Improved genetic algorithm for the context-free grammatical inference

Inductive learning of formal languages, often called grammatical inference, is an active area inmachine learning and computational learning theory. By learning a language we understandfinding the grammar of the language when some positive (words from language) and negativeexamples (words that are not in language) are given. Learning mechanisms use the naturallanguage learning model: people master a language, used by their environment, by the analysis ofpositive and negative examples. The problem of inferring context-free languages (CFG) has boththeoretical and practical motivations. Practical applications include pattern recognition (forexample finding DTD or XML schemas for XML documents) and speech recognition (the abilityto infer context-free grammars for natural languages would enable speech recognition to modify itsinternal grammar on the fly). There were several attempts to find effective learning methods forcontext-free languages (for example [1,2,3,4,5]). In particular, Y.Sakakibara [3] introduced aninteresting method of finding a context-free grammar in the Chomsky normal form with a minimalset of nonterminals. He used the tabular representation similar to the parse table used in the CYKalgorithm, simultaneously with genetic algorithms. In this paper we present several adjustments tothe algorithm suggested by Sakakibara. The adjustments are concerned mainly with the geneticalgorithms used and are as follows:– we introduce a method of creating the initial population which makes use of characteristicfeatures of context-free grammars,– new genetic operations are used (mutation with a path added, ‘die process’, ‘war/diseaseprocess’),– different definition of the fitness function,– an effective compression of the structure of an individual in the population is suggested.These changes allow to speed up the process of grammar generation and, what is more, theyallow to infer richer grammars than considered in [3]

Harnessing center-of-mass excitations in quantum metrology

In quantum metrology, one typically creates correlations among atoms or photons to enhance measurement precision. Here, we show how one can use other excitations to perform quantum-enhanced measurements on the example of center-of-mass excitations of a spin-orbit coupled Bose-Einstein condensate and a Coulomb crystal. We also present a method to simulate a homodyne detection of cent er-of-mass excitations in these systems, which is required for optimal estimation.journal articl

Enhancing interferometric sensitivity by non-classical light from quantum non-demolition measurements in cavity QED

We propose an enhanced optical interferometer based on tailored non-classical light generated by nonlinear dynamics and projective measurements in a three-level atom cavity QED system. A coherent state in the cavity becomes dynamically entangled with two ground states of the atom and is transformed to a macroscopic superposition state via a projective measurement on the atom. We show that the resulting highly non-classical state can improve interferometric precision measurements well beyond the shot-noise limit once combined with a classical laser pulse at the input of a Mach-Zehnder interferometer. For a practical implementation, we identify an efficient phase shift estimation scheme based on the counting of photons at the interferometer output. Photon losses and photon-counting errors deteriorate the interferometer sensitivity, but we demonstrate that it still can be significantly better than the shot-noise limit under realistic conditions.Comment: 9 pages, 10 figure

