On the role of coupling in mode selective excitation using ultrafast pulse shaping in stimulated Raman spectroscopy

The coherence of two, coupled two-level systems, representing vibrational modes in a semiclassical model, is calculated in weak and strong fields for various coupling schemes and for different relative phases between initial state amplitudes. A relative phase equal to $\pi$ projects the system into a dark state. The selective excitation of one of the two, two-level systems is studied as a function of coupling strength and initial phases.Comment: 7 pages, 4 figure

Impact of Decoherence on Internal State Cooling using Optical Frequency Combs

We discuss femtosecond Raman type techniques to control molecular vibrations, which can be implemented for internal state cooling from Feshbach states with the use of optical frequency combs with and without modulation. The technique makes use of multiple two-photon resonances induced by optical frequencies present in the comb. It provides us with a useful tool to study the details of molecular dynamics at ultracold temperatures. In our theoretical model we take into account decoherence in the form of spontaneous emission and collisional dephasing in order to ascertain an accurate model of the population transfer in the three-level system. We analyze the effects of odd and even chirps of the optical frequency comb in the form of sine and cosine functions on the population transfer. We compare the effects of these chirps to the results attained with the standard optical frequency comb to see if they increase the population transfer to the final deeply bound state in the presence of decoherence. We also analyze the inherent phase relation that takes place owing to collisional dephasing between molecules in each of the states. This ability to control the rovibrational states of a molecule with an optical frequency comb enables us to create a deeply bound ultracold polar molecules from the Feshbach state.Comment: 10 pages, 6 figure

Chirped Fractional Stimulated Raman Adiabatic Passage

Stimulated Raman Adiabatic Passage (STIRAP) is a widely used method for adiabatic population transfer in a multilevel system. In this work, we study STIRAP under novel conditions and focus on the fractional, F-STIRAP, which is known to create a superposition state with the maximum coherence. In both configurations, STIRAP and F-STIRAP, we implement pulse chirping aiming at a higher contrast, a broader range of parameters for adiabaticity, and enhanced spectral selectivity. Such goals target improvement of quantum imaging, sensing and metrology, and broaden the range of applications of quantum control techniques and protocols. In conventional STIRAP and F-STIRAP, two-photon resonance is required conceptually to satisfy the adiabaticity condition for dynamics within the dark state. Here, we account for a non-zero two-photon detuning and present control schemes to achieve the adiabatic conditions in STIRAP and F-STIRAP through a skillful compensation of the two-photon detuning by pulse chirping. We show that the chirped configuration - C-STIRAP - permits adiabatic passage to a predetermined state among two nearly degenerate final states, when conventional STIRAP fails to resolve them. We demonstrate such a selectivity within a broad range of parameters of the two-photon detuning and the chirp rate. In the C-F-STIRAP, chirping of the pump and the Stokes pulses with different time delays permits a complete compensation of the two-photon detuning and results in a selective maximum coherence of the initial and the target state with higher spectral resolution than in the conventional F-STIRAP

Theory of selective excitation in Stimulated Raman Scattering

A semiclassical model is used to investigate the possibility of selectively exciting one of two closely spaced, uncoupled Raman transitions. The duration of the intense pump pulse that creates the Raman coherence is shorter than the vibrational period of a molecule (impulsive regime of interaction). Pulse shapes are found that provide either enhancement or suppression of particular vibrational excitations.Comment: RevTeX4,10 pages, 5 figures, submitted to Phys.Rev.

Elements of mathematics in problems. Through olympiads and circles to profession

This is a collection of teaching materials used in several Russian universities, schools, and mathematical circles. Most problems are chosen in such a way that in the course of the solution and discussion a reader learns important mathematical ideas and theories. The materials can be used by pupils and students for self-study, and by teachers. This is an abridged pre-copyedit version of the published book submitted with the permission of the publisher. Each included individual material is self-contained and ready-for-use. Solutions to problems are not included intentionally. This collection consolidates updates of several arXiv submissions, e.g., arXiv:1305.2598.Comment: Edited by A. Skopenkov, M. Skopenkov, A. Zaslavsky. In Russian. Optimized for printing on A5 paper. Moscow Center for Continuous Mathematical Education, 2018, 592pp (in Russian

The study of the sorghum genetic diversity using the mul¬tiplex microsatellite analysis

This study is focused on evaluation of the genetic structure and diversity of the national sorghum collection. Analyzing the genetic diversity of crop species is of great importance for genetic resources management and food security of any country. Huge genetic diversity of sorghum provides a great opportunity to improve the agronomic characteristics of this crop. The efficiency of microsatellite  analysis has been demonstrated in many studies on the genetic diversity of different races and geographical groups of sorghum plants. Development of multiplex PCR analysis systems based on a set of polymorphic microsatellite loci will facilitate genetic tests on a large number of plant samples, thus making the research on sorghum diversity more efficient and comprehensive. A system of multiplex PCR analysis based on 12 polymorphic microsatellite loci was developed to perform single-stage high-throughput screening of cultivated and wild forms preserved in the sorghum germplasm collection. As a result of the microsatellite analysis of 200 sorghum plants, 229 alleles were detected. The studied loci showed high polymorphism. More than 17 alleles were identified in most loci, their polymorphic index content (PIC) ranging from 0.694 to 0.954. The value of the effective multiplex ratio (EMR) in the developed system was estimated at 0.833. The microsatellite analysis of sorghum accessions resulted in obtaining quantized gene expressions profiles, with a DNA profile for each accession, and revealed significant polymorphism among the plants of different sorghum varieties (races). The developed multiplex PCR system was shown to be efficient for evaluation of the genetic diversity and genetic relationships of sorghum plants from different races. The analysis of the obtained data using three bioinformatic techniques, NJ cluster analysis, PCoA, and the Bayesian model-based clustering, helped to classify the analyzed sorghum accessions into cluster groups according to their morphological and agronomic traits