Nonlinear optical signals and spectroscopy with quantum light

Conventional nonlinear spectroscopy uses classical light to detect matter properties through the variation of its response with frequencies or time delays. Quantum light opens up new avenues for spectroscopy by utilizing parameters of the quantum state of light as novel control knobs and through the variation of photon statistics by coupling to matter. We present an intuitive diagrammatic approach for calculating ultrafast spectroscopy signals induced by quantum light, focusing on applications involving entangled photons with nonclassical bandwidth properties - known as "time-energy entanglement". Nonlinear optical signals induced by quantized light fields are expressed using time ordered multipoint correlation functions of superoperators. These are different from Glauber's g- functions for photon counting which use normally ordered products of ordinary operators. Entangled photon pairs are not subjected to the classical Fourier limitations on the joint temporal and spectral resolution. After a brief survey of properties of entangled photon pairs relevant to their spectroscopic applications, different optical signals, and photon counting setups are discussed and illustrated for simple multi-level model systems

Model-Based Estimation Techniques for 3-D Reconstruction from Projections

A parametric estimation approach to reconstruction from projections with incomplete and very noisy data is described. Embedding prior knowledge about "objects" in the probed domain and about the data acquisition process into stochastic dynamic models, we transform the reconstruction problem into a computationally ,challenging nonlinear state-estimation problem, where the objects' parametrized descriptions are to be directly estimated from the projection data. This paper is a review in a common framework and a comparative study of two distinct algorithms which were developed recently for the solution of this problem. The first, is an approximate, globally optimal minimum-meansquare- error recursive algorithm. The second is a hierarchical suboptimal Bayesian algorithm. Simulation examples demonstrate accurate reconstructions with as few as four views in a 135 ~ sector, at an average signal to noise ratio of 0.6.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85941/1/Fessler114.pd

The Adjacency Graphs of Some Feedback Shift Registers

The adjacency graphs of feedback shift registers (FSRs) with characteristic function of the form g=(x_0+x_1)*f are considered in this paper. Some properties about these FSRs are given. It is proved that these FSRs contains only prime cycles and these cycles can be divided into two sets such that each set contains no adjacent cycles. When f is a linear function, more properties about these FSRs are derived. It is shown that, when f is a linear function and contains an odd number of terms, the adjacency graph of \mathrm{FSR}((x_0+x_1)*f) can be determined directly from the adjacency graph of \mathrm{FSR}(f). As an application of these results, we determine the adjacency graphs of \mathrm{FSR}((1+x)^4p(x)) and \mathrm{FSR}((1+x)^5p(x)), where p(x) is a primitive polynomial, and construct a large class of de Bruijn sequences from them

De Bruijn Sequences from Joining Cycles of Nonlinear Feedback Shift Registers

De Bruijn sequences are a class of nonlinear recurring sequences that have wide applications in cryptography and modern communication systems. One main method for constructing them is to join the cycles of a feedback shift register (FSR) into a full cycle, which is called the cycle joining method. Jansen et al. (IEEE Trans on Information Theory 1991) proposed an algorithm for joining cycles of an arbitrary FSR. This classical algorithm is further studied in this paper. Motivated by their work, we propose a new algorithm for joining cycles, which doubles the efficiency of the classical cycle joining algorithm. Since both algorithms need FSRs that only generate short cycles, we also propose efficient ways to construct short-cycle FSRs. These FSRs are nonlinear and are easy to obtain. As a result, a large number of de Bruijn sequences are constructed from them. We explicitly determine the size of these de Bruijn sequences. Besides, we show a property of the pure circulating register, which is important for searching for short-cycle FSRs

De Bruijn Sequences from Symmetric Shift Registers

We consider the symmetric Feedback Shift Registers (FSRs), especially a special class of symmetric FSRs (we call them scattered symmetric FSRs), and construct a large class of De Bruijn sequences from them. It is shown that, at least O(2^((n-6)(logn)/2)) De Bruijn sequences of order n can be constructed from just one n-stage scattered symmetric FSR. To generate the next bit in the De Bruijn sequence from the current state, it requires no more than 2n comparisons and n+1 FSR shifts. By further analyse the cycle structure of the scattered symmetric FSRs, other methods for constructing De Bruijn sequences are suggested