Kwantowa metrologia z atomami i światłem

The primary objective of this dissertation is to propose methods of generating nonclassical states of matter or light and examine the possibility of using such states in precise measurements of physical quantities. The first part of this objective is realised by using quantum-mechanical formalism with an emphasis on the theory of ultra-cold atomic gases and cavity quantum electrodynamics, and the second part is realised with methods of the theory of estimation with the Fisher information playing the pivotal role. The fusion of these methods is generally known as quantum metrology. In recent years, a lot of theoretical and experimental effort was put in the field of quantum metrology since it not only promises to develop measurement techniques that give better precision than the same measurements performed in a classical framework but also can be used to study the most fundamental aspects of quantum theory, like quantum entanglement. The first method which we consider is based on the mechanism of creating spinsqueezed states known as the one-axis twisting, which can be realised, for instance, in a Bose-Einstein condensate trapped in a double-well potential forming effectively a two-mode system. We show that the spin-squeezed states are just a small family of entangled states that can be generated by one-axis twisting Hamiltonian. This vast family of twisted states includes even the highest entangled state known as the Schrödinger’s cat. We also show how to exploit this quantum resource in a measurement of an unknown parameter with imperfect atomic detectors and when the strength of the interaction between the atoms is not precisely known. The second scheme for creating non-classical states is based on the quantum non-demolition measurement. This method involves an atom passing through an optical cavity which entangles with the photons inside the cavity and a subsequent measurement on the atom that collapses the combined matter-light state to a nonclassical state of light. To take into account photon losses in the cavity, we harness the master equation in Lindblad form. We show how such non-classical states can be extracted from the cavity and used later in a Mach-Zehnder interferometer. Based on the Wigner function, we also explain what features of this kind of states give rise to a high sensitivity of an interferometer. Finally, we show how a system that exhibits chaotic properties can be studied from the metrological perspective with the help of quantum Fisher information. Classical chaotic systems are systems that are highly sensitive to initial conditions. However, quantum systems can never exhibit this type of dynamics since the Schrödinger’s equation is linear. Therefore, one often says about quantum signatures of chaos. First, we show a textbook example of classical chaos, which is a double-rod pendulum, and, subsequently, we show how quantum Fisher information can serve to investigate characteristic time-scales of chaotic systems and the transition from integrable to chaotic dynamics. This could open a new possibility to study the relationship between the classical and quantum chaos.Głównym celem tej dysertacji jest zaproponowanie metod tworzenia kwantowych stanów materii oraz ´swiatła i sprawdzenie mozliwo´sci wykorzystania tych stanów ˙ do precyzyjnych pomiarów wielko´sci fizycznych. Pierwsza cz ˛e´s´c tego celu realizowana jest przy pomocy formalizmu kwantowo-mechanicznego w kontek´scie teorii ultra-zimnych gazów atomowych oraz kwantowej elektrodynamiki we wn ˛ece, natomiast druga cz ˛e´s´c realizowana jest za pomoc ˛a metod teorii estymacji z informacj ˛a Fishera w roli głównej. Poł ˛aczenie powyzszych metod jest znane ogólnie pod poj ˛eciem ˙ kwantowej metrologii. W ostatnich latach wiele teoretycznego i eksperymentalnego wysiłku zostało włozonego w dziedzin ˛e kwantowej metrologii, poniewa ˙ z dzi ˛eki niej ˙ mozliwy b ˛edzie nie tylko rozwój technik pomiarowych daj ˛acych lepsz ˛a precyzj ˛e ni ˙ z˙ te same pomiary wykonane w ramach klasycznej teorii, ale takze mo ˙ ze by´c u ˙ zyta do ˙ badania fundamentalnych aspektów mechaniki kwantowej takich jak spl ˛atanie. Pierwsz ˛a metod ˛a, któr ˛a rozwazamy to mechanizm tworzenia tworzenia stanów ˙ spinowo-´sci´sni ˛etych znany jako one-axis twisting, który moze by´c zastosowany na ˙ przykład w kondensacie Bosego-Einsteina uwi ˛ezionego w podwójnej studni potencjału tworz ˛ac efektywnie kondensat dwu składnikowy. Pokazujemy, ze stany spinowo- ˙ ´sci´sni ˛ete stanowi ˛a tylko mał ˛a rodzin ˛e stanów spl ˛atanych, które mog ˛a by´c wytworzone przez Hamiltonian one-axis twisting. Ta duza rodzina stanów typu ˙ twisted zawiera nawet najbardziej spl ˛atany stan znany jako kot Schroödingera. Pokazujemy równiez jak wykorzysta´c te kwantowe zasoby w pomiarze nieznanego parametru, ˙ wykorzystuj ˛ac nieidealne detektory atomowe oraz w przypadku kiedy oddziaływanie pomi ˛edzy atomami nie jest dokładnie znane. Drugi schemat tworzenia kwantowo-skorelowanych stanów jest oparty na quantum non-demolition measurement. W metodzie tej atom przelatuj ˛acy przez wn ˛ek ˛e optyczn ˛a zostaje spl ˛atany z obecnymi w niej fotonami, a w wyniku pomiaru wykonanego na atomie nast ˛epuje kolaps funkcji falowej ł ˛acznego stanu materii i ´swiatła do nieklasycznego stanu ´swiatła. W celu uwzgl ˛ednienia strat fotonów we wn ˛ece uzywamy równania ˙ master w formie Lindblada. Pokazujemy jak takie nieklasyczne stany mog ˛a zosta´c wydobyte z wn ˛eki oraz uzyte pó ´zniej w interferometrze Macha- ˙ Zehndera. Bazuj ˛ac na funkcji Wignera wyja´sniamy równiez jakie cechy tego rodzaju ˙ stanów przyczyniaj ˛a si ˛e do niezwykle wysokiej czuło´sci interferometru. Na koniec pokazujemy, jak układ wykazuj ˛acy wła´sciwo´sci chaotyczne moze zo- ˙ sta´c badany z perspektywy metrologicznej za pomoc ˛a kwantowej informacji Fishera. Klasyczne układy chaotyczne to układy, które s ˛a bardzo czułe na warunki pocz ˛atkowe. Jednakze, kwantowe uk ˙ łady nie mog ˛a wykazywa´c takiego rodzaju dynamiki, poniewaz równanie Schrödingera jest liniowe w funkcji falowej. Mo ˙ zna jed- ˙ nak mówi´c o tak zwanych kwantowych sygnaturach chaosu. Na pocz ˛atku pokazujemy podr˛ecznikowy przykład klasycznego chaosu, jakim jest podwójne wahadło, a nast ˛epnie pokazujemy jak kwantowa informacja Fishera moze pos ˙ łuzy´c do badania ˙ charakterystycznych skal czasowych układów chaotycznych i przej´scia pomi ˛edzy porz ˛adkiem a chaosem. Takie podej´scie otwiera nowe mozliwo´sci badania zwi ˛azku ˙ pomi ˛edzy kwantowym chaosem a porz ˛adkiem

