ИСТИНА

The main goal of this thesis is to elaborate the quantum properties of multifrequency fields, spatial single-mode and multimode, generated in coupled parametric wave interactions and their applications for teleportation of entangled quantum states. The coupled parametric processes under consideration are two five-frequency interactions. One of the coupled interactions comprises two parametric down-conversion processes accompanied by an up-conversion process. It involves the fields of two pumping waves with multiple frequencies: \omega_p = \omega_1 + \omega_2, 2\omega_p = \omega_2 + \omega_3, \omega_1 + \omega_p = \omega_3, (1) The other coupled interaction occures in the field of a single pumping wave and consists of the process of parametric down-conversion accompanied by two up- conversion processes: \omega_p = \omega_1 + \omega_2, \omega_1 + \omega_p = \omega_3, \omega_2 + \omega_p = \omega_4. (2) These interactions can be realized in aperiodic nonlinear photonic crystals (ANPC) having fulfilled the quasi-phase matching conditions for all the three- wave processes. It has been shown that the resulting three-mode field, formed in (1), is in three-mode entangled state. The analysis of the two-mode entanglement suggests that the presence of the up-conversion process may significantly decrease the noise influence of one parametric down-conversion process, involved in (1), on the other process. The optimal parameters for the noise influence decrease have been found. The entanglement analysis, carried out for (2), has proved that modes with frequencies \omega_1, \omega_2 (low-frequency modes) and modes with frequencies \omega_3, \omega_4 (high-frequency modes) exhibit two-mode entanglement. It has been shown by the analysis of block entanglement, which was fulfilled with the help of the symplectic eigenvalues criterion, that the low-frequency and high-frequency mode bunches are entangled. The investigation of spatial multimode fields was conducted for two configurations of quantum imaging schemes: the scheme with near located object, when the input image is directly projected on the ANPC, and the scheme with far located object, where the spatial spectrum of the initial image is put to the input face of the ANPC. For both configurations the signal-to-noise ration of the generated images is calculated and studied. The analysis has shown that the signal-to-noise ratio, normalized to its input value (for initial image), tends to 1/4 for all generated images, as the interaction length for coupled interaction (2) increases. In order to reveal the entanglement properties of generated images the statistics of difference of photon numbers for various pairs of images has been investigated. It has been determined that the output images with low-frequency carriers and images with high-frequency carriers are entangled. Entangled states play important role in quantum communication. In the work schemes for teleportation of entangled spatial single-mode states and entangled images using auxiliary quantum states obtained in interaction (2) are proposed and thoroughly analyzed. In order to qualify the performance of these schemes the two quantities were considered: fidelity and noise contribution that degrades the entanglement of the initial state. For the image teleportation scheme the quality of teleportation strongly depends on the relation of the widths of the spatial spectra of the images to be teleported and the four-frequency auxiliary fields. The quality of transfer of entangled states, both single-mode and images, depends on the amount of entanglement initial states possess: the more entangled states to be teleported, the more entangled auxiluary states should be in order to achieve the same fidelity. The influence of the pixel size of the detectors on the quality of teleportation has been analysed in detail. It has been shown that the increase of the pixel size results in decrease of quantum noise contribution which, in turn, leads to the increase in the quality of teleportation. Practical significance: • The entanglement of up-converted modes (spatial single-mode and multimode) in (2) offers the possibility to obtain ultra-violet entangled states, when the traditional methods can not be applied, due to the pumping frequency value falls into the absorption band. • The two-frequency entanglement, formed in two pairs of frequencies (2), can be exploited for teleportation of two-frequency entangled states, both single-mode and multimode. • Implementation of coupled parametric interactions, having place in a single crystal, offers a compact way to obtain multimode entangled states. The results of the thesis are published in 8 scientific papers and presented at 19 conferences.