Automated Design Space Exploration and Datapath Synthesis for Finite Field Arithmetic with Applications to Lightweight Cryptography

Today, emerging technologies are reaching astronomical proportions. For example, the Internet of Things has numerous applications and consists of countless different devices using different technologies with different capabilities. But the one invariant is their connectivity. Consequently, secure communications, and cryptographic hardware as a means of providing them, are faced with new challenges. Cryptographic algorithms intended for hardware implementations must be designed with a good trade-off between implementation efficiency and sufficient cryptographic strength. Finite fields are widely used in cryptography. Examples of algorithm design choices related to finite field arithmetic are the field size, which arithmetic operations to use, how to represent the field elements, etc. As there are many parameters to be considered and analyzed, an automation framework is needed. This thesis proposes a framework for automated design, implementation and verification of finite field arithmetic hardware. The underlying motif throughout this work is “math meets hardware”. The automation framework is designed to bring the awareness of underlying mathematical structures to the hardware design flow. It is implemented in GAP, an open source computer algebra system that can work with finite fields and has symbolic computation capabilities. The framework is roughly divided into two phases, the architectural decisions and the automated design genera- tion. The architectural decisions phase supports parameter search and produces a list of candidates. The automated design generation phase is invoked for each candidate, and the generated VHDL files are passed on to conventional synthesis tools. The candidates and their implementation results form the design space, and the framework allows rapid design space exploration in a systematic way. In this thesis, design space exploration is focused on finite field arithmetic. Three distinctive features of the proposed framework are the structure of finite fields, tower field support, and on the fly submodule generation. Each finite field used in the design is represented as both a field and its corresponding vector space. It is easy for a designer to switch between fields and vector spaces, but strict distinction of the two is necessary for hierarchical designs. When an expression is defined over an extension field, the top-level module contains element signals and submodules for arithmetic operations on those signals. The submodules are generated with corresponding vector signals and the arithmetic operations are now performed on the coordinates. For tower fields, the submodules are generated for the subfield operations, and the design is generated in a top-down fashion. The binding of expressions to the appropriate finite fields or vector spaces and a set of customized methods allow the on the fly generation of expressions for implementation of arithmetic operations, and hence submodule generation. In the light of NIST Lightweight Cryptography Project (LWC), this work focuses mainly on small finite fields. The thesis illustrates the impact of hardware implementation results during the design process of WAGE, a Round 2 candidate in the NIST LWC standardization competition. WAGE is a hardware oriented authenticated encryption scheme. The parameter selection for WAGE was aimed at balancing the security and hardware implementation area, using hardware implementation results for many design decisions, for example field size, representation of field elements, etc. In the proposed framework, the components of WAGE are used as an example to illustrate different automation flows and demonstrate the design space exploration on a real-world algorithm

