch vector, “gyrating moment” vector are considered as the elements of a one-dimensional vector space of quaternion H1, i.e. are represented as quaternion. Bloch equations in a quaternion formalism are noted. Solution method of the differential quaternion Bloch equation is obtained.