Squeezing and overcoming the Heisenberg scaling with spin-orbit coupled quantum gases

We predict that exploiting spin-orbit coupling in a harmonically trapped spinor quantum gas can lead to scaling of the optimal measurement precision beyond the Heisenberg scaling. We show that quadratic scaling with the number of atoms can be facilitated via squeezed center-of-mass excitations of the atomic motion using a 1D spin-orbit coupled fermions or strongly interacting bosons (Tonks-Girardeau gas). Based on predictions derived from analytic calculations of the corresponding quantum Fisher information, we then introduce a protocol which overcomes the Heisenberg scaling (and limit) with help of a tailored excited and entangled many-body state of a non-interacting Bose-Einstein condensate. We identify corresponding optimal measurements and argue that even finite temperature as a source of decoherence is, in principle, rather favorable for the obtainable precision scaling.Comment: 9 pages, 1 figure. Feedback and comments are greatly appreciate

Unique Steady-State Squeezing in a Driven Quantum Rabi Model

Squeezing is essential to many quantum technologies and our understanding of quantum physics. Here we develop a theory of steady-state squeezing that can be generated in the closed and open quantum Rabi as well as Dicke model. To this end, we eliminate the spin dynamics which effectively leads to an abstract harmonic oscillator whose eigenstates are squeezed with respect to the physical harmonic oscillator. The generated form of squeezing has the unique property of time-independent uncertainties and squeezed dynamics, a novel type of quantum behavior. Such squeezing might find applications in continuous back-action evading measurements and should already be observable in optomechanical systems and Coulomb crystals.Comment: 9 pages, 3 figure

Multipartite-Entanglement Dynamics in Regular-to-Ergodic Transition: a Quantum-Fisher-Information approach

The characterization of entanglement is a central problem for the study of quantum many-body dynamics. Here, we propose the quantum Fisher information as a useful tool for the study of multipartite-entanglement dynamics in many-body systems. We illustrate this by considering the regular-to-ergodic transition in the Dicke model---a fully-connected spin model showing quantum thermalization above a critical interaction strength. We show that the QFI has a rich dynamical behavior which drastically changes across the transition. In particular, the asymptotic value of the QFI, as well as its characteristic timescales, witness the transition both through their dependence on the interaction strength and through the scaling with the system size. Since the QFI also sets the ultimate bound for the precision of parameter estimation, it provides a metrological perspective on the characterization of entanglement dynamics in many-body systems. Here we show that quantum ergodic dynamics allows for a much faster production of metrologically useful states.Comment: 9 pages, 10 figure