Time-resolved studies of vibronic and vibrational transitions in complex media

In the present dissertation the vibronic and vibrational transitions in complex media are studied with optical methods. Two experiments along with interpretation of their results are presented. The first experiment is the generation of supercontiuum generation in diamond crystal. Diamond is subjected to highly intense off-resonant light pulses. The evolution of the pulse in time and space and the influence of intrapulse stimulated Raman scattering on this evolution is investigated. Self-phase modulation, self-steepening and interaction with photoionized free carriers are the main processes taking part in the supercontinuum generation. The influence of crystal vibrations on the pulse spectrum is small, yet it is observed and presented in the present thesis. It manifests itself mainly by a peak separated from the central pulse frequency by vibrational frequency of the diamond crystal. The interpretation of the experimental results is supported by results of simulation. For this purpose the three dimensional nonlinear envelope equation is solved with the split-step Fourier method. The model includes the effects of refractive index dispersion, diffraction, self-phase modulation and its saturation, self-steepening, photoionization, interaction with free-carriers and stimulated Raman scattering. The results of modeling agree well with experimental observations. The second experiment is the Time-Resolved Femtoecond Stimulated Raman Scattering studies of trans-β-apo-8’-carotenal molecule. The experimental setup has been constructed for this purpose. The time resolution of the setup is better than 100 fs and the frequency resolution is about 25 cm−1. The trans-β-apo-8’-carotenal molecule was excited electronically to the S2 state and it’s relaxation, through S1 state to the ground state was observed through measurements of FSRS spectra of the C=C symmetrical stretching vibration. The Raman line corresponding to S2 state decays within 120 fs after excitation, then a long living line at frequency corresponding to the optically forbidden S1 state appears. During the first 500 fs this line is negative, which is attributed to the transient vibrational inversion of population in S1 electronic level. Later the line becomes positive and then decays with the lifetime of S1 level. At the same time the frequency of the line up-shifts. The results of experiment are analyzed by comparison with the femtosecond stimulated Raman scattering time resolved signal calculated on the basis of the quantum mechanical approach, using the formalism of projection operators. It is shown that the predictions of numerical models agree well with the experimental results. No additional electronic level (apart of S0, S1 and S2) was required for explanation of the experimental results, instead a set of vibrational sublevels of S1 state were proposed.W niniejszej dysertacji przedstawione zostały wyniki badań przejść między stanami wibracyjnymi i wibracyjno-elektronowymi w materiałach złożonych. Opisane zostały dwa eksperymenty oraz zaprezentowana dyskusja ich wyników. Pierwszy eksperyment to generacja superkontinuum w krysztale diamentu. Kryształ diamentu został oświetlony impulsami laserowymi o dużej energii. Zbadane zostały zmiany impulsu w czasie i przestrzeni oraz wpływ wewnątrzimpulsowego wymuszonego rozpraszania Ramana na te zmiany. Samomodulacja fazy, wystromienie oraz oddziaływanie z ładunkami powstałymi w wyniku fotojonizacji to główne procesy biorące udział w generacji superkontinuum. Wpływ drgań kryształu na widmo impulsu jest niewielki, niemniej występuje i został zaobserwowany, co przedstawiono w niniejszej pracy. Głównym przejawem oddziaływania drgań kryształu z impulsem światła jest pik oddzielony od centralnej częstości impulsu o częstość równą częstości drgań diamentu. Interpretacja wyników ekspertymentalnych jest wsparta wynikami symulacji numerycznej. Rozwiązano trójwymiarowe „nieliniowe równanie obwiedni” przy pomocy Fourierowskiej metody małych kroków. Model uwzględnia efekty dyspersji współczynnika załamania, dyfrakcję, samo-modulację oraz jej nasycenie, wystromienie impulsu, fotojonizację, interakcje z wolnymi nośnikami oraz wymuszone rozpraszanie Ramana. Wyniki modelowania zgadzają się z wynikami pomiarów. Drugim eksperymentem był badanie cząsteczek trans-β-apo-8’-karotenu przy pomocy czasowo-rozdzielczego, femtosekundowego, wymuszonego rozpraszania Ramana (CR-FWRR). Do tego celu zbudowano układ pomiarowy o rozdzielczość czasowej 100 fs i rozdzielczość częstości około 25 cm−1. Cząsteczka trans-β-apo-8’-karotenu była wzbudzana do elektronowego stanu S2 a jej relaksacja przez stan S1 do stanu podstawowego obserwowano przez pomiar widma FWRR symetrycznych, rozciągających drgań wiązania C=C. Linia ramanowska odpowiadająca rozpadowi stanu S2 w zanika w czasie 120 fs po wzbudzeni, następnie pojawia się linia długo żyjącego stanu S1. Podczas pierwszych 500 fs linia ta jest ujemna, co przypisano przejściowej wibracyjnej inwersji obsadzeń w elektronowym stanie S1. Następnie linia staje się dodatnia I dalej zanika w czasie równym czasowi życia poziomu S1. Jednocześnie częstość linii wzrasta. Wyniki doświadczenia przeanalizowano w porównaniu z wynikami obliczeń wykonanych na podstawie modeli kwantowych stworzonych z użyciem formalizmu operatorów rzutowania. Pokazano, że przewidywania modeli numerycznych są w zgodności z wynikami pomiarów. Do wyjaśnienia wyników doświadczalnych nie było potrzebne wprowadzenia dodatkowych poziomów elektronowych (innych niż S0, S1 i S2), w zamian zaproponowano zbiór wibracyjnych podpoziomów stanu S1